# Mathematics Grade 12 P2 North West June 2024 QP (Eng) > Grade 12 Mathematics Paper 2 question paper from the North West June Exam 2024 (English), 12 pages. Read online or download the free PDF. - Page: https://www.hlayiso.com/library/grade-12-mathematics-2024-north-west-june-exam-question-paper-paper-2-english/818b00d0-8464-41b2-a280-ab7cd3c24071 - Updated: 2026-09-28 - Subject: Mathematics - Grade: Grade 12 - Language: English - Document type: Question paper - Year: 2024 - Exam period: North West June Exam - Paper: 2 - Curriculum: CAPS - Pages: 12 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 North West June 2024 QP (Eng)](https://www.hlayiso.com/library/grade-12-mathematics-2024-north-west-june-exam-question-paper-paper-2-english/818b00d0-8464-41b2-a280-ab7cd3c24071) ## About this document Mathematics · Grade 12 · North West June Exam · 2024 · English. Question paper, 12 pages. Read online or download the PDF. Read it free online on the page above; download the PDF from there. ## Document text Text extracted from the PDF. Layout, diagrams and tables may not survive extraction. ### Page 1 PROVINCIAL ASSESSMENT GRADE 12 MATHEMATICS P2 JUNE 2024 MARKS: 150 TIME: 3 hours This question paper consists of 11 pages, 1 information sheet and an answer book of 21 pages. Copyright reserved Please turn over ### Page 2 Mathematics/P2 2 NW/June 2024 Grade 12 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of 9 questions. 2. Answer ALL the questions. 3. Write ALL the answers in the ANSWER BOOK provided. 4. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining the answers. 5. Answers only will NOT necessarily be awarded full marks. 6. You may use an approved scientific calculator (non-programmable and non- graphical), unless stated otherwise. 7. If necessary, answers should be rounded off to TWO decimal places, unless stated otherwise. 8. Diagrams are NOT necessarily drawn to scale. 9. Number the answers correctly according to the numbering system used in this question paper. 10. An information sheet with formulae is included at the end of the question paper. 11. Write neatly and legibly. Copyright reserved Please turn over ### Page 3 Mathematics/P2 3 NW/June 2024 Grade 12 QUESTION 1 In the figure below, A ( – 2; – 6), B(3; 6), C(9; 5) and D are joined to from a kite. y B (3; 6) C (9; 5) E x D A (– 2; – 6 ) 1.1 Calculate the length of AC and give your answer in simplest surd form. (2) 1.2 Calculate the gradient of AC. (2) 1.3 Determine the equation of AC. (2) 1.4 Give a reason why AE  BD. (1) 1.5 Determine the equation of BD. (3) 1.6 Determine the coordinates of E. (3) 1.7 Determine, with reasons, the coordinates of D. (3) 1.8 Calculate the size of AD̂C . (5) [21] Copyright reserved Please turn over ### Page 4 Mathematics/P2 4 NW/June 2024 Grade 12 QUESTION 2 In the diagram, the circle is centred at M (2; 2). Radius KM is produced to L, a point outside the circle, such that KML || y-axis. LTP is a tangent to the circle at T (–2; b). S  6 ;  4  is the midpoint of PK. 2.1 Given that the radius of the circle is 5 units, show that b = 5. (4) 2.2 Determine: 2.2.1 The coordinates of K. (2) 2.2.2 The equation of the tangent LTP in the form y  mx  c . (4) 2.2.3 The area of Δ LPK. (7) Another circle with equation ( x  2)  ( y  n)  25 is drawn. Determine, with 2.3 2 2 an explanation, the value(s) of n for which the two circles will touch each other externally. (4) [21] Copyright reserved Please turn over ### Page 5 Mathematics/P2 5 NW/June 2024 Grade 12 QUESTION 3 3.1 Simplify the expression below to a single trigonometric ratio: cos(90  x).sin( 540   x) (6) tan( x  180  ). cos( x) 3.2 Given cos(P  Q)  cosP.cosQ sinP.sinQ Use the above identity and express cos 2P in terms of cos P. (4) 4 3.3 If tan A  , where A  [90 ;360 ] 3 Use a sketch to determine the following: 3.3.1 sin A (3) 3.3.2 cos(A  30  ) (4) Given: cos12  p . With the aid of the diagram, determine the following without  3.4 using a calculator, in terms of p. 3.4.1 sin 78  (2) 3.4.2 sin 6  (4) [23] QUESTION 4 sin 2 x  cos 2 x  1 4.1 Prove that:  tan x (7) sin 2 x  cos 2 x  1 4.2 Hence, or otherwise, determine the value of tan 22,5 , without using the calculator. (Leave your answer in SURD form). (3) 4.3 Determine the general solution of the equation: 3 cos 2x  1  5 cos x . (7) [17] Copyright reserved Please turn over ### Page 6 Mathematics/P2 6 NW/June 2024 Grade 12 QUESTION 5 The sketch below, shows the graphs of f ( x)  a sin x and g ( x)  sin