Mathematics Grade 10 P2 November Mock Exam 2 2026 QP (Eng)

Mock hlayiso mock exams Practice Series: Grade 10 Exam Preparation WWW.HLAYISO.COM NATIONAL SENIOR CERTIFICATE GRADE 10 MATHEMATICS P2 NOVEMBER EXAMINATION 2026 (MOCK) MARKS: 100 TIME: 2 hours This question paper consists of 9 pages, 1 information sheet and 1 answer sheet. 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 10 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. An ANSWER SHEET for QUESTIONS 1.5 and 6.2 is attached at the end of this question paper. Write your name on the answer sheet and hand it 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 A community health worker visited 30 households in a street and recorded the number of people living in each household. The results are shown in the bar graph below. Number of households 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 Number of people in the household 1.1 How many households have more than 4 people living in them? (1) 1.2 Write down the modal number of people per household. (1) 1.3 Determine the median number of people per household. (2) 1.4 Determine the lower quartile and the upper quartile of the data. (2) 1.5 On the scaled line provided on the ANSWER SHEET, draw a box-and-whisker diagram to represent the data. (2) [8] Copyright reserved Please turn over

Mathematics/P2 4 Hlayiso/Mock 2026 NSC Mock QUESTION 2 A farm stall weighed 60 watermelons. The histogram below shows the masses, m (in kg), of the watermelons. Frequency 20 18 16 14 12 10 8 6 4 2 0 m (kg) 2 4 6 8 10 12 2.1 Write down the number of watermelons with a mass of at least 4 kg but less than 6 kg. (1) 2.2 Calculate the estimated mean mass of the watermelons. (4) 2.3 Determine the interval in which the upper quartile of the masses lies. (2) 2.4 Watermelons with a mass of 8 kg or more are sold as “jumbo” watermelons. Calculate the percentage of the watermelons that are jumbo watermelons. (2) [9] Copyright reserved Please turn over

Mathematics/P2 5 Hlayiso/Mock 2026 NSC Mock QUESTION 3 In the diagram, A(−2 ; −1), B(1 ; 3), C(6 ; 3) and D are the vertices of quadrilateral ABCD. The diagonals AC and BD intersect at M, the midpoint of AC. M is also the midpoint of BD. y B(1 ; 3) C(6 ; 3) O M x A(−2 ; −1) D 3.1 Calculate the length of AB. (2) 3.2 Determine the coordinates of M. (2) 3.3 Hence, determine the coordinates of D. (3) 3.4 Show that AC ⊥ BD. (3) 3.5 Hence, prove that ABCD is a rhombus. (2) 3.6 Calculate the area of ABCD. (3) [15] QUESTION 4 4.1 Given: x = 56,2◦ and y = 21,7◦ . Use a calculator to determine the value of the following, correct to TWO decimal places: 4.1.1 cos(x + 2y) (1) 4.1.2 cosec2 x (2) 4.2 Determine the value of the following WITHOUT using a calculator: cos2 30◦ − sin2 45◦ + tan2 60◦ (4) tan 45◦ . sin 30◦ 4.3 Solve for θ , correct to TWO decimal places, if 0◦ ≤ θ ≤ 90◦ : 4.3.1 5 sec θ = 8 (2) ( ) θ ◦ 4.3.2 tan + 25 = 1,8 (3) 2 [12] Copyright reserved Please turn over

Mathematics/P2 6 Hlayiso/Mock 2026 NSC Mock QUESTION 5 Given: 17 sin α + 8 = 0 and 180◦ ≤ α ≤ 270◦ WITHOUT using a calculator and with the aid of a sketch, determine the value of: 5.1 cos α (3) 5.2 tan α + sec α (2) 5.3 cosec2 α − cot2 α (2) [7] QUESTION 6 The graph of f (x) = a cos x + q is drawn below for x ∈ [0◦ ; 360◦ ]. The graph passes through the points (0◦ ; 1) and (360◦ ; 1) and has a minimum turning point at (180◦ ; −3). y (0◦ ; 1) (360◦ ; 1) x 0 90◦ 180◦ 270◦ f (180◦ ; −3) 6.1 Determine the values of a and q. (2) 6.2 The graph of f is also drawn on the ANSWER SHEET. On the same system of axes, sketch the graph of g(x) = sin x − 1 for x ∈ [0◦ ; 360◦ ]. Clearly show ALL intercepts with the axes, the turning points and the end points of the graph. (3) 6.3 Write down the amplitude of f . (1) 6.4 Write down the range of f . (2) 6.5 The graphs of f and g intersect at x = 63,43◦ and x = 243,43◦ . Use your graphs to determine the values of x for which f (x) < g(x). (2) 6.6 The graph of f is reflected about the x-axis and then moved 3 units upwards to form the graph of h. Write down the equation of h in the form h(x) = . . . (2) [12] Copyright reserved Please turn over

