# Mathematics Grade 12 P2 Eastern Cape Mock 2022 QP (Eng) > Grade 12 Mathematics Paper 2 question paper from the Eastern Cape Mock Exam 2022 (English), 14 pages. Read online or download the free PDF. - Page: https://www.hlayiso.com/library/maths-p2-gr12-qp-sept-2022-english/93f3b9eb-c364-40f9-8f8d-91dd9e2d9b3c - Updated: 2026-09-27 - Subject: Mathematics - Grade: Grade 12 - Language: English - Document type: Question paper - Year: 2022 - Exam period: Eastern Cape Mock Exam - Paper: 2 - Curriculum: CAPS - Pages: 14 Breadcrumbs: [Home](https://www.hlayiso.com/) › [Library](https://www.hlayiso.com/library) › [Grade 12](https://www.hlayiso.com/library/grade-12) › [Mathematics](https://www.hlayiso.com/library/grade-12/mathematics) › [Mathematics Grade 12 P2 Eastern Cape Mock 2022 QP (Eng)](https://www.hlayiso.com/library/maths-p2-gr12-qp-sept-2022-english/93f3b9eb-c364-40f9-8f8d-91dd9e2d9b3c) ## About this document Mathematics · Grade 12 · Eastern Cape Mock Exam · 2022 · English. Question paper, 14 pages. Read online or download the PDF. Read it free online on the page above; download the PDF from there. ## Matching paper and memo - [MATHS P2 GR12 MEMO SEPT 2022 Afr English](https://www.hlayiso.com/library/maths-p2-gr12-memo-sept-2022-afr-english/484afb47-d30d-4a37-b0fc-e0cc6e34a50f) — Memo · 2022 · Eng ## Document text Text extracted from the PDF. Layout, diagrams and tables may not survive extraction. ### Page 1 Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE GRADE 12 SEPTEMBER 2022 MATHEMATICS P2 MARKS: 150 TIME: 3 hours This question paper consists of 14 pages, including a 1-page information sheet, and an answer book of 18 pages. ### Page 2 Downloaded from hlayiso.com 2 MATHEMATICS P2 (EC/SEPTEMBER 2022) INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of 10 questions. 2. Answer ALL the questions in the SPECIAL ANSWER BOOK provided. 3. Clearly show ALL calculations, diagrams, graphs, etc. which you have used in determining your answers. 4. Answers only will NOT necessarily be awarded full marks. 5. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 6. If necessary, round off answers correct to TWO decimal places, unless stated otherwise. 7. Diagrams are NOT necessarily drawn to scale. 8. An information sheet with formulae is included at the end of the question paper. 9. Write neatly and legibly. Copyright reserved Please turn over ### Page 3 Downloaded from hlayiso.com (EC/SEPTEMBER 2022) MATHEMATICS P2 3 QUESTION 1 A hundred athletes took part in a long jump competition. The distance, in centimetres, of their best jumps is summarised in the table below. Number of Distance of Jumps (in cm) athletes 420 < d ≤ 460 6 460 < d ≤ 500 14 500 < d ≤ 540 16 540 < d ≤ 580 42 580 < d ≤ 620 14 620 < d ≤ 660 2 660 < d ≤ 700 3 700 < d ≤ 740 2 740 < d ≤ 780 1 1.1 Complete the cumulative frequency column in your ANSWER BOOK. (2) 1.2 Draw an ogive (cumulative frequency curve) to represent the above information in your ANSWER BOOK. (4) 1.3 Use your graph to estimate the median jump of the competition. (2) 1.4 What percentage of athletes jumped over 560 cm? (2) [10] Copyright reserved Please turn over ### Page 4 Downloaded from hlayiso.com 4 MATHEMATICS P2 (EC/SEPTEMBER 2022) QUESTION 2 The following table shows a comparison of the distances (centimetres) jumped by 6 long jumpers and the hours