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</div><h2>SL Paper 1</h2><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The Venn diagram below shows events <em>A</em> and <em>B</em> where \({\rm{P}}(A) = 0.3\) , \({\rm{P}}(A \cup B) = 0.6\) </span><span style="font-family: times new roman,times; font-size: medium;">and \({\rm{P}}(A \cap B) = 0.1\) . The values <em>m</em> , <em>n</em> , <em>p</em> and <em>q</em> are probabilities.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/beach.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Write down the value of <em>n</em> .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Find the value of <em>m</em> , of <em>p</em> , and of <em>q</em> .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \({\rm{P}}(B')\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">A box contains six red marbles and two blue marbles. Anna selects a marble from </span><span style="font-family: times new roman,times; font-size: medium;">the box. She replaces the marble and then selects a second marble.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the probability that the first marble Anna selects is red.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the probability that Anna selects two red marbles.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the probability that one marble is red and one marble is blue.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Consider the events <em>A</em> and <em>B</em>, where \({\rm{P}}(A) = 0.5\) , \({\rm{P}}(B) = 0.7\) and \({\rm{P}}(A \cap B) = 0.3\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The Venn diagram below shows the events <em>A</em> and <em>B</em>, and the probabilities <em>p</em>, <em>q</em> and <em>r</em>.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/baba.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Write down the value of</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) <em>p</em> ;</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) <em>q</em> ;</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(iii) <em>r</em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a(i), (ii) and (iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the value of \({\rm{P}}(A|B')\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Hence, or otherwise, show that the events <em>A</em> and <em>B</em> are <strong>not</strong> independent.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(f(x) = \frac{1}{2}{x^2} + kx + 8\) , where \(k \in \mathbb{Z}\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the values of <em>k</em> such that \(f(x) = 0\) has two equal roots.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Each value of <em>k</em> is equally likely for \( - 5 \le k \le 5\) . Find the probability that </span><span style="font-family: times new roman,times; font-size: medium;">\(f(x) = 0\) has no roots.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let <em>X</em> be normally distributed with mean 100 cm and standard deviation 5 cm.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">On the diagram below, shade the region representing \({\rm{P}}(X > 105)\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/raymond.png" alt></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Given that \({\rm{P}}(X < d) = {\rm{P}}(X > 105)\) , find the value of \(d\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Given that \({\rm{P}}(X > 105) = 0.16\) (correct to two significant figures), find \({\rm{P}}(d < X < 105)\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The ages of people attending a music concert are given in the table below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/chandler.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find <em>p</em> .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The cumulative frequency diagram is given below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/joey.png" alt></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Use the diagram to estimate</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(i) the 80th percentile;</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) the interquartile range.</span></p>
<p> </p>
<div class="marks">[5]</div>
<div class="question_part_label">b(i) and (ii).</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The letters of the word PROBABILITY are written on 11 cards as shown below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/probability.png" alt></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Two cards are drawn at random without replacement.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Let <em>A</em> be the event the first card drawn is the letter A.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Let <em>B</em> be the event the second card drawn is the letter B.</span></p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \({\rm{P}}(A)\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \({\rm{P}}(B|A)\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \({\rm{P}}(A \cap B)\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The random variable \(X\) is normally distributed with a mean of 100. The following diagram shows the normal curve for \(X\).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-11_om_16.32.27.png" alt="M17/5/MATME/SP1/ENG/TZ2/03"></p>
<p>Let \(R\) be the shaded region under the curve, to the right of 107. The area of \(R\) is 0.24.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down \({\text{P}}(X > 107)\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \({\text{P}}(100 < X < 107)\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \({\text{P}}(93 < X < 107)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A <strong>four-sided</strong> die has three blue faces and one red face. The die is rolled.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Let <em>B</em> be the event a blue face lands down, and <em>R</em> be the event a red face lands down.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(i) P(<em>B</em>);</span><br><span style="font-family: times new roman,times; font-size: medium;">(ii) P(<em>R</em>).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">If the blue face lands down, the die is not rolled again. If the red face lands down, the die is rolled once again. This is represented by the following tree diagram, where <em>p</em>, <em>s</em>, <em>t</em> are probabilities.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt width="398" height="262"></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find the value of <em>p</em>, of <em>s</em> and of <em>t</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Guiseppi plays a game where he rolls the die. If a blue face lands down, he scores 2 and is finished. If the red face lands down, he scores 1 and rolls one more time. Let <em>X</em> be the total score obtained.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(i) Show that \({\text{P}}(X = 3) = \frac{3}{{16}}\) .</span><br><span style="font-family: times new roman,times; font-size: medium;">(ii) Find \({\text{P}}(X = 2)\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(i) Construct a probability distribution table for <em>X</em>.</span></p>
