[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-446604-105":3,"doc-detail-446604-en":81,"detail-sidebar-cat-0-en-105":98},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","practice-mat-solutions-read-and-answer-past-mat-questions","Practice MAT Solutions - read and answer past MAT questions","","Practice MAT solutions compiled for a Pearson VUE MAT practice test created ahead of MAT 2024, using past MAT questions from 2007–2022. The document provides worked solutions across a range of mathematics topics including geometry with displacement vectors, integrals using algebraic identities, arithmetic progressions, circle area decomposition, differentiation and tangents, trigonometric optimization, logarithms, vectors, and equation transformations. Answers are presented for each numbered problem, enabling step-by-step checking and revision.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/practice-mat-solutions-read-and-answer-past-mat-questions/446604/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/practice-mat-solutions-read-and-answer-past-mat-questions/446604.png","ImageObject",300,407,{"name":42,"@type":43},"Blue Pony","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-17","2026-09-29",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",11,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is this document used for?","Question",{"text":63,"@type":64},"It contains solutions for a MAT practice test on the Pearson VUE system, created ahead of MAT 2024. The questions are drawn from past MAT papers from 2007–2022.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How are answers presented?",{"text":68,"@type":64},"Each numbered problem includes the reasoning steps and concludes with a final “The answer is …” statement. This makes it suitable for self-checking and revision.",{"name":70,"@type":61,"acceptedAnswer":71},"What math topics are covered in the solutions?",{"text":72,"@type":64},"The problems include a mix of geometry (vectors and circle areas), calculus (integrals and tangents), algebra (factorisation and completing the square), and trigonometry/logarithms for optimization and equation solving.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},446604,1790762788,{"code":4,"msg":82,"data":83},"success",{"doc_id":79,"user_id":84,"nickname":42,"user_avatar":85,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":86,"file_id":87,"file_url":88,"file_type":89,"file_size":90,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":91,"language":92,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":93,"faqs":94,"seo_title":95,"seo_description":12,"update_tm":96,"read_time":97},962090760266,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","PRACTICE MAT SOLUTIONS  \nThese solutions are for the practice test on the Pearson VUE system, created ahead of MAT 2024 . The questions are all past MAT questions from 2007–2022 . The answers are collated below.  \n1. The centre is at (3 , 4) and one corner is at (1 , 5), which is a displacement of (−2 , 1) . There’s another corner opposite, at (3 , 4) − (−2 , 1) = (5 , 3), but this is not one of the options. To find the other corners, we need to find a vector with equal magnitude, but at right-angles to (−2 , 1) . Rotating by 90◦ gives (1 , 2) . The other corners are at (3 , 4) ± (1 , 2), which includes (2 , 2) . The answer is (2,2) .  \n2. Using the difference of two squares, this is Z01 e2x − x2 dx. Notice that, since the derivative of e2x is 2e2x, this integral is  \n􀀔 12e2x − x33􀀕 10 = e22 − 13 − 12 = 3e26−~~ ~~5  \nThe answer is 3e2 − 5  \n6 .  \n3. Pair the terms to get −3 − 7 − · · · − 199. This is the sum of an arithmetic progression and is equal to (−3 − 199) × 50/2 = −5050  \nThe answer is −5050.  \n4. Connect each point to the centre of the circle to split the shape into 12 isosceles triangles, each with angle 30◦ at the centre. Then the area of each triangle is ~~1~~2 × 1 × 1 × sin30◦ = ~~1~~4, and there are 12 triangles, for a total area of 3 .  \nThe answer is 3 .  \n5. The integral is  \nZ0 a √x + x2 dx = Z0 a x 1/2 + x2 dx = 􀀔 23x3/2 + 13x3􀀕 a0 = 23a3/2 + 13a3 .  \nSo we have 2a3/2 + a3 = 15 . This factorises as (a3/2 − 3)(a3/2 + 5) = 0 . Since a > 0 we want a3/2 > 0, so it’s 3, so a = 32/3 .  \nThe answer is a = 32/3 .  \n6. The gradient at p is ep and so the tangent is y = ep (x − p) + ep. This crosses the x-axis when ep (a−p)+ep = 0 which happens if a = p−1 . Similarly q = 1−b so p−a = q−b (they’re both 1) .  \na = p − 1 b = q − 1  \nThe answer is p − a = q − b.  \n7. The intersection point is at ex = 1 − ex which happens when 2ex = 1, that is x = − ln2 \u003C 0.  \nThe area has reflectional symmetry in the line y = ~~1~~2 so we want  \n2 Z−0ln 2 ex − 12 dx = 2 hex − x2iln 2 = 2 􀀒 (1) − 􀀒 12 + ln22 􀀓􀀓 = 1 − ln2 The answer is 1 − ln2 .  \n8. Either x ≥ 0 and x2 + 1 = 3x or x \u003C 0 and −x2 + 1 = −3x. The first equation has solutions  \n~~1~~2 􀀀3 ±√5􀀁 which are both positive. The second equation has solutions ~~1~~2 􀀀3 ±√13􀀁 and only one of these is actually negative. So there are three solutions in total.  \nThe answer is 3 .  \n9. The relationship between circle Cn of radius rn and circle Cn+1 of radius rn+1 is shown below.  \nThe tangent is at right-angles to the radius, so there’s a right-angled triangle with hypotenuse rn+1 and other sides rn and 1 . Pythagoras gives r2n+1 = r2n + 1 . Since r 21 = 1, we have r22 = 2 and r23 = 3 and so on, up to r 2100 = 100, so the radius of C100 is 10 .  \nThe answer is 10 .  \n10. Complete the square for x and for y (x − 2k)2 − 4k2 + (y − 2)2 − 4 + 8 = k 3 − k This is the equation of a circle with centre (2k, 2) and r 2 = k 3 + 4k2 − k − 4 provided that expression is positive. Factorising the cubic as (k + 4)(k − 1)(k + 1) reveals that this happens if and only if either −4 \u003C k \u003C −1 or if k > 1.  \nThe answer is “if and only if either −4 \u003C k \u003C −1 or k > 1”.  \n11. 3cos2 x + 2sin x + 1 = 3(1 − sin2 x) + 2sin x + 1 = −3(sin x − 1/3)2 + 1/3 + 4 . This takes its maximum value when sin x = 1/3, and that value is 4 + 1/3 = 13/3.  \nThe answer is 13 .  \n12. The tangent is y = 2ax − a2 , which crosses the x-axis at (a/2 , 0) .  \nThe area is Z0 a x2 dx − (area of APQ) where A is (a, a2 ), P is (a, 0) and Q is (a/2 , 0) . This is a3 a3 a3  \n~~ ~~ − ~~ ~~ = ~~ ~~  \n3 4 12  \nThe answer is a3  \n12 .  \n13. Factorise the numbers from 1 to 10; this gives  \nlog 10 (2 × 5 × 32 × 23 × 7 × 2 × 3 × 5 × 22 × 3 × 2) = log 10 (283452 7) .  \nUse log 10 (2252 ) = 2 . Use 2434 = 64 . This gives 2+log 10 (2264 7) = 2+2log 10 2+4log 10 6+log 10 7. The answer is 2 + 2log 10 2 + 4log 10 6 + log 10 7.  \n14. The turning points have dydx = 0 at x = 1 and at x = 3, so 3 + 2a + b = 0 and 27 + 6a + b = 0 . Solve these for a = −6, b = 9 . Now ","cbCaifVsH2vDRZ7M","https://ap.wps.com/l/cbCaifVsH2vDRZ7M","pdf",167752,8,"English","# Solutions\n## Geometry, vectors, and circle problems\n## Calculus and algebraic manipulation\n## Trigonometry, logarithms, and optimization\n## Equations and probability-style counting","[{\"question\":\"What is this document used for?\",\"answer\":\"It contains solutions for a MAT practice test on the Pearson VUE system, created ahead of MAT 2024. The questions are drawn from past MAT papers from 2007–2022.\"},{\"question\":\"How are answers presented?\",\"answer\":\"Each numbered problem includes the reasoning steps and concludes with a final “The answer is …” statement. This makes it suitable for self-checking and revision.\"},{\"question\":\"What math topics are covered in the solutions?\",\"answer\":\"The problems include a mix of geometry (vectors and circle areas), calculus (integrals and tangents), algebra (factorisation and completing the square), and trigonometry/logarithms for optimization and equation solving.\"}]","Practice MAT Solutions - read and answer past MAT questions | PDF",1790716284,20,{"code":4,"msg":82,"data":99},[100,104,108,111,116,121,126,130,134,137,141],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":105,"show_sort_weight":106,"slug":107},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":109,"slug":110},70,"exam",{"id":112,"doc_module":4,"doc_module_name":25,"category_name":113,"show_sort_weight":114,"slug":115},5,"Comic",60,"comic",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":118,"show_sort_weight":119,"slug":120},6,"Technology",50,"technology",{"id":122,"doc_module":4,"doc_module_name":25,"category_name":123,"show_sort_weight":124,"slug":125},7,"Healthcare",40,"healthcare",{"id":91,"doc_module":4,"doc_module_name":25,"category_name":127,"show_sort_weight":128,"slug":129},"Research & Report",30,"research-report",{"id":131,"doc_module":4,"doc_module_name":25,"category_name":132,"show_sort_weight":97,"slug":133},9,"Religion & Spirituality","religion-spirituality",{"id":97,"doc_module":4,"doc_module_name":25,"category_name":135,"show_sort_weight":97,"slug":136},"World Cup","world-cup",{"id":138,"doc_module":4,"doc_module_name":25,"category_name":139,"show_sort_weight":138,"slug":140},10,"Lifestyle","lifestyle",{"id":142,"doc_module":4,"doc_module_name":25,"category_name":143,"show_sort_weight":112,"slug":144},19,"General","general"]