Technical Mathematics Grade 10 P2 2026 QP (Eng)

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, P(−2 ; 2), Q(0 ; 5), R(6 ; 1) and S(k ; −2) are the vertices of quadrilateral PQRS. The diagonals PR and QS intersect at M. y Q(0 ; 5) P(−2 ; 2) M R(6 ; 1) x O S(k ; −2) 1.1 Calculate the gradient of PQ. (2) 1.2 Determine the size of PQ̂R, giving a reason. (3) 1.3 Determine the equation of the line through R that is parallel to PQ. Write your answer in the form y = mx + c. (3) 1.4 S lies on the line in QUESTION 1.3. Show that k = 4. (2) 1.5 Determine the coordinates of the midpoints of QS and PR. Hence, show that the diagonals bisect each other at M. (2) 1.6 Calculate the lengths of PQ and QR in simplest surd form. Hence, using your answers to QUESTIONS 1.2 and 1.5, name the type of quadrilateral that PQRS is, giving a reason. (3) [15] Copyright reserved Please turn over

Technical Mathematics/P2 4 Hlayiso/Mock 2026 NSC Mock QUESTION 2 2.1 Given: α = 52,3◦ and β = 21,8◦ Use a calculator to determine the value of: 2.1.1 cos(2α − β ) (2) cosec α 2.1.2 (2) tan β 2.2 In the diagram below, P(−8 ; t), with t > 0, is a point in the Cartesian plane such that OP = 17 units. θ is the angle between OP and the positive x-axis. y P(−8 ; t) 17 θ x O WITHOUT using a calculator, determine: 2.2.1 The value of t (2) 2.2.2 sin θ + cos θ (2) 2.2.3 cosec θ − cot θ (2) 2.3 Solve for x: 3 cos(2x − 10◦ ) = 2 sin 38◦ for x ∈ [0◦ ; 90◦ ] (4) [14] Copyright reserved Please turn over

Technical Mathematics/P2 5 Hlayiso/Mock 2026 NSC Mock QUESTION 3 3.1 The diagram below shows a roof truss ABC with a span AC of 9,6 m. The roof slopes at 28◦ on both sides, so BÂC = BĈA = 28◦ . The vertical king post BD meets AC at its midpoint D, with BD ⊥ AC. A strut DE is fixed from D to the rafter AB such that DE ⊥ AB. B E 28◦ 28◦ A D C 9,6 m 3.1.1 Calculate the height BD of the truss. (2) 3.1.2 Calculate the length of the rafter AB. (2) 3.1.3 Calculate the length of the strut DE. (3) 3.2 PQ is a building that is 15 m high and T R is a vertical floodlight pole at a sports field. Q and R lie on the same horizontal ground, 40 m apart. X is a point on T R such that PX is horizontal. The angle of elevation of T from P is 22◦ . T P 22◦ X 15 m Q 40 m R 3.2.1 Calculate the height T R of the pole. (3) 3.2.2 Calculate the angle of depression of Q from T . (2) [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 cos x − 1 and g(x) = tan x 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, the end points and the asymptotes. (6) 4.2 Write down the period of g. (1) 4.3 Write down the range of f . (2) 4.4 The graph of f is shifted 3 units upwards to form the graph of h. Write down the equation of h. (1) 4.5 Use your graphs to determine the values of x, for x ∈ [0◦ ; 180◦ ], for which BOTH f (x) < 0 AND g(x) > 0. (2) [12] Give reasons for your statements in QUESTIONS 5 and 6. QUESTION 5 5.1 Complete the following statement: Two triangles are similar if their corresponding angles are equal OR if their corresponding sides are … (1) 5.2 In △PQR below, QR is produced to S and RT is drawn parallel to QP. P̂ = 58◦ and Q̂ = 64◦ . P T 58◦ 64◦ 1 2 3 Q R S Determine, stating reasons, the size of: 5.2.1 R̂1 (2) 5.2.2 R̂2 (2) 5.2.3 R̂3 (2) 5.2.4 Hence, name the type of triangle that PQR is and state which two sides are equal. (2) Copyright reserved Please turn over

Technical Mathematics/P2 7 Hlayiso/Mock 2026 NSC Mock 5.3 In △ABC below, AB̂C = 90◦ and D is a point on AC such that BD ⊥ AC. AD = 3,2 units and AC = 5 units. A D B C 5.3.1 Prove that △ADB ||| △ABC. (3) 5.3.2 Hence, calculate the length of AB. (2) [14] QUESTION 6 6.1 ABCD below is a trapezium with AD ∥ BC. Â = 3x − 10◦ , B̂ = 2x + 15◦ and Ĉ = 4x − 55◦ . A D 3x − 10◦ 2x + 15◦ 4x − 55◦ B C 6.1.1 Calculate, giving a reason, the value of x. (3) 6.1.2 Hence, show that ABCD is an isosceles trapezium. (3) Copyright reserved Please turn over

Technical Mathematics/P2 8 Hlayiso/Mock 2026 NSC Mock 6.2 KLMN below is a kite with KL = KN and ML = MN. The diagonals KM and LN intersect at O. LN = 16 cm, KO = 6 cm and MO = 15 cm. K L N O M 6.2.1 Prove that △KLM ≡ △KNM. (3) 6.2.2 Calculate the perimeter of the kite KLMN. (3) [12] QUESTION 7 The following formulae may be used: Area of a rectangle = length × breadth Volume of a cylinder = π r2 h Curved (lateral) surface area of a cylinder = 2π rh 7.1 The diagram below shows the L-shaped floor plan of a workshop. 7m 8m 5m 12 m 7.1.1 Calculate the floor area of the workshop. (2) 7.1.2 The floor is to be covered with square tiles of side 60 cm. An extra 10% of tiles must be bought to allow for breakages and cutting. Calculate the number of tiles that must be bought. (3) Copyright reserved Please turn over

Technical Mathematics/P2 9 Hlayiso/Mock 2026 NSC Mock 7.2 A concrete drainage pipe is a hollow cylinder with an outer diameter of 1,2 m, an inner diameter of 1 m and a length of 2,5 m, as shown below. outer inner diameter 1 m diameter 1,2 m 2,5 m 7.2.1 Calculate the volume of concrete used to make the pipe. (4) 7.2.2 The outside curved surface of the pipe must be coated with a waterproof sealant. Calculate the area that must be coated. (3) [12] QUESTION 8 8.1 Convert: 8.1.1 63,745◦ to degrees, minutes and seconds (2) 8.1.2 112◦ 17′ 24′′ to degrees (decimal form) (2) 8.2 Simplify WITHOUT using a calculator. Leave your answer in degrees. 7π π + 40◦ − (2) 6 4 8.3 An arc of length 42 cm is cut off on a circle with a diameter of 0,6 m, as shown below. Calculate the size of the central angle θ that subtends the arc. Give your answer in degrees. (3) 42 cm θ O [9] TOTAL: 100 Copyright reserved