Mathematics Grade 12 P2 NSC June 2025 Question Paper (Eng)

Confidential basic education ‘df Department: X Oy | Basic Education ‘424g REPUBLIC OF SOUTH AFRICA SENIOR CERTIFICATE EXAMINATIONS/ NATIONAL SENIOR CERTIFICATE EXAMINATIONS MATHEMATICS P2 MAY/JUNE 2025 ae ee ee a ie ae ee ee ee ee MARKS: 150 TIME: 3 hours This question paper consists of 13 pages and 1 information sheet. Copyright reserved Please turn over

Mathematics/P2 2 DBE/May/June 2025 SC/NSC Confidential 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 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

Mathematics/P2 3 DBE/May/June 2025 SC/NSC Confidential QUESTION 1 An insurance broker signed contracts with 15 people. The monthly premium (in rands) payable on each contract is given below. 134 | 215 | 325 | 326 | 362 | 429 | 515 | 531 | 598 | 610 | 624 | 728 | 923 | 1034 | 1200 1.1 Calculate the mean of the data. (2) 1.2 Write down the standard deviation of the data. (1) 1.3 Calculate how many monthly premiums are within ONE standard deviation of the mean. (2) 1.4 The insurance company decided to increase the monthly premiums. ¢ Monthly premiums that were less than R500 increased by 18% e Monthly premiums that were equal to or more than R500 increased by k% After these increases were applied to the above data, the new mean monthly premium was R686,44. Calculate the value of k. (4) 19] Copyright reserved Please turn over

Mathematics/P2 4 SC/NSC Confidential QUESTION 2 The manager of a supermarket decided to do a survey on the number of items that a customer ordered online and the time (in minutes) that a packer took to have the order ready for delivery. The supermarket received 10 online orders on a certain day. The information for these 10 orders is shown in the table below. DBE/May/June 2025 Number ofitems | ig | 3 | 20 | 14 | 17 | 9 | 12 | 18 | as | 19 Time (in minutes) (y) 5 5 9 7 6 6 8 11 10 12 2.1 Draw a scatter plot on the grid provided in the ANSWER BOOK. (3) 2.2 Determine the equation of the least squares regression line. (3) 2.3 Write down the correlation coefficient of the data. qd) 2.4 The supermarket received an online order for 13 items. Predict how long (in minutes) it will take a packer to pack the order and have it ready for delivery. (2) 2.5 Explain why the y-intercept of the least squares regression line in QUESTION 2.2 : does NOT make sense in this context. (1) [10] Copyright reserved Please turn over

Mathematics/P2 5 DBE/May/June 2025 SC/NSC Confidential QUESTION 3 In the diagram below, ASRT is drawn where R lies on the x-axis and S lies to the left of R. T lies on the y-axis and the coordinates of S are (m1). The equation of RT is 2x-y+10=0. y T Vv, Sqm ; 1) x R 0 . 3.1 Calculate the coordinates of R. (2) 3.2 Calculate the length of RT. Leave your answer in surd form. (3) 3.3 If it is also given that 2RT? =5SR’, calculate the value of m. (4) 3.4 It is further given that V lies on ST such that VR is perpendicular to ST. Determine the equation of VR in the form y= mx +c. (5) 3.5 Hence, show that the coordinates of V are (-8; 4). (2) 3.6 If R’ is the reflection of R about the line x =0, calculate the areaof RVTR’. (5) [21} Copyright reserved Please turn over

Mathematics/P2 6 DBE/May/June 2025 SC/NSC Confidential QUESTION 4 In the diagram, M is the centre of the circle having equation (x-3)? +y” =25. E(-1;3) and T are points on the circle. EC is a tangent to the circle at E and cuts the x-axis at D. ED = = units. MT is produced to meet the tangent at C(—7 ; p). y E(-1 ; 3) D fe} M io T C(-7 ; p) 4.1 Write down the size of CEM. (1) 4.2 Determine the equation of the tangent EC in the form y = mx +c. (4) 43 Calculate the length of DM. (3) 4.4 Show that p =—5 qd) 45 Calculate the coordinates of S if SEMC isa parallelogram and x, <0. (3) 4.6 If the radius of the circle, centred at M, is increased by 7 units, determine whether S lies inside or outside the new circle. Support your answer with the necessary calculations. (3) 47 If ET is drawn, calculate the size of ETM. 6) [20] Copyright reserved Please turn over

Mathematics/P2 7 DBE/May/June 2025 SC/NSC Confidential QUESTION 5 5.1 If cos@ = -< where 180° <6@< 360°, determine, without using a calculator, the value of: 5.1.1 sin? @ 5.1.2 tan(360°— 4) 5.1.3 cos(@-135°) 5.2 Simplify the expression to a single trigonometric term: ooo sO wanes) 1-2cos* (90° — x) 5.3 Calculate the value of the following expression without using a calculator: (tan 92°)(tan 94°)(tan 96°) ... (tan 176°)(tan 178°) QUESTION 6 61 Prove that 2cos?(45°+x)=1-sin2x. 6.2 Consider the expression: sin(A —B)-sin(A +B) 6.2.1 Prove that sin(A-—B)-sin(A +B) =—2cosAsinB. 6.2.2 Simplify the following expression to a single term: sin4x—sin10x 6.2.3 Hence, determine the solution for sin4x—sin10x=sin3x for x €[0°;30°]. Copyright reserved Please turn over (3) (2) (4) (6) (4) [19] (4) (2) (2) (5) [13]