spent practising their jumps in a week. Long jumper 1 2 3 4 5 6 x: Hours practised 4,5 2 3,5 4 8 3 y: Distance jumped (cm) 650 420 580 490 780 525 2.1 Determine the equation for the least squares regression line for the data. (3) 2.2 Predict the distance jumped by a long jumper who practiced for 5,4 hours. (2) 2.3 Comment on the validity of your answer in QUESTION 2.2. Motivate your answer. (2) 2.4 At the end of the event, they found that the measuring tape used was broken and all distances were decreased by 13 cm. How will this influence the: 2.4.1 Mean jump of the event? (1) 2.4.2 Range of the jumps during this event? (1) 2.4.3 Standard deviation? (1) [10] Copyright reserved Please turn over ### Page 5 Downloaded from hlayiso.com (EC/SEPTEMBER 2022) MATHEMATICS P2 5 QUESTION 3 In the diagram below, E(p; 8), F(–2; –3), G and H(8; 7) are vertices of rhombus EFGH. The diagonals EG and HF intersect at M and cut the x-axis at K and R respectively. y E(p ; 8) H(8 ; 7) M x R K F(–2 ; –3) G 3.1 Calculate the: 3.1.1 Coordinates of M (2) 3.1.2 Gradient of FH (2) 3.1.3 �R Size of MK (4) 3.2 Use the properties of a rhombus to calculate the value of p. (4) 3.3 Calculate the coordinates of G. (2) 3.4 The rhombus is reflected about the line x = –3. N is the image of M after the reflection. Calculate the length of MN. (3) [17] Copyright reserved Please turn over ### Page 6 Downloaded from hlayiso.com 6 MATHEMATICS P2 (EC/SEPTEMBER 2022) QUESTION 4 In the diagram below, a circle centred at R(4; 2) passes through the origin O, S and N(6 ; y). From P, a point outside the circle, tangents are drawn to O and N. Determine the equation of the circle in the form ( x − a ) + ( y − b ) = 2 2 4.1 r2 . (3) 4.2 Calculate the value of k. (4) 4.3 y mx + c . Determine the equation of NP in the form = (5) 4.4 It is further given that the equation of OP is y = −2 x. Calculate the: 4.4.1 Coordinates of P (3) 4.4.2 Perimeter of PNRO (4) 4.5 Another circle, centred at T, is drawn to touch the circle, centred at R, at S externally. The radii of both circles are equal in length. Determine the coordinates of T. (4) [23] Copyright reserved Please turn over ### Page 7 Downloaded from hlayiso.com (EC/SEPTEMBER 2022) MATHEMATICS P2 7 QUESTION 5 5.1 Given that: cos 26° = p Express each of the following in terms of p, without using a calculator. 5.1.1 sin 26° (2) 5.1.2 tan154° (3) 5.1.3 sin13°.cos13° (2) 5.2 Determine, without using a calculator, the value of the following expressions: 5.2.1 cos ( -θ). tan ( 180° + θ) 2 cos ( 90°+ θ) (5) 5.2.2 1 + 2 cos105°.sin15° (4) 5.3 Consider: 1 − cos 2 x − sin x = tan x sin 2 x − cos x 5.3.1 Prove the identity. (4) 5.3.2 For which value(s) of x, in the interval 𝑥𝑥 ∈ [–180° ; 180°], is the identity not valid? (3) 5.4 Determine the general solution of: sin2 x + 2 sin x cos x = 3 cos2 x (7) [30] Copyright reserved Please turn over ### Page 8 Downloaded from hlayiso.com 8 MATHEMATICS P2 (EC/SEPTEMBER 2022) QUESTION 6 x Sketched below is the graph of f(x) = cos � �, in the interval 𝑥𝑥 ∈ [–180°; 180°]. 