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class="fa fa-star-o"></i></a> </h1> <ol class="breadcrumb"> <li><a href="../../../mathsapplications.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../3011/examination-questions.html">Examination Questions</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Geometry & Trigonometry Exam Style Questions</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 120 minutes"><i class="fa fa-clock-o"></i> 120'</span> </ol> <article id="main-article"> <div class="greyBg"> <h2><img alt="" src="../../images/gt-1.jpg" style="float: left; width: 200px; height: 121px;">Geometry & Trigonometry Exam Questions</h2> <p>The following are exam style questions for the sub-topics in the functions unit. There are questions with video solutions here for here for Volume and Surface area, right angled trigonometry, Nin right angled trigonometry, applications of trigonometry, circles and Voronoi diagrams.</p> </div> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander pull-right" href="#"><span class="fa fa-plus"></span></a> <div> <p>Volume & Surface Area - Exam Style Questions</p> </div> </div> <div class="panel-body"> <p>The following are exam style questions on this topic that you should try on your own before checking against the video solution.</p> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 1</p> </div> </div> <div class="panel-body"><img alt="" src="../../images/dans-images/v-sa_exq1.png" style="width: 625px; height: 530px;"></div> <div class="panel-body">Video Solution</div> <div class="panel-body"> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/672506818"></iframe></div> </section> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 2</p> </div> </div> <div class="panel-body"><img alt="" src="../../images/dans-images/v-sa_exq2.png" style="width: 625px; height: 494px;"></div> <div class="panel-body">Video Solution</div> <div class="panel-body"> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/672507261"></iframe></div> </section> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 3</p> </div> </div> <div class="panel-body"><img alt="" src="../../images/dans-images/v-sa_exq3.png" style="width: 625px; height: 529px;"></div> <div class="panel-body">Video Solution</div> <div class="panel-body"> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/672508177"></iframe></div> </section> </div> </div> </div> <div class="panel-footer"> <div> <p>text</p> </div> </div> </div> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Right angled trigonometry - Exam Style Questions</p> </div> </div> <div class="panel-body"> <div> <p>The following questions are based on IB exam style questions from past exams. You should print these off (from the document at the top) and try to do these questions under exam conditions. Then you can check your work with the video solution. NOTE - Make sure that you have set your GDC to be in degrees. See the <a href="../1054/your-graphical-display-calculator.html" title="Your Graphical Display Calculator">Your Graphical Display Calculator</a> page for help with this.</p> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 1</p> </div> </div> <div class="panel-body"> <div> <p><img alt="" src="../../files/GT/RAT/RATQ1.jpg" style="width: 700px; height: 382px;"></p> <p>Video solution</p> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 2</p> </div> </div> <div class="panel-body"> <div> <p><img alt="" src="../../files/GT/RAT/RATQ2.jpg" style="width: 700px; height: 373px;"></p> <p>Video solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/593177691"></iframe></div> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 3</p> </div> </div> <div class="panel-body"> <div> <p><img alt="" src="../../files/GT/RAT/RATQ3.jpg" style="width: 700px; height: 398px;"></p> <p>Video solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/593178109"></iframe></div> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <p><span id="cke_bm_805E" style="display: none;"> </span></p> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Non right angled trigonometry - Exam Style Questions</p> </div> </div> <div class="panel-body"> <div> <p>The following questions are based on IB exam style questions from past exams. You should print these off (from the document at the top) and try to do these questions under exam conditions. Then you can check your work with the video solution.</p> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 1</p> </div> </div> <div class="panel-body"> <div> <p><img alt="" src="../../files/GT/NRAT/NRAT1.jpg" style="width: 658px; height: 407px;"></p> <p>Video solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/593197102"></iframe></div> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 2</p> </div> </div> <div class="panel-body"> <div> <p><img alt="" src="../../files/GT/NRAT/NRAT2.jpg" style="width: 700px; height: 224px;"></p> <p>Video solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/593197828"></iframe></div> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 3</p> </div> </div> <div class="panel-body"> <div> <p><img alt="" src="../../files/GT/NRAT/NRAT3.jpg" style="width: 700px; height: 416px;"></p> <p>Video solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/593198598"></iframe></div> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <h3> </h3> <p style="text-align: center;"><br> <span id="cke_bm_805E" style="display: none;"> </span></p> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Applications of Trigonometry - Exam Style Questions</p> </div> </div> <div class="panel-body"> <div> <p>The following questions are based on IB exam style questions from past exams. You should print these off (from the document at the top) and try to do these questions under exam conditions. Then you can check your work with the video solution.