Mathematics Grade 11 P2 November Mock Exam 2 2026 QP (Eng)

Mock hlayiso mock exams Practice Series: Grade 11 Exam Preparation WWW.HLAYISO.COM NATIONAL SENIOR CERTIFICATE GRADE 11 MATHEMATICS P2 NOVEMBER EXAMINATION 2026 (MOCK) MARKS: 150 TIME: 3 hours This question paper consists of 10 pages, 1 information sheet and 2 answer sheets. Copyright reserved Please turn over

Mathematics/P2 2 Hlayiso/Mock 2026 NSC Mock INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of 12 questions. 2. Answer ALL the questions. 3. Number the answers correctly according to the numbering system used in this question paper. 4. Clearly show ALL calculations, diagrams, graphs, etc. that you have used in determining your 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, round off answers to TWO decimal places, unless stated otherwise. 8. Diagrams are NOT necessarily drawn to scale. 9. ANSWER SHEETS for QUESTIONS 2.1, 2.2 and 7.1 are attached at the end of this question paper. Write your name on the answer sheets and hand them in together with your ANSWER BOOK. 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

Mathematics/P2 3 Hlayiso/Mock 2026 NSC Mock QUESTION 1 The number of books borrowed from a community library on 10 Saturdays is given below. 38 45 52 41 60 47 55 43 49 70 1.1 Calculate the mean number of books borrowed per Saturday. (2) 1.2 Calculate the standard deviation of the data. (1) 1.3 On what percentage of the Saturdays was the number of books borrowed more than ONE standard deviation above the mean? (2) 1.4 Determine the median and the interquartile range of the data. (3) 1.5 The library recorded the number of books borrowed on two more Saturdays: x books on the first and (x + 12) books on the second. The mean for all 12 Saturdays is 52 books. Calculate the value of x. (3) [11] QUESTION 2 A traffic officer recorded the speeds (in km/h) of 100 vehicles that passed a speed camera on a road near a school. The results are shown in the table below. SPEED, v (IN KM/H) NUMBER OF VEHICLES CUMULATIVE FREQUENCY 40 ≤ v < 50 6 50 ≤ v < 60 14 60 ≤ v < 70 28 70 ≤ v < 80 30 80 ≤ v < 90 15 90 ≤ v < 100 7 2.1 Complete the cumulative frequency column in the table on the ANSWER SHEET provided. (2) 2.2 Draw an ogive (cumulative frequency graph) of the data on the grid provided on the ANSWER SHEET. (3) 2.3 Write down the modal class of the data. (1) 2.4 Use the ogive to estimate the number of vehicles that travelled faster than 75 km/h. (2) 2.5 Use the ogive to estimate the interquartile range of the speeds. (2) [10] Copyright reserved Please turn over

Mathematics/P2 4 Hlayiso/Mock 2026 NSC Mock QUESTION 3 In the diagram, P(−4 ; −2), Q(6 ; 3) and R(0 ; 5) are the vertices of △PQR. S is a point on PQ such that RS ⊥ PQ. y R(0 ; 5) Q(6 ; 3) S x O P(−4 ; −2) 3.1 Show that the equation of PQ is y = 12 x. (3) 3.2 Determine the equation of RS. (2) 3.3 Determine the coordinates of S. (3) 3.4 Calculate the area of △PQR. (4) 3.5 Calculate the size of PQ̂R. (4) [16] Copyright reserved Please turn over

Mathematics/P2 5 Hlayiso/Mock 2026 NSC Mock QUESTION 4 In the diagram, A(−2 ; 1), B(3 ; −4), C(4 ; 3) and D are the vertices of parallelogram ABCD. The diagonals AC and BD intersect at M. DC produced meets the x-axis at E. y D C(4 ; 3) M A(−2 ; 1) x O E B(3 ; −4) 4.1 Determine the coordinates of M. (2) 4.2 Determine the coordinates of D. (2) 4.3 Prove that ABCD is a rhombus. (3) 4.4 Determine the coordinates of E. (3) 4.5 AE is drawn. Calculate the size of AÊC. (4) [14] Copyright reserved Please turn over