3 y 2 1 x –180° –90° 0° 90° 180° –1 –2 6.1 On the grid given in the ANSWER BOOK, draw the graph of g ( = x) sin x + 1 , clearly showing ALL intercepts with the axes as well as the coordinates of all turning points. (3) 6.2 Write down the: 6.2.1 Period of f (1) 6.2.2 Range of g ( x) − 3 (2) 6.3 Determine the maximum distance of g ( x) − h( x) , where h is the reflection of g in the x-axis, in the interval x ∈ [ −180°;180°] . (2) 6.4 For which values of x in the interval 𝑥𝑥 ∈ [ − 180°; 180°] will f(x).g' (x)>0? (2) 6.5 The graph of g undergoes a transformation to form a new graph ) sin( x − 15°) . Describe in words the transformation from g to k. k ( x= (2) [12] Copyright reserved Please turn over ### Page 9 Downloaded from hlayiso.com (EC/SEPTEMBER 2022) MATHEMATICS P2 9 QUESTION 7 In the diagram below, TP represents the height of a building. The foot of the building P and the points Q and R are in the same horizontal plane. From Q, the angle of elevation to the � R = 150°, QP� R = 𝑥𝑥 and the distance between P and R is top of the building is 60°. PQ 300 metres. T 60° P x Q 150° R 7.1 � in terms of x. Write down R (1) 7.2 Determine the length of PQ in terms of x. (3) 7.3 Hence, show that: TP = 300 3(cos x − 3 sin x) (4) [8] Copyright reserved Please turn over ### Page 10 Downloaded from hlayiso.com 10 MATHEMATICS P2 (EC/SEPTEMBER 2022) QUESTION 8 In the diagram, PRQT is a cyclic quadrilateral in the circle with QR = QT. Chord RT is produced to S and radii OP and OT are drawn. PR� T = 42° and QT �S = 146°. Q R 1 O 42° 146° T S P Determine, giving reasons, the size of the following angles: 8.1 �T PO (2) 8.2 � R1 (2) 8.3 �T RP (3) [7] Copyright reserved Please turn over ### Page 11 Downloaded from hlayiso.com (EC/SEPTEMBER 2022) MATHEMATICS P2 11 QUESTION 9 In the diagram, the two circles touch internally at M. MK is a common tangent to the circles. A, E and C are points on the larger circle and B and D are points on the smaller circle. Chord CA is produced to meet the tangent at K. ∆MEC is drawn. CA and EM meet at B. KB is a tangent to the smaller circle at B. D is a point on CM. AM and BD are drawn. Let KM � B = 𝑥𝑥. K A 1 2 x E B 1 4 1 2 2 3 M 3 1 2 1 2 D C 9.1 Name, giving reasons, FOUR other angles each equal to x. (5) 9.2 Prove, giving reasons, that: 9.2.1 BD || EC (2) 9.2.2 �2 = � A B2 (3) 9.2.3 ME × MD = MC × MB (2) [12] Copyright reserved Please turn over ### Page 12 Downloaded from hlayiso.com 12 MATHEMATICS P2 (EC/SEPTEMBER 2022) QUESTION 10 10.1 � =� In the diagram below, ΔABC and ΔDEF are given such that A � = F� . � = �E and C D, B A D • ♣ E F • ♣ B C Prove the theorem that states if two triangles are equiangular, then their sides are in DE DF proportion, i.e., prove that: = AB AC (6) Copyright reserved Please turn over ### Page 13 Downloaded from hlayiso.com (EC/SEPTEMBER 2022) MATHEMATICS P2 13 10.2 In the diagram, AB is a diameter of the circle centred at O. ∆ABS is drawn with S a point on the circle. M is a point on BS and OM is produced to T such that AS || OM. TS is drawn such that BOST is a cyclic quadrilateral. B 1 O 2 M 1 3 2 A T 2 1 S Prove, giving reasons, that: 10.2.1 TS is a tangent to the circle at S (4) 10.2.2 TS is the diameter of a circle passing through points T, M and S (5) 10.2.3 ΔABS ||| ΔSTM (3) 10.2.4 AS . MT = 2SM2 (3) [21] TOTAL: 150 Copyright reserved Please turn over ### Page 14 Downloaded from hlayiso.com 14 MATHEMATICS P2 (EC/SEPTEMBER 2022) INFORMATION SHEET: MATHEMATICS − b ± b 2 − 4ac x= 2a A = P (1 + ni ) A = P (1 − ni ) A = P(1 − i) n A = P(1 + i) n n n n(n + 1) n ∑1 = n i =1 ∑i = i =1 2 Tn = a + (n − 1)d Sn = 2 (2a + (n − 1)d ) Tn = ar n −1 Sn = ( a