</p> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 1</p> </div> </div> <div class="panel-body"> <div> <p><img alt="" src="../../images/examq1.png" style="width: 600px; height: 200px;"></p> <p>Video Solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"><iframe allowfullscreen="" frameborder="0" height="auto" mozallowfullscreen="" src="https://player.vimeo.com/video/471347614" webkitallowfullscreen="" width="100%"></iframe></section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 2</p> </div> </div> <div class="panel-body"> <div> <p><img alt="" src="../../images/examq2.png" style="width: 600px; height: 145px;"></p> <p>Video Solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"><iframe allowfullscreen="" frameborder="0" height="auto" mozallowfullscreen="" src="https://player.vimeo.com/video/471348399" webkitallowfullscreen="" width="100%"></iframe></section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 3</p> </div> </div> <div class="panel-body"> <div> <p><img alt="" src="../../images/examq3.png" style="width: 600px; height: 295px;"></p> <p>Video Solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"><iframe allowfullscreen="" frameborder="0" height="auto" mozallowfullscreen="" src="https://player.vimeo.com/video/471349346" webkitallowfullscreen="" width="100%"></iframe></section> </div> </div> </div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Circles - Exam Style Questions</p> </div> </div> <div class="panel-body"> <p>The following questions are based on IB exam style questions from past exams. You should print these off (from the document at the top) and try to do these questions under exam conditions. Then you can check your work with the video solution.</p> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 1</p> </div> </div> <div class="panel-body"> <div> <p dir="ltr"><span id="docs-internal-guid-ac6c73c0-7fff-f8b1-2a99-7fb95e122ac5">Nigel is buying a wedge of cheese from a round of cheese of diameter 25cm and height 6cm. He cuts a wedge with an angle of 100 degrees</span> . What is the volume of cheese that he buys? </p> <p dir="ltr" style="text-align: right;"><span id="docs-internal-guid-ac6c73c0-7fff-f8b1-2a99-7fb95e122ac5">(4 marks)</span></p> <p dir="ltr">Video solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/603268842?badge=0&autopause=0&player_id=0&app_id=58479&h=801170331b"></iframe></div> <script src="../../../api/player.js"></script></section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 2</p> </div> </div> <div class="panel-body"> <p dir="ltr"><span id="docs-internal-guid-12fe5dfb-7fff-6d83-3976-db37f0f36b6c">Nigel now wants to make a cylindrical candle with a volume of <span class="math-tex">\(300cm^3\)</span></span>, with a diameter of 4cm. How tall should the candle be? </p> <p dir="ltr" style="text-align: right;"><span id="docs-internal-guid-12fe5dfb-7fff-6d83-3976-db37f0f36b6c">(4 marks)</span></p> <p dir="ltr">Video solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/603276204?badge=0&autopause=0&player_id=0&app_id=58479&h=ed8eefcc31"></iframe></div> <script src="../../../api/player.js"></script></section> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 3</p> </div> </div> <div class="panel-body"> <div> <p dir="ltr"><span id="docs-internal-guid-54938793-7fff-0a89-4e1b-615bd55641fd">A terrace is in the shape of a rectangle, ABCD, and a semicircle, AB. AB is the diameter of the semicircle. </span></p> <p dir="ltr"><img alt="" src="../../circlesx.png" style="width: 492px; height: 480px;"></p> <p dir="ltr"><span id="docs-internal-guid-11931a4e-7fff-93d7-e782-7bf57d9e4d4c"></span></p> <p dir="ltr"><span id="docs-internal-guid-11931a4e-7fff-93d7-e782-7bf57d9e4d4c">Nigel is going to cover the garden with grass, which costs $4.99 per m</span>2. Work out the cost of covering the garden with grass. </p> <p dir="ltr" style="text-align: right;"><span id="docs-internal-guid-11931a4e-7fff-93d7-e782-7bf57d9e4d4c">(6 marks)</span></p> </div> <p>Video solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/603273352?badge=0&autopause=0&player_id=0&app_id=58479&h=4abf7cd55c"></iframe></div> <script src="../../../api/player.js"></script></section> </div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Voronoi Diagrams - Exam Style Questions</p> </div> </div> <div class="panel-body"> <div> <p>The following questions are based on IB exam style questions from past exams. You should print these off (from the document at the top) and try to do these questions under exam conditions. Then you can check your work with the video solution.</p> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 1</p> </div> </div> <div class="panel-body"> <p><img alt="" src="../../images/exam1_image.png" style="width: 600px; height: 513px;"></p> <p>Video Solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/500578923"></iframe></div> </section> </div> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p> Question 2</p> </div> </div> <div class="panel-body"> <p><img alt="" src="../../images/exam2_image(1).png" style="width: 600px; height: 377px;"></p> <p>Video Solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/500579451"></iframe></div> </section> </div> </div> <div class="panel panel-has-colored-body panel-default panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 3 </p> </div> </div> <div class="panel-body"> <div> <p><img alt="" src="../../images/exam3a_image.png" style="width: 600px; height: 151px;"></p> <p>Video Solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/500579893"></iframe></div> </section> </div> <p><img alt="" src="../../images/picture1(7).png" style="width: 600px; height: 137px;"></p> <p>Video solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/500580294"></iframe></div> </section> </div> <div class="panel panel-default panel-expandable panel-has-colored-body"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 4</p> </div> </div> <div class="panel-body"> <div> <p dir="ltr"><span id="docs-internal-guid-336c7471-7fff-3ffc-d43d-968a9548160c">Gil is designing his garden ABCD, and is planning on a set of coordinate axes. Each unit represents 1 metre of his garden. </span></p> <p dir="ltr"><img alt="" src="../../screenshot-2022-04-11-at-20.46.51.png" style="width:400px;height:353px;"></p> <p dir="ltr" role="presentation"><span id="docs-internal-guid-336c7471-7fff-3ffc-d43d-968a9548160c">a. Find the area of his garden </span></p> <p dir="ltr"><span id="docs-internal-guid-336c7471-7fff-3ffc-d43d-968a9548160c">b.He is building a path (represented by EBGF). What is the gradient of the line through EB?</span></p> <p dir="ltr"><span id="docs-internal-guid-336c7471-7fff-3ffc-d43d-968a9548160c">c. What is the equation of the line through EB? Give your answer in the form ax+by+d=0</span></p> <p dir="ltr"><span id="docs-internal-guid-336c7471-7fff-3ffc-d43d-968a9548160c">d. He wants to make a new path from A that meets the original path at a right angle. 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