<p><span style="font-size: medium;"><span style="font-family: times new roman,times;">(ii) Calculate the expected value of</span> <span style="font-family: times new roman,times;"><em>X</em></span>.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">If the total score is 3, Guiseppi wins \(\$ 10\). If the total score is 2, Guiseppi gets nothing.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Guiseppi plays the game twice. Find the probability that he wins exactly \(\$ 10\).</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Jar A contains three red marbles and five green marbles. Two marbles are drawn </span><span style="font-family: times new roman,times; font-size: medium;">from the jar, one after the other, without replacement.</span></p>
</div>
<div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Jar B contains six red marbles and two green marbles. A fair six-sided die is tossed. </span><span style="font-family: times new roman,times; font-size: medium;">If the score is \(1\) or \(2\), a marble is drawn from jar A. Otherwise, a marble is drawn from </span><span style="font-family: times new roman,times; font-size: medium;">jar B.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Find the probability that</span></p>
<p style="margin-left: 30px;" align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"> (i) none of the marbles are green;</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> (ii) exactly one marble is green.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the expected number of green marbles drawn from the jar.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Write down the probability that the marble is drawn from jar B.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) Given that the marble was drawn from jar B, write down the probability </span><span style="font-family: times new roman,times; font-size: medium;">that it is red.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Given that the marble is red, find the probability that it was drawn from jar A.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Adam travels to school by car (\(C\)) or by bicycle (\(B\)). On any particular day he is equally likely to travel by car or by bicycle.</p>
<p class="p1">The probability of being late (\(L\)) for school is \(\frac{1}{6}\) if he travels by car.</p>
<p class="p1">The probability of being late for school is \(\frac{1}{3}\) if he travels by bicycle.</p>
<p class="p1">This information is represented by the following tree diagram.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-14_om_05.16.45.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of \(p\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the probability that Adam will travel by car and be late for school.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the probability that Adam will be late for school.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Given that Adam is late for school, find the probability that he travelled by car.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Adam will go to school three times next week.</p>
<p class="p1">Find the probability that Adam will be late exactly once.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Bag A contains three white balls and four red balls. Two balls are chosen at random </span><span style="font-family: times new roman,times; font-size: medium;">without replacement.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(i) Copy and complete the following tree diagram.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/M12P1TZ2Q9.jpg" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Find the probability that two white balls are chosen.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">a(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Bag A contains three white balls and four red balls. Two balls are chosen at random </span><span style="font-family: times new roman,times; font-size: medium;">without replacement.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Bag B contains four white balls and three red balls. When two balls are chosen at </span><span style="font-family: times new roman,times; font-size: medium;">random without replacement from bag B, the probability that they are both white is \(\frac{2}{7}\) .</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">A standard die is rolled. If 1 or 2 is obtained, two balls are chosen without replacement </span><span style="font-family: times new roman,times; font-size: medium;">from bag A, otherwise they are chosen from bag B.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find the probability that the two balls are white.</span></p>