Mathematics/P2 6 Hlayiso/Mock 2026 NSC Mock QUESTION 5 5.1 Given: 12 tan A + 5 = 0 and sin A < 0 WITHOUT using a calculator and with the aid of a diagram, determine the value of: 5.1.1 cos A (2) 5.1.2 sin(180◦ + A) . cos(−A) (3) 5.2 If cos 32◦ = k, express the following in terms of k WITHOUT using a calculator: 5.2.1 sin 302◦ (2) 5.2.2 tan 212◦ (2) sin(180◦ + x) . cos(90◦ − x) 5.3 Simplify fully: (5) cos(−x) . tan(180◦ + x) 5.4 Determine the value of the following expression WITHOUT using a calculator: sin 150◦ . tan 225◦ (3) cos 240◦ 1 1 5.5 Prove the identity: tan x + = (3) tan x sin x . cos x [20] QUESTION 6 6.1 Determine the general solution of: 2 cos2 x − 5 sin x + 1 = 0 (6) 6.2 Solve for x if 4 sin x = 3 cos x and x ∈ [−180◦ ; 180◦ ]. (4) [10] QUESTION 7 Given: f (x) = cos(x − 60◦ ) and g(x) = − sin x for x ∈ [−180◦ ; 180◦ ] 7.1 Sketch the graphs of f and g on the same system of axes on the grid provided on the ANSWER SHEET. Clearly show ALL intercepts with the axes, the coordinates of the turning points and the end points of each graph. (6) 7.2 The graphs of f and g intersect at x = −15◦ and x = 165◦ . Use your graphs to determine the values of x for which g(x) − f (x) > 0. (2) 7.3 The graph of f is reflected in the x-axis and then translated 1 unit upwards to form the graph of h. Write down the equation of h. (2) 7.4 Write down the minimum value of 2 f (x) − 1. (1) [11] Copyright reserved Please turn over

Mathematics/P2 7 Hlayiso/Mock 2026 NSC Mock QUESTION 8 A vertical cellphone mast AC stands at point C on level ground. B and D are points on the ground in a straight line with C, with D between B and C. BD = x metres. The angle of elevation of A from B is α and the angle of elevation of A from D is β . A α β B x D C 8.1 Write down the size of BÂD in terms of α and β . (1) x sin α 8.2 Prove that AD = (3) sin(β − α ) x sin α . sin β 8.3 Hence, show that the height of the mast is AC = (2) sin(β − α ) 8.4 Calculate the height of the mast if x = 40 m, α = 32◦ and β = 51◦ . (3) [9] QUESTION 9 A gas storage tank is made up of a cylinder with a hemisphere at each end, as shown in the diagram. The radius of the cylinder and of each hemisphere is 0,5 m. The length of the cylindrical part is h metres. The tank must hold exactly 2,5 m3 of gas. 0,5 m Volume of a cylinder = π r2 h Volume of a sphere = 43 π r3 Curved surface area of a cylinder = 2π rh h Surface area of a sphere = 4π r2 9.1 Calculate h, the length of the cylindrical part of the tank. (4) 9.2 The outside of the tank will be painted. Calculate the outer surface area of the tank. (3) [7] Copyright reserved Please turn over

Mathematics/P2 8 Hlayiso/Mock 2026 NSC Mock Give reasons for your statements in QUESTIONS 10, 11 and 12. QUESTION 10 10.1 In the diagram, O is the centre of the circle and ABCD is a cyclic quadrilateral. A D O B C Use the diagram to prove the theorem which states that the opposite angles of a cyclic quadrilateral are supplementary, that is, prove that  + Ĉ = 180◦ . (5) 10.2 In the diagram, O is the centre of the circle and AB is a diameter. C and D are points on the circle such that AD = DC. AC, BC, AD, DC and OD are drawn. BÂC = 34◦ . C D 34◦ A B O Calculate, with reasons, the size of: 10.2.1 AĈB (2) 10.2.2 AD̂C (2) 10.2.3 DÂC (2) 10.2.4 Prove that OD ∥ BC. (3) [14] Copyright reserved Please turn over