r n −1 ) ; r ≠1 S∞ = a ; −1 < r < 1 r −1 1− r F= [ x (1 + i ) − 1 n ] P= x[1 − (1 + i ) − n ] i i f ( x + h) − f ( x ) f ' ( x) = lim h→ 0 h  x + x2 y1 + y 2  d = ( x 2 − x1 ) 2 + ( y 2 − y1 ) 2 M  1 ;   2 2  y 2 − y1 y = mx + c y − y1 = m( x − x1 ) m= m = tan θ x 2 − x1 ( x − a )2 + ( y − b )2 = r 2 a b c In ∆ABC: = = a 2 = b 2 + c 2 − 2bc. cos A area ∆ABC = 1 ab. sin C sin A sin B sin C 2 sin (α + β ) = sin α . cos β + cos α . sin β sin (α − β ) = sin α . cos β − cos α . sin β cos(α + β ) = cos α . cos β − sin α . sin β cos(α − β ) = cos α . cos β + sin α . sin β cos 2 α − sin 2 α  cos 2α = 1 − 2 sin 2 α sin 2α = 2 sin α . cos α 2 cos 2 α − 1  n 2 ∑x ∑ (x − x ) i x= σ = 2 i =1 n n n( A) P( A) = P(A or B) = P(A) + P(B) – P(A and B) n(S ) yˆ = a + bx b= ∑ (x − x )( y − y ) ∑ (x − x) 2 Copyright reserved Please turn over ## Related documents - [MATHS P2 GR12 ANSWER BOOK SEPT 2022 Afr Engl](https://www.hlayiso.com/library/maths-p2-gr12-answer-book-sept-2022-afr-engl/4744df95-ec05-48bc-b20c-0ae44310bc55) — Mathematics · Addendum · 2022 · Afr - [Gr12 Mathematics P1 (English) SEP 2022 Question Paper](https://www.hlayiso.com/library/gr12-mathematics-p1-english-sep-2022-question-paper/14941e0e-8578-4c8c-ba9e-f87f93e33e32) — Mathematics · QP · 2022 · Eng - [MATHS P1 QP GR12 SEPT 2021 English](https://www.hlayiso.com/library/maths-p1-qp-gr12-sept-2021-english/12f7db49-5bd7-414f-af58-65ed09d4c3e4) — Mathematics · QP · 2021 · Eng - [MATHS P1 QP Gr12 September 2014 English](https://www.hlayiso.com/library/maths-p1-qp-gr12-september-2014-english/bc7b1c66-4908-4bdc-8143-7ee244f10867) — Mathematics · QP · 2014 · Eng - [Mathematics P2 (English) QP](https://www.hlayiso.com/library/mathematics-p2-english-qp/484d317b-3177-4b73-b05a-5cb2a2cacf34) — Mathematics · QP · 2023 · Eng - [NW MATHS P2 ENGLISH SEPTEMBER 2019](https://www.hlayiso.com/library/nw-maths-p2-english-september-2019/f2f23402-6726-460e-bb8f-16840aaabbcc) — Mathematics · QP · 2019 · Eng ## More from Grade 12 Mathematics - [MATHS P2 MEMO GR12 SEPT 2025 E+A watermark](https://www.hlayiso.com/library/maths-p2-memo-gr12-sept-2025-e-a-watermark/838d50ea-fdac-4e70-8d62-e365a012252f) — Memo · 2025 - [Maths Grade 12 NSC P2 MEMO September 2025 Eng Northern Cape](https://www.hlayiso.com/library/maths-grade-12-nsc-p2-memo-september-2025-eng-northern-cape/f00a552e-132c-4871-bf72-c887cfc67272) — Memo · 2025 · Eng - [MATHS P2 ANSWER BOOK GR12 JUNE 2024 Afr+English](https://www.hlayiso.com/library/maths-p2-answer-book-gr12-june-2024-afr-english/4a71e975-4ac4-4f55-8e23-0b8155a5b0c6) — Addendum · 2024 · Eng - [MATHS P2 MEMO GR12 JUNE 2024 Afr+English](https://www.hlayiso.com/library/maths-p2-memo-gr12-june-2024-afr-english/4a5f997e-e38d-4abb-b726-8b72e6672832) — Memo · 2024 · Eng - [MATHS P2 MEMO GR12 SEPT 2024 Afr+English](https://www.hlayiso.com/library/maths-p2-memo-gr12-sept-2024-afr-english/37629bb0-a0ca-41e1-8c4d-1efde6df8237) — Memo · 2024 · Eng - [KZN Maths Grade 12 March 2024 QP and Memo](https://www.hlayiso.com/library/kzn-maths-grade-12-march-2024-qp-and-memo/49c516f7-1294-466c-8f55-9d573aae2c13) — QP + Memo · 2024 ## Collection - [Grade 12 past papers](https://www.hlayiso.com/grade-12/past-papers) --- Hlayiso: free CAPS and IEB past papers, memos, notes and study guides for South African learners. 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