<p align="LEFT"> </p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Bag A contains three white balls and four red balls. Two balls are chosen at random without replacement.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Bag B contains four white balls and three red balls. When two balls are chosen at </span><span style="font-family: times new roman,times; font-size: medium;">random without replacement from bag B, the probability that they are both white is \(\frac{2}{7}\) . </span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">A standard die is rolled. If 1 or 2 is obtained, two balls are chosen without replacement </span><span style="font-family: times new roman,times; font-size: medium;">from bag A, otherwise they are chosen from bag B.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Given that both balls are white, find the probability that they were chosen from bag A.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The following is a cumulative frequency diagram for the time <em>t</em>, in minutes, taken by 80 students to complete a task.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><img src="images/maths_3.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the number of students who completed the task in less than 45 minutes.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the number of students who took between 35 and 45 minutes to complete the task.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Given that 50 students take less than <em>k </em>minutes to complete the task, find the value of \(k\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Let <em>A</em> and <em>B</em> be independent events, where \({\text{P}}(A) = 0.6\) and \({\text{P}}(B) = x\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down an expression for \({\text{P}}(A \cap B)\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Given that \({\text{P}}(A \cup B) = 0.8\) ,</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) find <em>x</em> ;</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) find \({\text{P}}(A \cap B)\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Hence</strong>, explain why <em>A</em> and <em>B</em> are <strong>not</strong> mutually exclusive.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A discrete random variable \(X\) has the following probability distribution.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-01-13_om_05.16.18.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find \(p\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find \({\text{E}}(X)\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">There are 20 students in a classroom. Each student plays only one sport. The table </span><span style="font-family: times new roman,times; font-size: medium;">below gives their sport and gender.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/tour.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">One student is selected at random.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Calculate the probability that the student is a male or is a tennis player.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) Given that the student selected is female, calculate the probability that the </span><span style="font-family: times new roman,times; font-size: medium;">student does not play football.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Two students are selected at random. Calculate the probability that neither </span><span style="font-family: times new roman,times; font-size: medium;">student plays football.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-size: medium;"><span style="font-family: times new roman,times;">Let \(\boldsymbol{A} = \left( {\begin{array}{*{20}{c}}<br> 0&3 \\ <br> { - 2}&4 <br>\end{array}} \right)\)</span><span style="font-family: times new roman,times;"> and \(\boldsymbol{B} = \left( {\begin{array}{*{20}{c}}<br> { - 4}&0 \\ <br> 5&1 <br>\end{array}} \right)\)</span><span style="font-family: times new roman,times;">.</span></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find <strong><em>AB</em></strong> .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-size: medium;"><span style="font-family: TimesNewRomanPSMT;">Given that </span><span style="font-family: TimesNewRomanPS-BoldItalicMT;">\({\boldsymbol{X}} - 2{\boldsymbol{A}} = {\boldsymbol{B}}\)</span><span style="font-family: TimesNewRomanPSMT;">, find <em><strong>X</strong></em></span><span style="font-family: TimesNewRomanPSMT;">.</span></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The probability distribution of a discrete random variable <em>X</em> is given by \[{\rm{P}}(X = x) = \frac{{{x^2}}}{{14}}{\text{, }}x \in \left\{ {1{\text{, }}2{\text{, }}k} \right\}{\text{, where}} k > 0\] .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down \({\rm{P}}(X = 2)\) .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Show that \(k = 3\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \({\rm{E}}(X)\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-size: medium;"><span style="font-family: TimesNewRomanPSMT;">The following table shows the probability distribution of a discrete random variable </span><em><span style="font-family: TimesNewRomanPS-ItalicMT;">X </span></em><span style="font-family: TimesNewRomanPSMT;">.</span></span></p>
<p align="LEFT"><span style="font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-size: medium;"><span style="font-family: TimesNewRomanPSMT;">Find the value of </span><em><span style="font-family: TimesNewRomanPS-ItalicMT;">k </span></em><span style="font-family: TimesNewRomanPSMT;">.</span></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Find \({\text{E}}(X)\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>In a group of 20 girls, 13 take history and 8 take economics. Three girls take both history and economics, as shown in the following Venn diagram. The values \(p\) and \(q\) represent numbers of girls.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-11_om_08.39.12.png" alt="M17/5/MATME/SP1/ENG/TZ1/01"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(p\);</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(q\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A girl is selected at random. Find the probability that she takes economics but not history.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Ann and Bob play a game where they each have an eight-sided die. Ann’s die has three green faces and five red faces; Bob’s die has four green faces and four red faces. They take turns rolling their own die and note what colour faces up. The first player to roll green wins. Ann rolls first. Part of a tree diagram of the game is shown below.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-01-13_om_11.04.17.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the probability that Ann wins on her first roll.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>The probability that Ann wins on her third roll is \(\frac{5}{8} \times \frac{4}{8} \times p \times q\ \times \frac{3}{8}\).</p>
<p class="p1">Write down the value of \(p\) and of \(q\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>The probability that Ann wins on her tenth roll is \(\frac{3}{8}{r^k}\) where \(r \in \mathbb{Q},{\text{ }}k \in \mathbb{Z}\).</p>