Mathematics/P2 9 Hlayiso/Mock 2026 NSC Mock QUESTION 11 11.1 In the diagram, O is the centre of the circle. AB and CD are parallel chords on opposite sides of O. AB = 16 units, CD = 30 units and the radius of the circle is 17 units. OM ⊥ AB and ON ⊥ CD, with M on AB and N on CD. N C D O A B M 11.1.1 Write down, with a reason, the length of AM. (2) 11.1.2 Calculate the length of MN. (4) 11.2 In the diagram, O is the centre of the circle. PA and PB are tangents to the circle at A and B. C is a point on the major arc AB. AB, AC, BC, OA and OB are drawn. P̂ = 48◦ . C O B A 48◦ P Calculate, with reasons, the size of: 11.2.1 PÂB (2) 11.2.2 AĈB (2) 11.2.3 AÔB (2) 11.2.4 OÂB (2) 11.3 Prove that PAOB is a cyclic quadrilateral. (2) [16] Copyright reserved Please turn over

Mathematics/P2 10 Hlayiso/Mock 2026 NSC Mock QUESTION 12 In the diagram, P, Q, R and S are points on the circle. TPV is a tangent to the circle at P and chord QS ∥ TV. PR intersects QS at K. TP̂Q = x. T P V x K Q S R 12.1 Prove that PQ = PS. (4) 12.2 Prove that RP bisects QR̂S. (3) 12.3 Prove that PQ is a tangent to the circle that passes through Q, K and R. (3) 12.4 Show that QP̂S = 180◦ − 2x. (2) [12] TOTAL: 150 Copyright reserved Please turn over

Mathematics/P2 11 Hlayiso/Mock 2026 NSC Mock INFORMATION SHEET: MATHEMATICS GRADE 11 √ −b ± b2 − 4ac x= 2a A = P(1 + ni) A = P(1 − ni) A = P(1 − i)n A = P(1 + i)n √ ( ) x 1 + x2 y 1 + y2 d = (x2 − x1 )2 + (y2 − y1 )2 M ; 2 2 y2 − y1 y = mx + c y − y1 = m(x − x1 ) m= m = tan θ x2 − x1 a b c In △ABC : = = sin A sin B sinC a2 = b2 + c2 − 2bc. cos A area △ABC = 12 ab. sinC 2 ∑x ∑ni=1 (xi − x̄) x̄ = σ2 = n n n(A) P(A) = P(A or B) = P(A) + P(B) − P(A and B) n(S) Copyright reserved

Mathematics/P2 12 Hlayiso/Mock 2026 NSC Mock ANSWER SHEET 1 NAME: QUESTION 2.1 SPEED, v (IN KM/H) NUMBER OF VEHICLES CUMULATIVE FREQUENCY 40 ≤ v < 50 6 50 ≤ v < 60 14 60 ≤ v < 70 28 70 ≤ v < 80 30 80 ≤ v < 90 15 90 ≤ v < 100 7 QUESTION 2.2 Speeds of vehicles 100 90 80 70 Cumulative frequency 60 50 40 30 20 10 v 40 50 60 70 80 90 100 Speed (in km/h) Copyright reserved

Mathematics/P2 13 Hlayiso/Mock 2026 NSC Mock ANSWER SHEET 2 NAME: QUESTION 7.1 y 1,5 1 0,5 0◦ x −180◦ −150◦ −120◦ −90◦ −60◦ −30◦ 30◦ 60◦ 90◦ 120◦ 150◦ 180◦ −0,5 −1 −1,5 Copyright reserved