Technical Mathematics Grade 10 P2 November Mock 2026 QP

Mock hlayiso mock exams Practice Series: Grade 10 Exam Preparation WWW.HLAYISO.COM NATIONAL SENIOR CERTIFICATE GRADE 10 TECHNICAL MATHEMATICS P2 NOVEMBER EXAMINATION 2026 (MOCK) MARKS: 100 TIME: 2 hours This question paper consists of 9 pages and a special answer book. Copyright reserved Please turn over

Technical 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 EIGHT questions. 2. Answer ALL the questions in the SPECIAL ANSWER BOOK provided. 3. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your answers. 4. Answers only will NOT necessarily be awarded full marks. 5. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 6. If necessary, round off answers to TWO decimal places, unless stated otherwise. 7. Diagrams are NOT necessarily drawn to scale. 8. Write neatly and legibly. Copyright reserved Please turn over

Technical Mathematics/P2 3 Hlayiso/Mock 2026 NSC Mock QUESTION 1 In the diagram below, A(−2 ; 1), B(2 ; 4), C(5 ; 0) and D(1 ; −3) are the vertices of quadrilateral ABCD. The diagonals AC and BD intersect at M. y B(2 ; 4) A(−2 ; 1) M x O C(5 ; 0) D(1 ; −3) 1.1 Calculate the length of AB. (2) 1.2 Calculate the gradient of AB. (2) 1.3 Calculate the gradient of BC and hence show that AB ⊥ BC. (3) 1.4 Determine the coordinates of M, the midpoint of AC. (2) 1.5 Determine the equation of the diagonal BD in the form y = mx + c. (3) 1.6 Hence, show that M lies on the diagonal BD. (1) 1.7 Given that BC = CD = DA = 5 units, name the type of quadrilateral ABCD. Give a reason for your answer. (2) [15] Copyright reserved Please turn over

Technical Mathematics/P2 4 Hlayiso/Mock 2026 NSC Mock QUESTION 2 2.1 Given: A = 37,4◦ and B = 18,6◦ Use a calculator to determine the value of: 2.1.1 sin(A + B) (2) 2.1.2 sec A − tan B (2) 2.2 Given: 5 tan θ − 12 = 0 and θ ∈ [180◦ ; 360◦ ] With the aid of a sketch and WITHOUT using a calculator, determine the value of: 2.2.1 sin θ (4) 2.2.2 cosec θ + cot θ (3) 2.3 Solve for x: 2 cos x − 1,3 = 0 for x ∈ [0◦ ; 90◦ ] (3) [14] Copyright reserved Please turn over

Technical Mathematics/P2 5 Hlayiso/Mock 2026 NSC Mock QUESTION 3 3.1 A wheelchair ramp PR at the entrance of a clinic is 4,5 m long and makes an angle of 6◦ with the horizontal ground PQ, as shown below. RQ ⊥ PQ. R 4,5 m 6◦ P Q 3.1.1 Calculate the height RQ of the ramp. (2) 3.1.2 Calculate the horizontal distance PQ. (2) 3.2 AB is a vertical cellphone mast that is 30 m high. A guy wire AC is anchored to the ground at C. A technician stands at D. B, C and D lie on the same horizontal line. The angle of elevation of A from C is 65◦ and the angle of elevation of A from D is 40◦ . A 30 m 65◦ 40◦ B C D 3.2.1 Calculate the distance BC. (3) 3.2.2 Calculate the length of the guy wire AC. (2) 3.2.3 Calculate the distance CD. (3) [12] Copyright reserved Please turn over