<p class="p1">Find the value of \(r\) and of \(k\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the probability that Ann wins the game.</p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A data set has a mean of 20 and a standard deviation of 6.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Each value in the data set has 10 added to it. Write down the value of</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) the new mean;</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) the new standard deviation.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Each value in the original data set is multiplied by 10.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Write down the value of the new mean.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Find the value of the new variance.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b(i) and (ii).</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following box-and-whisker plot represents the examination scores of a group of students.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2016-01-22_om_06.17.41.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the median score.</p>
<p class="p1">The range of the scores is 47 marks, and the interquartile range is 22 marks.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p2">Find the value of</p>
<p class="p2">(i) <span class="Apple-converted-space"> </span>\(c\);</p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span>\(d\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A data set has <em>n</em> items. The sum of the items is 800 and the mean is 20.</p>
</div>
<div class="specification">
<p>The standard deviation of this data set is 3. Each value in the set is multiplied by 10.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <em>n</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of the new mean.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of the new variance.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">There are <span class="s1">10 </span>items in a data set. The sum of the items is <span class="s1">60</span>.</p>
</div>
<div class="specification">
<p class="p1">The variance of this data set is <span class="s1">3</span>. Each value in the set is multiplied by <span class="s1">4</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the mean.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) Write down the value of the new mean.</p>
<p class="p1">(ii) Find the value of the new variance.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">José travels to school on a bus. On any day, the probability that José will miss the bus is \(\frac{1}{3}\) </span><span style="font-family: times new roman,times; font-size: medium;">.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">If he misses his bus, the probability that he will be late for school is \(\frac{7}{8}\) </span><span style="font-family: times new roman,times; font-size: medium;">.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">If he does not miss his bus, the probability that he will be late is \(\frac{3}{8}\) </span><span style="font-family: times new roman,times; font-size: medium;">.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let <em>E</em> be the event “he misses his bus” and <em>F</em> the event “he is late for school”.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The information above is shown on the following tree diagram.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/party.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Find</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) \({\rm{P}}(E \cap F)\) ;</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) \({\rm{P}}(F)\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Find the probability that</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) José misses his bus and is not late for school;</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) José missed his bus, given that he is late for school.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The cost for each day that José catches the bus is 3 euros. José goes to school on </span><span style="font-family: times new roman,times; font-size: medium;">Monday and Tuesday.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Copy and complete the probability distribution table.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="images/bus.png" alt></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">The cost for each day that José catches the bus is 3 euros. José goes to school on </span><span style="font-family: times new roman,times; font-size: medium;">Monday and Tuesday.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find the expected cost for José for both days.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">In a group of 16 students, 12 take art and 8 take music. One student takes neither </span><span style="font-family: times new roman,times; font-size: medium;">art nor music. The Venn diagram below shows the events art and music. The values </span><span style="font-family: times new roman,times; font-size: medium;"><em>p</em> , <em>q</em> , <em>r</em> and <em>s</em> represent numbers of students.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/titanic.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Write down the value of <em>s</em> .</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) Find the value of <em>q</em> .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(iii) Write down the value of <em>p</em> and of <em>r</em> .</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">a(i), (ii) and (iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) A student is selected at random. Given that the student takes music, </span><span style="font-family: times new roman,times; font-size: medium;">write down the probability the student takes art.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) <strong>Hence</strong>, show that taking music and taking art are <strong>not</strong> independent events.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Two students are selected at random, one after the other. Find the probability </span><span style="font-family: times new roman,times; font-size: medium;">that the first student takes <strong>only</strong> music and the second student takes <strong>only</strong> art.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">A running club organizes a race to select girls to represent the club in a competition.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The times taken by the group of girls to complete the race are shown in the table below.</span></p>