Mathematics/P2 7 Hlayiso/Mock 2026 NSC Mock QUESTION 7 A drone, D, hovers vertically above point F on level ground. Two learners stand at points A and B on the ground, on opposite sides of F, such that A, F and B lie in a straight line. The straight-line distance from A to the drone is 85 m. The angle of elevation of D from A is 32◦ and the angle of elevation of D from B is 47◦ . D 85 m 32◦ 47◦ A F B 7.1 Calculate DF, the height of the drone above the ground. (2) 7.2 Calculate the length of AF. (2) 7.3 Calculate the distance between the two learners, AB. (4) 7.4 Write down the angle of depression of B from D. (1) [9] QUESTION 8 A solid metal right circular cone has a base radius of 5 cm and a perpendicular height of 12 cm. 12 cm s Volume of a cone = 13 π r2 h Total surface area of a cone = π r2 + π rs 5 cm Volume of a sphere = 43 π r3 8.1 Show that the slant height, s, of the cone is 13 cm. (1) 8.2 Calculate the total surface area of the cone. (2) 8.3 The cone is melted down and ALL the metal is used to make one solid sphere. Calculate the radius of the sphere. (3) [6] Copyright reserved Please turn over

Mathematics/P2 8 Hlayiso/Mock 2026 NSC Mock Give reasons for ALL statements in QUESTIONS 9 and 10. QUESTION 9 9.1 In the diagram, PQRS is a parallelogram with PQ ∥ SR and PS ∥ QR. Diagonal QS is drawn. P Q 1 2 2 1 S R Prove the theorem which states that the opposite sides of a parallelogram are equal, that is PQ = SR and PS = QR. (4) 9.2 In the diagram, ABCD is a parallelogram. AE bisects DÂB and meets DC at E. AB = 12 cm and AD = 7 cm. D E C 7 cm 1 2 A 12 cm B 9.2.1 Prove that AD = DE. (3) 9.2.2 Hence, calculate the length of EC. (1) [8] Copyright reserved Please turn over

Mathematics/P2 9 Hlayiso/Mock 2026 NSC Mock QUESTION 10 10.1 KLMN is a rectangle. The diagonals KM and LN intersect at O. KÔL = 124◦ . K L 124◦ O N M Calculate, with reasons: 10.1.1 OL̂K (2) 10.1.2 OL̂M (2) 10.1.3 the value of y, if KM = 3y + 2 and ON = y + 4 (2) 10.2 ABCD is a trapezium with AD ∥ BC. E is the midpoint of AB and G is the midpoint of diagonal AC. EG is produced to meet DC at F. AD = 8 cm and BC = 14 cm. A 8 cm D E F G B 14 cm C 10.2.1 Calculate the length of EG. (2) 10.2.2 Prove that F is the midpoint of DC. (3) 10.2.3 Calculate the length of EF. (3) [14] TOTAL: 100 Copyright reserved Please turn over

Mathematics/P2 10 Hlayiso/Mock 2026 NSC Mock INFORMATION SHEET: MATHEMATICS GRADE 10 A = P(1 + ni) A = P(1 − ni) A = P(1 − i)n A = P(1 + i)n √ ( ) x1 + x2 y1 + y2 d = (x2 − x1 )2 + (y2 − y1 )2 M ; 2 2 y2 − y1 y = mx + c m= x2 − x1 ∑x ∑ fx x̄ = x̄ = n n n(A) P(A) = P(A or B) = P(A) + P(B) − P(A and B) n(S) Copyright reserved

Mathematics/P2 11 Hlayiso/Mock 2026 NSC Mock ANSWER SHEET NAME: QUESTION 1.5 0 1 2 3 4 5 6 7 8 Number of people in the household QUESTION 6.2 y 1,5 1 0,5 x 0 30◦ 60◦ 90◦ 120◦ 150◦ 180◦ 210◦ 240◦ 270◦ 300◦ 330◦ 360◦ −0,5 −1 −1,5 −2 −2,5 −3 f −3,5 Copyright reserved