x  b , for x  [360  ;360  ]. Use the given graphs to answer the following questions: 5.1 Write down the values of a and b. (2) 5.2 What is the amplitude of g? (1) 5.3 Determine the value(s) of x, where x  [360 ;360 ] , for which:   5.3.1 f ( x)  g ( x) . (2) 5.3.2 f / ( x).g ( x)  0 . (3) 5.3.3 g decreases as x is increases. (2) [10] Copyright reserved Please turn over ### Page 7 Mathematics/P2 7 NW/June 2024 Grade 12 QUESTION 6 In the diagram below, a pole LY is placed at the corner of a triangular field XYZ. The area of the field is A m2 . XŶZ  2 , YẐL   and XY = p metres. LY = h metres and YZ = r metres and XZ = t metres 6.1 Determine, A, the area of ΔXYZ in terms of r, p and  . (1) 6.2 Express r in terms of A, p and  . (2) 6.3 Hence, show that the height of the pole, h, is given by: A h p cos2  (5) 6.4 If h = 20m, p = 10m and   60 .  Determine: 6.4.1 A, the area of ΔXYZ. (2) 6.4.2 The length of t correct to 2 decimal places (4) [14] Copyright reserved Please turn over ### Page 8 Mathematics/P2 8 NW/June 2024 Grade 12 QUESTION 7 7.1 In the diagram below, O is the centre of the circle. P, Q, S and R, are points on the circumference of the circle. PQ = QS and PQ̂S  130  . R O 2 1 2 P 1 2 1 S 1300 Q Determine, giving reasons, the sizes of: 7.1.1 Ŝ1 (3) 7.1.2 R̂ (2) 7.1.3 Ô1 (3) Copyright reserved Please turn over ### Page 9 Mathematics/P2 9 NW/June 2024 Grade 12 7.2 In the diagram below, O is the centre of the circle. AB is perpendicular to diameter DC. CM: MD = 2 : 7 and AB = 14 units. If CM = 2x: 7.2.1 Express DC in terms of x. (1) 7.2.2 Express OM in terms of x. (2) 7.2.3 Hence, or otherwise, calculate the length of the radius. (5) [16] Copyright reserved Please turn over ### Page 10 Mathematics/P2 10 NW/June 2024 Grade 12 QUESTION 8 8.1 In the diagram below,  MNC is drawn. A is a point on MN and B is a point on MC such that AB || NC. AC and NC are drawn. M A > B N > C Use the diagram to prove the theorem which states that: MA MB (7)  AN BC 8.2 The figure below shows  ABC with BC produced to D. RD is drawn with point T on AC and R on BA. CS is drawn. TC = 9 cm, AT = 27 cm, AR = 60 cm and AS = 80 cm. 8.2.1 Prove that SC || RT (3) 8.2.2 Determine the length of RS (1) 8.2.3 If AR : RB = 2 : 3 and BC = 30 cm, calculate the length of CD. (5) [16] Copyright reserved Please turn over ### Page 11 Mathematics/P2 11 NW/June 2024 Grade 12 QUESTION 9 In the figure below, KL is a tangent to the circle. L, J and R are points on the circle and MN is parallel to KL. J 1 2 M 3 T 1 2 N 1 2 3 R 1 1 2 2 K V L Prove that: 9.1 JMRN is a cyclic quadrilateral. (3) 9.2 ΔJNR ||| ΔLMK (3) 9.3 NL.JT LM.NR  (6) TV MK [12] TOTAL : 150 Copyright reserved ### Page 12 Mathematics/P2 NW/June 2024 Grade 12 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 Tn  a  (n  1)d Sn  n 2a  (n  1)d  2 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  y1 y  mx  c y  y1  m( x  x1 ) m 2 m  tan  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 sin A sin B sin C 1 area ABC  ab. sin C 2 sin      sin  . cos   cos  . sin  sin      sin  . cos   cos  . sin  cos      cos  . cos   sin  . sin  cos      cos  . cos   sin  . sin  cos2   sin 2   cos 2  1  2 sin 2  sin 2  2 sin  . cos 2 cos2   1  n 2  fx  x  x  i x   i 1 2 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 ## Related documents - [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) — Mathematics · 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) — Mathematics · 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) — Mathematics · Memo · 2024 · 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 - [Mathematics P2 English November 2014(amended)](https://www.hlayiso.com/library/mathematics-p2-english-november-2014-amended/aea5827e-f832-419b-a9da-32ae8428f67c) — Mathematics · QP · 2014 · 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 - [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 - [KZN GR 12 MATHS P2 SEPT 2024](https://www.hlayiso.com/library/kzn-gr-12-maths-p2-sept-2024/6db62b2f-3c0b-4c51-8d6b-e875f4b5d67a) — QP · 2024 - [LP Maths Grade 12 June 2024 P2 and Memo](https://www.hlayiso.com/library/lp-maths-grade-12-june-2024-p2-and-memo/ae975968-03fb-478d-83f9-e424fe245c15) — Memo · 2024 - [Limpopo Mathematics P1 Sept 2024 Grade 12](https://www.hlayiso.com/library/limpopo-mathematics-p1-sept-2024-grade-12/46a0450b-f1ea-4b00-b93e-f64991cd70c2) — QP · 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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