<p><span style="font-family: TimesNewRomanPSMT;"><br><img style="display: block; margin-left: auto; margin-right: auto;" src="images/brit.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the value of \(p\) and of \(q\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">A girl is chosen at random.</span></p>
<p style="margin-left: 30px;" align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"> (i) Find the probability that the time she takes is less than \(14\) minutes.</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> (ii) Find the probability that the time she takes is at least \(26\) minutes.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">A girl is selected for the competition if she takes less than \(x\) minutes to complete the </span><span style="font-family: times new roman,times; font-size: medium;">race.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Given that \(40\%\) of the girls are not selected,</span></p>
<p style="margin-left: 30px;" align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"> (i) find the number of girls who are not selected;</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> (ii) find \(x\) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Girls who are not selected, but took less than \(25\) minutes to complete the race, are </span><span style="font-family: times new roman,times; font-size: medium;">allowed another chance to be selected. The new times taken by these girls are shown </span><span style="font-family: times new roman,times; font-size: medium;">in the cumulative frequency diagram below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/crop.png" alt></span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Write down the number of girls who were allowed another chance.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Find the percentage of the whole group who were selected.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following Venn diagram shows the events \(A\) and \(B\)<span class="s1">, where \({\text{P}}(A) = 0.4,{\text{ P}}(A \cup B) = 0.8\) and \({\text{P}}(A \cap B) = 0.1\)</span>. The values \(p\) and \(q\) are probabilities.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-01-31_om_17.49.37.png" alt="M16/5/MATME/SP1/ENG/TZ1/02"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Write down the value of \(q\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Find the value of \(p\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find \({\text{P}}(B)\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Events \(A\) and \(B\) are independent with \({\text{P}}(A \cap B) = 0.2\) and \({\text{P}}(A' \cap B) = 0.6\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \({\text{P}}(B)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \({\text{P}}(A \cup B)\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The following diagram shows a board which is divided into three regions \(A\), \(B\) and \(C\).</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-13_om_16.53.51.png" alt></p>
<p class="p1">A game consists of a contestant throwing one dart at the board. The probability of hitting each region is given in the following table.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-13_om_16.54.43.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the probability that the dart does <strong>not </strong>hit the board.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The contestant scores points as shown in the following table.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-13_om_17.03.42.png" alt></p>
<p class="p1">Given that the game is fair, find the value of \(q\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The cumulative frequency curve below represents the marks obtained by 100 students.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/M12P2TZ2Q1.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the median mark.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the interquartile range.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The following box-and-whisker plot shows the number of text messages sent by students in a school on a particular day.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of the interquartile range.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>One student sent<em> k</em> text messages, where <em>k</em> > 11 . Given that <em>k</em> is an outlier, find the least value of <em>k</em>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">The random variable X has the following probability distribution.<br></span></p>
<p><img src="data:image/png;base64,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" alt></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Given that \({\rm{E}}(X) = 1.7\) , find <em>q</em> .</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">In a class of <span class="s1">21 </span>students, <span class="s1">12 </span>own a laptop, <span class="s1">10 </span>own a tablet, and <span class="s1">3 </span>own neither.</p>
<p class="p1">The following Venn diagram shows the events “own a laptop” and “own a tablet”.</p>
<p class="p1">The values \(p\), \(q\), \(r\) and \(s\) represent numbers of students.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-02-02_om_09.38.31.png" alt="M16/5/MATME/SP1/ENG/TZ2/08"></p>
</div>
<div class="specification">
<p class="p1">A student is selected at random from the class.</p>
</div>
<div class="specification">
<p class="p1">Two students are randomly selected from the class. Let \(L\) be the event a “student owns a laptop”.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Write down the value of \(p\).</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Find the value of \(q\).</p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>Write down the value of \(r\) and of \(s\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) Write down the probability that this student owns a laptop.</p>
<p class="p1">(ii) Find the probability that this student owns a laptop or a tablet but not both.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span><strong>Copy </strong>and complete the following tree diagram. (Do <strong>not </strong>write on this page.)</p>