Technical Mathematics/P2 6 Hlayiso/Mock 2026 NSC Mock QUESTION 4 Given the functions defined by f (x) = −2 sin x and g(x) = cos x + 1 for x ∈ [0◦ ; 360◦ ]. 4.1 Sketch the graphs of f and g on the same set of axes on the grid provided in the SPECIAL ANSWER BOOK. Clearly indicate ALL the intercepts with the axes, the turning points and the end points. (6) 4.2 Write down the amplitude of f . (1) 4.3 Write down the period of g. (1) 4.4 Write down the range of g. (2) 4.5 Use your graphs to determine the values of x for which f (x) < 0. (2) [12] Give reasons for your statements in QUESTIONS 5 and 6. QUESTION 5 5.1 Complete the following statement: The line joining the midpoints of two sides of a triangle is parallel to the third side and … (1) 5.2 In △PQR below, S and T are the midpoints of PQ and PR respectively. ST = 7 cm, Q̂ = 68◦ and R̂ = 52◦ . P 7 cm S T 68◦ 52◦ Q R Determine, stating reasons: 5.2.1 The length of QR (2) 5.2.2 The size of PŜT (2) 5.2.3 The size of P̂ (2) Copyright reserved Please turn over

Technical Mathematics/P2 7 Hlayiso/Mock 2026 NSC Mock 5.3 In △ABC below, D is a point on AB and E is a point on AC such that DE ∥ BC. AD = 4 units, DB = 6 units and DE = 5 units. A 4 5 D E 6 B C 5.3.1 Prove that △ADE ||| △ABC. (3) 5.3.2 Hence, calculate the length of BC. (2) 5.4 Name any TWO conditions (cases) which prove that two triangles are congruent. (2) [14] QUESTION 6 6.1 ABCD below is a parallelogram with  = 3x + 10◦ and Ĉ = 5x − 30◦ . D C 5x − 30◦ 3x + 10◦ A B 6.1.1 Calculate, giving a reason, the value of x. (3) 6.1.2 Hence, calculate the size of B̂. (2) Copyright reserved Please turn over

Technical Mathematics/P2 8 Hlayiso/Mock 2026 NSC Mock 6.2 PQRS below is a rhombus. The diagonals PR and QS intersect at T . PR = 16 cm and QS = 12 cm. Q P R T S 6.2.1 Write down, with a reason, the size of PT̂ Q. (2) 6.2.2 Calculate the length of PQ. (3) 6.2.3 Hence, write down the perimeter of PQRS. (1) 6.3 Complete the following statement: A parallelogram with one right angle is a … (1) [12] QUESTION 7 The following formulae may be used: Volume of a cylinder = π r2 h Total surface area of a closed cylinder = 2π r2 + 2π rh Volume of a right prism = area of base × height Area of a triangle = 12 × base × perpendicular height 7.1 A closed cylindrical water tank has a diameter of 1,4 m and a height of 1,8 m. 1,4 m 1,8 m 7.1.1 Calculate the volume of the tank in m3 . (3) 7.1.2 Calculate the total external surface area of the tank. (3) Copyright reserved Please turn over

Technical Mathematics/P2 9 Hlayiso/Mock 2026 NSC Mock 7.2 A solid concrete ramp has the shape of a right triangular prism, as shown below. The triangular end ABC has a right angle at B, with AB = 2,4 m and BC = 0,6 m. The ramp is 1,5 m wide. C 0,6 m 1,5 m A 2,4 m B 7.2.1 Calculate the area of the triangular end ABC. (2) 7.2.2 Calculate the volume of concrete needed to build the ramp. (2) 7.2.3 Calculate the length of the sloping edge AC. (2) [12] QUESTION 8 8.1 Convert: 8.1.1 47,385◦ to degrees, minutes and seconds (2) 8.1.2 18◦ 36′ 45′′ to degrees (decimal form) (2) 8.2 Convert 150◦ to radians. Leave your answer in terms of π . (2) 8.3 The arm of a windscreen wiper is 45 cm long. The tip of the arm sweeps through an angle of 75◦ , as shown below. Calculate the length of the arc travelled by the tip of the arm. (3) 75◦ 45 cm O [9] TOTAL: 100 Copyright reserved