# Mathematics Grade 12 P2 NSC November 2022 QP (Eng) > Grade 12 Mathematics Paper 2 question paper from the NSC November Exam 2022 (English), 14 pages. Read online or download the free PDF. - Page: https://www.hlayiso.com/library/mathematics-p2-nov-2022-eng/6d1dd83b-ef32-47e7-b7b9-f12940ca2cd6 - Updated: 2026-09-27 - Subject: Mathematics - Grade: Grade 12 - Document type: Question paper - Year: 2022 - Exam period: NSC November 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 NSC November 2022 QP (Eng)](https://www.hlayiso.com/library/mathematics-p2-nov-2022-eng/6d1dd83b-ef32-47e7-b7b9-f12940ca2cd6) ## About this document Mathematics · Grade 12 · NSC November Exam · 2022. Question paper, 14 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 Downloaded from hlayiso.com ey 7 =e basic education WWE. (y (a Department: iG) Basic Education REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE GRADE 12 MATHEMATICS P2 " it au " NOVEMBER 2022 " ay y Pee CCC CCC CCC CeCe CeCe eee errr rrr errr ee ee eee eee ee MARKS: 150 TIME: 3 hours This question paper consists of 13 pages and 1 information sheet. Copyright reserved Please turn over ### Page 2 Downloaded from hlayiso.com Mathematics/P2 , 2 ‘DBE/November 2022 NSC INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1, 2. This question paper consists of 10 questions. Answer ALL the questions in the SPECIAL ANSWER BOOK provided. Clearly show ALL calculations, diagrams, graphs, etc. which you have used in determining your answers. Answers only will NOT necessarily be awarded full marks. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. If necessary, round off answers correct to TWO decimal places, unless stated otherwise. Diagrams are NOT necessarily drawn to scale. An information sheet with formulae is included at the end of the question paper. Write neatly and legibly. Copyright reserved Please turn over ### Page 3 Downloaded from hlayiso.com Mathematics/P2~ 3 DBE/November 2022 NSC QUESTION 1 The matric class of a certain high school had to vote for the chairperson of the RCL (representative council of learners). The scatter plot below shows the IQ (intelligence quotient) of the 10 learners who received the most votes and the number of votes that they received. SCATTER PLOT 2? ES : 2 2 S 20 > tS © 15 5 2 e 10 z5 r = ——- = = = es ee Ce ae a 98 103 108 113 118 123 Intelligence quotient (IQ) Before the election, the popularity of each of these ten learners was established and a popularity score (out of a 100) was assigned to each. The popularity scores and the number of votes of the same 10 learners who received the most votes are shown in the table below. Popularity score (x) 32 89 35 82 50 59 81 40 79 65 Number of votes (y) 9 22 10 21 ll 15 20 12 19 16 1.1 Calculate the: 1.1.1 Mean number of votes that these 10 learners received (2) 1.1.2 Standard deviation of the number of votes that these 10 learners received Q) 1.2 The learners who received fewer votes than one standard deviation below the mean were not invited for an interview. How many learners were invited? (2) 1.3 Determine the equation. of the least squares regression line for the data given in the table. @) 1.4 Predict the number of votes that a learner with a popularity score of 72 will receive. (2) 1.5 Using the scatter plot and table above, provide a reason why: 1.5.1 IQ is not a good indicator of the number of votes that a learner could receive qd) 1.5.2. The prediction in QUESTION 1.4 is reliable qd) {12] Copyright reserved Please turn over ### Page 4 Downloaded from hlayiso.com Mathematics/P2 4 . DBE/November 2022 NSC QUESTION 2 A company conducted research among all its employees on what percentage of their monthly salary was spent on fuel in a particular month. The data is represented in the ogive (cumulative frequency graph) below. 