<p class="p2" style="text-align: center;"><img src="images/Schermafbeelding_2017-02-02_om_13.55.21.png" alt="M16/5/MATME/SP1/ENG/TZ2/08.c"></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Write down the probability that the second student owns a laptop given that the first owns a laptop.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Two boxes contain numbered cards as shown below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/anne.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Two cards are drawn at random, one from each box.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Copy and complete the table below to show all nine equally likely outcomes.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/bt.png" alt></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Let <em>S</em> be the sum of the numbers on the two cards.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find the probability of each value of <em>S</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the expected value of <em>S</em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Anna plays a game where she wins \(\$ 50\) if <em>S</em> is even and loses \(\$ 30\) if <em>S</em> is odd.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Anna plays the game 36 times. Find the amount she expects to have at the end </span><span style="font-family: times new roman,times; font-size: medium;">of the 36 games.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Jim heated a liquid until it boiled. He measured the temperature of the liquid as it cooled. The following table shows its temperature, \(d\) degrees Celsius, \(t\) minutes after it boiled.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-11_om_08.45.05.png" alt="M17/5/MATME/SP1/ENG/TZ1/04"></p>
</div>
<div class="specification">
<p>Jim believes that the relationship between \(d\) and \(t\) can be modelled by a linear regression equation.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the independent variable.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the boiling temperature of the liquid.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Jim describes the correlation as <strong>very strong</strong>. Circle the value below which best represents the correlation coefficient.</p>
<p>\[0.992\quad \quad \quad 0.251\quad \quad \quad 0\quad \quad \quad - 0.251\quad \quad \quad - 0.992\]</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Jim’s model is \(d = - 2.24t + 105\), for \(0 \leqslant t \leqslant 20\). Use his model to predict the decrease in temperature for any 2 minute interval.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Bill and Andrea play two games of tennis. The probability that Bill wins the first game is \(\frac{4}{5}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">If Bill wins the first game, the probability that he wins the second game is \(\frac{5}{6}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">If Bill loses the first game, the probability that he wins the second game is \(\frac{2}{3}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Copy</strong> and complete the following tree diagram. <em>(Do <strong>not</strong> write on this page.)</em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em> </em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"><em><br><img src="images/maths_9a_1.png" alt></em></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the probability that Bill wins the first game and Andrea wins the second game.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Find the probability that Bill wins at least one game.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Given that Bill wins at least one game, find the probability that he wins both games.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Two standard six-sided dice are tossed. A diagram representing the sample space is </span><span style="font-family: times new roman,times; font-size: medium;">shown below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/dice.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Let \(X\) be the sum of the scores on the two dice.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Find \({\rm{P}}(X = 6)\) .</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) Find \({\rm{P}}(X > 6)\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(iii) Find \({\rm{P}}(X = 7|X > 6)\) .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">a(i), (ii) and (iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Elena plays a game where she tosses two dice.</span></p>
<p style="margin-left: 60px;" align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">If the sum is 6, she <strong>wins</strong> 3 points.</span></p>
<p style="margin-left: 60px;" align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">If the sum is greater than 6, she <strong>wins</strong> 1 point.</span></p>
<p style="margin-left: 60px;" align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">If the sum is less than 6, she <strong>loses</strong> <em>k </em>points.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Find the value of <em>k</em> for which the game is fair.</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">There are nine books on a shelf. For each book, <em>x</em> is the number of pages, and <em>y</em> is the </span><span style="font-family: times new roman,times; font-size: medium;">selling price in pounds (£). Let <em>r</em> be the correlation coefficient.</span></p>
</div>
<div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><img src="images/diving.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the possible minimum and maximum values of <em>r</em> .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Given that \(r = 0.95\) , which of the following diagrams best represents the data.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/cow.png" alt></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">For the data in diagram D , which <strong>two</strong> of the following expressions describe </span><span style="font-family: times new roman,times; font-size: medium;">the correlation between <em>x</em> and <em>y</em> ?</span></p>