Mathematics/P2 8 DBE/May/June 2025 SC/NSC Confidential QUESTION 7 In the diagram, the graphs of f(x)=2cosx+1 and g(x)=sin2x are drawn for the interval x €[-180°; 180°]. y & —180° 0 180° x f TA Write down the range of f/ qd) 7.2 Write down the period of g. (1) 73 For which values of x, in the interval x <[-180°;180°], is f increasing? qd) 7.4 Use the graphs to determine the values of x, in the interval x e[—180°;180°], for which: TAA g(x). f'(x) <0 (2) 1 74.2 cosxs “3 (3) 75 Graph g is shifted 45° to the right to obtain a new graph h. Determine the equation of f in its simplest form. (2) [10] Copyright reserved Please turn over

Mathematics/P2 9 SC/NSC Confidential QUESTION 8 DBE/May/June 2025 In the diagram, A, B and C lie in the same horizontal plane with AB = AC. D is directly above A such that 2AD=BC. Also, AD=p, ABC=x and DBA= ye B 8.1 Determine AB interms of p and y. 8.2 Show that cos x = tan y. 8.3 If x = 60°, calculate the size of y. Copyright reserved Please turn over 2) (4) (2) [8]

Mathematics/P2 10 DBE/May/June 2025 SC/NSC Confidential Provide reasons for your statements in QUESTIONS 9 and 10. QUESTION 9 91 In the diagram, ADEF is drawn. Line GH intersects DF and EF at G and H respectively such that GH || DE and = = : D G E H F 9.1.1 Write down, with a reason, the value of = (2) 9.1.2 If EF = 21 cm, calculate the length of EH. (2) 9.1.3 Write down a triangle which is similar to AFGH. (1) GH 9.1.4 Hence, calculate the value of DE. (2) Copyright reserved Please turn over

Mathematics/P2 il DBE/May/June 2025 SC/NSC Confidential 9.2 In the diagram, POL is a diameter of the larger circle with centre O. TMR .is a diameter of the smaller circle with centre M. The two circles intersect at L and R. PLK isa tangent to the smaller circle at L and TR is a tangent to the larger circle at R. OM intersects the smaller circle at N. Straight lines LT, LR, LN and PR are drawn. Prove, giving reasons, that: 9.2.1 LT||PR (4) 9.2.2 LORM isa cyclic quadrilateral, if it is also given that LT {| OM (5) 9.2.3 LN bisects OLR (4) [20] Copyright reserved Please turn over

12 DBE/May/June 2025 Mathematics/P2 SC/NSC Confidential QUESTION 10 10.1 In the diagram, AABC and APKL are drawn such that A=P, B=K and C= L. A P K L a ° B Cc Use the diagram in the ANSWER BOOK to prove the theorem which states that if two triangles are equiangular, then the corresponding sides are in proportion, AB_ AC ie. that — =—_. PK PL (6) Copyright reserved Please turn over

Mathematics/P2 13 DBE/May/June 2025 SC/NSC Confidential 10.2 In the diagram, O is the centre of the circle. Points D and B lie on the circle. Points A and C_ lie outside the circle such that side AC of AADC passes through B. F isa point on BC such that FO ||BD. DR=RB and RO is drawn. 10.2.1 Prove, with reasons, that ACFO ||| ACBD. (3) 10.2.2 If it is given that RDO =FCO, show, with reasons, that OF.CD = CO.BC (2) : : : : RO 3 10.2.3 It is further given that DC = 19,2 units, BD = 12 units and RD = a Prove, with reasons, that BF = B 16 (6) 10.2.4 Calculate the size of ABD. (3) [20] TOTAL: 150 Copyright reserved

Mathematics/P2 DBE/May/June 2025 SC/NSC Confidential INFORMATION SHEET: MATHEMATICS _ —b+ 1b’ —4ac x 2a A=P(1+ni) A =P(1—ni) A=P(1-i)" A=P(l+i)” T, =a+(n-Nd S, = Fa +(n-1a] T, =ar"" 3, -2C Dea S$, =-—+;-I<r<l r-1 l-r pals)" -1 p_al-a+)" i i 11) = fin LOAD =SO) x +X, Wty. d= (x) -%, +0.-n) m{ 5 2 in) y=mxte y-y, =m(x-%x,) m= 22 * m=tan@ 2 %y (x-a)? +(y—by =r? In AABC: a ns sn A sinB sinc a =b’ +c” —2becosA area AABC = 5absin Cc sin(a + 8) =sinacos f +cosasin 8 sin(a — f) = sina cos 8 — cosa sin B cos(a + 8) = cosa cos # —sinasin B cos(a — 8) = cosa cos $+ sinasin B cos’ @ sin? a cos2a=4 1-2sin’a sin 2a = 2sinacosa 2cos’ a1 Sx S6-9 y= i=l o = i=l n n _ nA) _ _ (= 75) P(A or B) = P(A) + P(B)- P(A and B) n peatbx p= e239) ¥ (x-x/ Copyright reserved