2.1 2.2 2.3 2.4 2.5 OGIVE 70 60 50 40 30 20 Cumulative frequency 10 Percentage of salary spent on fuel How many people are employed at this company? Write down the modal class of the data. How many employees spent more than 22,5% of their monthly salary on fuel? An employee spent R2 400 of his salary on fuel in that particular month. Determine the monthly salary of this employee if he spends 7% of his salary on fuel. The monthly salaries of these employees remains constant and the number of litres of fuel used in each month also remains constant. If the fuel price iricreases from R21,43 per litre to R22,79 per litre at the beginning of the next month, how will the above ogive change? Copyright reserved Please turn over a) a) Q) (2) (2) 3] ### Page 5 Downloaded from hlayiso.com Mathematics/P2 5 DBE/November 2022 NSC QUESTION 3 In the diagram, A(4; 2), B(6;-4) and C(—2; -3) are vertices of AABC. T is the midpoint of CB. The equation of line AC is 5x—6y=8. The angle of inclination of AB is a. ADCT is drawn such that CD || BA. The lines AC and DT intersect at S, the y-intercept of AC. P, F and R are the x-intercepts of DC, AC and AB respectively. D y A(4 ; 2) a P x C2 ;-3) BE ; -4) 3.1 Calculate the: 3.1.1. Gradient of AB (2) 3.1.2 Size of a (2) 3.1.3. Coordinates of T (2) 3.1.4 Coordinates of S (2) 3.2 Determine the equation of CD inthe form y=mx+e. (3) 3.3 Calculate the: 3.3.1 Size of DCA @) 3.3.2 Area of POSC (5) [20] Copyright reserved Please turn over ### Page 6 Downloaded from hlayiso.com Mathematics/P2 6 DBE/November 2022 , NSC QUESTION 4 In the diagram, M(3 ; —5) is the centre of the circle having PN as its diameter. KL is a tangent to the circle at N(7 ; --2). y K x P 41 Calculate the coordinates of P. (2) 4.2 Determine the equation of: 4.2.1 The circle in the form (x—a@)? +(y~b)? =7? (3) 4.2.2 KL inthe form y=mx+c (5) 4.3 For which values of & will y= -x +k bea secant to the circle? (4) 44 Points A(t; 7) and B are not shown on the diagram. From point A, another tangent is drawn to touch the circle with centre M at B. 4.4.1 Show that the length of tangent AB is givenby V2t?+4¢+9. (2) 4.4.2 Determine the minimum length of AB. (4) [20] Copyright reserved Please turn over ### Page 7 Downloaded from hlayiso.com Mathematics/P2 7 DBE/November 2022 NSC QUESTION 5 5.1 Given that 13 sinx +3 =0, where x €(90° ; 270°). 5.2 5.3 5.4 3.5 Without using a calculator, determine the value of: $1.1 sin(360°+ x) (2) 5.1.2 tanx 3) 5.1.3. cos(180°+ x) 2) Determine the value of the following expression, without using a calculator: cos(90° + 6) 5 sin(@ - 180°) +3 sin(-0) 6) Determine the general solution of the following equation: (cosx + 2sin x)(3sin2x-1)=0 (6) Given the identity: cos(x + y).cos(x — y) =1-sin? x—sin? y 5.4.1 Prove the identity. (4) 5.4.2 Hence, determine the value of 1-sin? 45°—sin?15°, without using a calculator. @) Consider the trigonometric expression: 16sin x.cos* x —8sin x.cosx 5.5.1 Rewrite the expression as a single trigonometric ratio. (4) 5.5.2 For which value of x in the interval x €[0°; 90°] will 16sin x.cos’ x—8sinx.cosx have its minimum value? qd) [30] Copyright reserved Please turn over ### Page 8 Downloaded from hlayiso.com Mathematics/P2 8 DBE/November 2022 NSC QUESTION 6 In the diagram below, the graphs of f(x)=tanx and g(x)=2sin2x are drawn for the interval x €[—180° ; 180°] A(60°; 4) and B are two points of intersection of f and g. g& —180° —908 0° * 6.1 Write down the period of g. qd) 6.2 Calculate the: 6.2.1 Value of k qd) 6.2.2 Coordinates of B qd) 63 Write down the range of 2g(x). 2) 6.4 For which values of x will g(x+5°)—f(x+5°)<0 in the interval x €[-90° ; 0°]? (2) 6.5 Determine the values of p for which sinx.cosx=p will have exactly two real roots in the interval x e€[-180° ; 180°]. @G) [10] Copyright reserved Please turn over ### Page 9 Downloaded from hlayiso.com Mathematics/P2 9 DBE/November 2022 NSC QUESTION 7 AB isa vertical flagpole that is V5, p metres long. AC and AD are two cables anchoring the flagpole. B, C and D are in the same horizontal plane. BD = 2p metres, ACD=x and ADC =45°. A TA Determine the length of AD in terms of p. (2) 7.2 Show that the length of CD = 3p(sinx + cosx) . (5) V2sinx 73 If it is further given that p= 10 and x = 110°, calculate the area of AADC. (3) [10] Copyright reserved Please turn over ### Page 10 Downloaded from