<p style="text-align: center;" align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">perfect, zero, linear, strong positive, strong negative, </span><span style="font-family: times new roman,times; font-size: medium;">weak positive, weak negative</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">A box contains 100 cards. Each card has a number between one and six written on it. </span><span style="font-family: times new roman,times; font-size: medium;">The following table shows the frequencies for each number.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/take_that.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Calculate the value of <em>k</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">Find</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) the median;</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) the interquartile range.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b(i) and (ii).</div>
</div>
<br><hr><br><div class="specification">
<p>A city hired 160 employees to work at a festival. The following cumulative frequency curve shows the number of hours employees worked during the festival.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_07.01.49.png" alt="M17/5/MATME/SP1/ENG/TZ2/08.a.ii"></p>
</div>
<div class="specification">
<p>The city paid each of the employees £8 per hour for the first 40 hours worked, and £10 per hour for each hour they worked after the first 40 hours.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the median number of hours worked by the employees.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of employees who worked 50 hours or less.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the amount of money an employee earned for working 40 hours;</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the amount of money an employee earned for working 43 hours.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of employees who earned £200 or less.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Only 10 employees earned more than £\(k\). Find the value of \(k\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Events <em>A</em> and <em>B</em> are such that \({\rm{P}}(A) = 0.3\) , \({\rm{P}}(B) = 0.6\) and \({\rm{P}}(A \cup B) = 0.7\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/washing.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The values <em>q</em> , <em>r</em> , <em>s</em> and <em>t</em> represent probabilities.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the value of <em>t</em> .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Show that \(r = 0.2\) . </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Write down the value of <em>q</em> and of <em>s</em> .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Write down \({\rm{P}}(B')\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Find \({\rm{P}}(A|B')\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c(i) and (ii).</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">In a class of 100 boys, 55 boys play football and 75 boys play rugby. Each boy must play </span><span style="font-family: times new roman,times; font-size: medium;">at least one sport from football and rugby.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Find the number of boys who play both sports.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Write down the number of boys who play only rugby.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">One boy is selected at random.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(i) Find the probability that he plays only one sport.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">(ii) Given that the boy selected plays only one sport, find the probability that he </span><span style="font-family: times new roman,times; font-size: medium;">plays rugby.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Let <em>A</em> be the event that a boy plays football and <em>B</em> be the event that a boy plays rugby.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Explain why <em>A</em> and <em>B</em> are <strong>not</strong> mutually exclusive.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Show that <em>A</em> and <em>B</em> are <strong>not</strong> independent.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The diagram below shows the probabilities for events <em>A</em> and <em>B</em> , with \({\rm{P}}(A') = p\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/tree.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Write down the value of <em>p</em> .</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \({\rm{P}}(B)\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find \({\rm{P}}(A'|B)\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">Celeste wishes to hire a taxicab from a company which has a large number of taxicabs.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">The taxicabs are randomly assigned by the company.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"> The probability that a taxicab is yellow is 0.4.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"> The probability that a taxicab is a Fiat is 0.3.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"> The probability that a taxicab is yellow or a Fiat is 0.6.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font: 17.0px 'Times New Roman';"> </span>Find the probability that the taxicab hired by Celeste is <strong>not </strong>a yellow Fiat.</span></p>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the probability distribution of a discrete random variable \(A\), in terms of an angle \(\theta \).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-11_om_09.10.36.png" alt="M17/5/MATME/SP1/ENG/TZ1/10"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \(\cos \theta = \frac{3}{4}\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that \(\tan \theta > 0\), find \(\tan \theta \).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let \(y = \frac{1}{{\cos x}}\), for \(0 < x < \frac{\pi }{2}\). The graph of \(y\)between \(x = \theta \) and \(x = \frac{\pi }{4}\) is rotated 360° about the \(x\)-axis. Find the volume of the solid formed.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;">A scientist has 100 female fish and 100 male fish. She measures their lengths to the </span><span style="font-family: times new roman,times; font-size: medium;">nearest cm. These are shown in the following box and whisker diagrams.</span></p>
<p align="LEFT"><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/fish.png" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the range of the lengths of <strong>all</strong> 200 fish.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Four cumulative frequency graphs are shown below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/females.png" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Which graph is the best representation of the lengths of the <strong>female</strong> fish?</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A bag contains 5 green balls and 3 white balls. Two balls are selected at random without replacement.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Complete the following tree diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-11_om_09.35.12.png" alt="N17/5/MATME/SP1/ENG/TZ0/01.a"></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that exactly one of the selected balls is green.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The random variable <em>X</em> has the following probability distribution, with \({\rm{P}}(X > 1) = 0.5\) .</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><br><img src="images/M12P1TZ2Q4.jpg" alt> </span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the value of <em>r</em> .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Given that \({\rm{E}}(X) = 1.4\) , find the value of <em>p</em> and of <em>q</em> .</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A school collects cans for recycling to raise money. Sam’s class has <span class="s1">20 </span>students.</p>
<p class="p1">The number of cans collected by each student in Sam’s class is shown in the following stem and leaf diagram.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-01-31_om_18.02.34.png" alt="M16/5/MATME/SP1/ENG/TZ1/08"></p>
</div>
<div class="specification">
<p class="p1">The following box-and-whisker plot also displays the number of cans collected by students in Sam’s class.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2017-01-31_om_18.04.35.png" alt="M16/5/MATME/SP1/ENG/TZ1/08.b+c+d+e"></p>
</div>
<div class="specification">
<p class="p1">There are <span class="s1">80 </span>students in the school.</p>
</div>
<div class="specification">
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-01-31_om_18.13.01.png" alt="M16/5/MATME/SP1/ENG/TZ1/08.e"></p>
<p class="p1">The mean number of cans collected is <span class="s1">39.4</span>. The standard deviation is <span class="s1">18.5</span>.</p>
<p class="p1">Each student then collects <span class="s1">2 </span>more cans.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the median number of cans collected.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) Write down the value of \(a\).</p>
<p class="p1">(ii) The interquartile range is <span class="s1">14</span>. Find the value of \(b\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Sam’s class collected <span class="s1">745 </span>cans. They want an average of <span class="s1">40 </span>cans per student.</p>
<p class="p1">How many more cans need to be collected to achieve this target?</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The students raise $0.10 for each recycled can.</p>
<p class="p1">(i) Find the largest amount raised by a student in Sam’s class.</p>
<p class="p1">(ii) The following cumulative frequency curve shows the amounts in dollars raised by all the students in the school. Find the percentage of students in the school who raised more money than anyone in Sam’s class.</p>
<p class="p1"><img src="data:image/png;base64,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" alt></p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) Write down the new mean.</p>
<p class="p1">(ii) Write down the new standard deviation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Pablo drives to work. The probability that he leaves home before 07:00 is \(\frac{3}{4}\).</p>
<p>If he leaves home before 07:00 the probability he will be late for work is \(\frac{1}{8}\).</p>
<p>If he leaves home at 07:00 or later the probability he will be late for work is \(\frac{5}{8}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>Copy</strong> and complete the following tree diagram.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that Pablo leaves home before 07:00 and is late for work.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that Pablo is late for work.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that Pablo is late for work, find the probability that he left home before 07:00.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Two days next week Pablo will drive to work. Find the probability that he will be late at least once.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: 'times new roman', times; font-size: medium;">The weekly wages (in dollars) of 80 employees are displayed in the cumulative </span><span style="font-family: 'times new roman', times; font-size: medium;">frequency curve below.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">(i) Write down the median weekly wage.</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Find the interquartile range of the weekly wages.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a(i) and (ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">The box-and-whisker plot below displays the weekly wages of the employees.<br></span></p>
<p><br><img src="data:image/png;base64,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" alt></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;">Write down the value of</span></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \(a\) ;</span></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \(b\) ;</span></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) \(c\) .</span></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b(i), (ii), (iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">Employees are paid \($\ 20\) per hour.</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">Find the median number of <strong>hours</strong> worked per week.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
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<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">Employees are paid \(\$ 20\) per hour.</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">Find the number of employees who work more than \(25\) hours per week.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
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