hlayiso.com 10 * DBE/November 2022 Mathematics/P2 NSC QUESTION 8 8.1 In the diagram, O is the centre of the circle. MNPR is a cyclic quadrilateral and SN is a diameter of the circle. Chord MS and radius OR are drawn. M, =64. Determine, giving reasons, the size of the following angles: 81.1 Pp (2) 8.1.2 M, (2) 8.13 6, (2) Please turn over Copyright reserved ### Page 11 Downloaded from hlayiso.com Mathematics/P2 ll . DBE/November 2022 NSC 8.2 In the diagram, AABG is drawn. D and E are midpoints of AB and AG respectively. AG and BG are produced to C and H respectively. F is a point on BC such that FG || CH. 8.2.1 Give areason why DE || BH. (1) 8.2.2 If it is further given that oe =i: DE =3x-—1 and GH=x+1, calculate, giving reasons, the value of x. (6) [13] Copyright reserved Please turn over ### Page 12 Downloaded from hlayiso.com Mathematics/P2_ 12 . DBE/November 2022 NSC QUESTION 9 9.1 In the diagram, O is the centre of a circle. OD bisects chord AB. Prove the theorem that states that the line from the centre of a circle that bisects a chord is perpendicular to the chord, i.e. OD L AB. (5) 92 In the diagram, E, B, F, S and P are points on the circle centred at O. GB isa tangent to the circle at B. FE is produced to meet the tangent at G. OT is drawn such that T is the midpoint of EF. GO and BO are drawn. BS is drawn through T. PS || GF. Prove, giving reasons, that: 9.2.1 OTBG isa cyclic quadrilateral (5) 9.2.2 GOB=§ @) [14] Copyright reserved Please turn over ### Page 13 Downloaded from hlayiso.com Mathematics/P2 QUESTION 10 In the diagram, PQRS is a cyclic quadrilateral. KP is a tangent to the circle at P. C and D are points on chords PQ and PS respectively and CD produced meets RS produced at A. CA||QS. RC isdrawn. P, =R,. DBE/November 2022 Prove, giving reasons, that: 10.1 S=T AD _ AS 10.2 AR AG 10.3 AC x SD= AR x TC Copyright reserved TOTAL: @4) G) 4) [13] 150 ### Page 14 Downloaded from hlayiso.com Mathematics/P2 . DBE/November 2022 , NSC INFORMATION SHEET yoo tve’ -4ac 2a A= P(1+ni) A= P(I-ni) A=P(\-i" A=P(+i)" T, =a+(n-Nd 8, =5Pa+(n—1d] T, =ar"" g ae al sre#l S,= aos _ierel ” r- l-r pazilti =1 P xil-(1+i)" q i _ f(xth)— fe) 1 =| PO + + d=, X—%) +0, yy u[ 2222) y=mxt+ce yy, =m(x—x) m=22 m=tan@ x2 ~X (x-al +(y-4f =P? In AdBC: 2-28 _ sind sinB sinC a’ =b’ +¢? —2be.cos A area AABC = ab.sinC sin(a+ f) =sin a.cos 8+cosa.sinZ sin(a—f) =sina.cos B—cosa@.sinf cos(a+ ) = cos a.cos f—sina.sin# cos(a— f)=cosa.cos f+sina.sinB cos’ asin’ & cos2a =41—2sin’ a sin 2a = 2sina.cosa 2cos* a —1 (x, - x)? n n n(A) = P(A) 6) P(A or B) = P(A) + P(B) — P(A and B) n (x-3)-9) y=ath b= Le-xy-y) yeare Yi(e-x) Copyright reserved ## Related documents - [Mathematics P2 Nov 2022 Answer Book Eng Afr](https://www.hlayiso.com/library/mathematics-p2-nov-2022-answer-book-eng-afr/59f5f409-6bc6-455e-ba28-da6a96e11a91) — Mathematics · Addendum · 2022 · Eng - [MATHS P2 QP GR12 JUNE 2022 Afrikaans](https://www.hlayiso.com/library/maths-p2-qp-gr12-june-2022-afrikaans/49feb536-3d0c-4e63-b857-c88def50a8c1) — Mathematics · QP · 2022 · Afr - [Mathematics P2 Nov 2023 Eng](https://www.hlayiso.com/library/mathematics-p2-nov-2023-eng/40715b6b-8bd6-423b-a1f5-07e7c1d1efa3) — Mathematics · QP · 2023 · 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 - [Mathematics P2 Nov 2013 Eng](https://www.hlayiso.com/library/mathematics-p2-nov-2013-eng/4eca21de-3399-46c7-be27-80cd5e3a59a2) — Mathematics · QP · 2013 · Eng - [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 ## More from Grade 12 Mathematics - [MATHS P1 ANSWER BOOK GR12 SEPT 2025 English Afrikaans watermark](https://www.hlayiso.com/library/maths-p1-answer-book-gr12-sept-2025-english-afrikaans-watermark/d78c3fd3-dcd5-4f3f-911b-e5635b4686cc) — Addendum · 2025 · Afr - [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 P1 GR 12 MEMO SEPT 2024 English+Afrikaans](https://www.hlayiso.com/library/maths-p1-gr-12-memo-sept-2024-english-afrikaans/f0eedb8f-ec6f-4f46-9885-3933cd274781) — Memo · 2024 · Afr ## 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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