Technical Mathematics Grade 11 P2 November Mock 2026 QP

Mock hlayiso mock exams Practice Series: Grade 11 Exam Preparation WWW.HLAYISO.COM NATIONAL SENIOR CERTIFICATE GRADE 11 TECHNICAL MATHEMATICS P2 NOVEMBER EXAMINATION 2026 (MOCK) MARKS: 150 TIME: 3 hours This question paper consists of 11 pages and a 2-page information sheet. 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 TEN 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. An information sheet with formulae is included at the end of the question paper. 9. Write neatly and legibly. Copyright reserved Please turn over

Technical Mathematics/P2 3 Hlayiso/Mock 2026 NSC Mock QUESTION 1 In the diagram below, △ABC has vertices A(−2 ; −1), B(4 ; 2) and C(1 ; 8). The line AB passes through the origin and makes an angle of inclination θ with the positive x-axis. y C(1 ; 8) B(4 ; 2) θ x O A(−2 ; −1) 1.1 Complete the following statement: If two lines are parallel, then their gradients are … (1) Determine: 1.2 The length of AB (leave your answer in simplest surd form) (3) 1.3 The gradient of AB (2) 1.4 The gradient of BC, and hence show that AB ⊥ BC (3) 1.5 The coordinates of M, the midpoint of AC (2) 1.6 The equation of the line BC in the form y = mx + c (3) 1.7 The size of θ (2) 1.8 The coordinates of D such that ABCD is a rectangle (3) 1.9 The area of △ABC (4) 1.10 The equation of the line through C that is parallel to AB, in the form y = mx + c (3) [26] Copyright reserved Please turn over

Technical Mathematics/P2 4 Hlayiso/Mock 2026 NSC Mock QUESTION 2 2.1 Given: A = 56,3◦ and B = 23,8◦ Use a calculator to determine the value of: 2.1.1 cos(A + B) (2) tan A 2.1.2 (3) cosec B 2.2 Given: 13 sin θ = 5 and θ ∈ [90◦ ; 270◦ ] With the aid of a sketch and WITHOUT using a calculator, determine the value of: 2.2.1 cos θ (3) 2.2.2 sec θ + tan θ (3) 2.3 Solve for θ , correct to ONE decimal place: 2 cos θ = −1,3 for θ ∈ [0◦ ; 360◦ ] (4) [15] QUESTION 3 sin(180◦ + θ ) · tan(360◦ − θ ) 3.1 Simplify: (6) cos(180◦ − θ ) · tan(180◦ + θ ) 1 3.2 Prove that: − cos x = sin x · tan x (4) cos x [10] 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] Copyright reserved Please turn over

Technical Mathematics/P2 5 Hlayiso/Mock 2026 NSC Mock QUESTION 5 A farmer’s field has the shape of quadrilateral ABCD, as shown in the diagram below. A straight fence BD divides the field into two triangular camps. • AB = 50 m, AD = 70 m and BÂD = 65◦ • DB̂C = 72◦ and BĈD = 48◦ C 48◦ B 72◦ 50 m 65◦ A 70 m D 5.1 Calculate the length of the fence BD. (3) 5.2 Write down the size of BD̂C. (1) 5.3 Calculate the length of BC. (3) 5.4 Calculate the total area of the field ABCD. (4) [11] Copyright reserved Please turn over

Technical Mathematics/P2 6 Hlayiso/Mock 2026 NSC Mock Give reasons for your statements in QUESTIONS 6, 7 and 8. QUESTION 6 6.1 Complete the following statement: The angle subtended by a diameter at the circumference of a circle is … (1) 6.2 In the diagram below, O is the centre of the circle and P, Q, R and S are points on the circle. PR is a diameter. Chords PQ, QR, RS, SP and SQ, and radius OQ are drawn. QP̂R = 34◦ and SP̂Q = 100◦ S O P R 34◦ Q Determine, stating reasons, the size of: 6.2.1 PQ̂R (2) 6.2.2 PR̂Q (2) 6.2.3 QÔR (2) 6.2.4 PŜQ (2) 6.3 Complete the following statement: The opposite angles of a cyclic quadrilateral are … (1) 6.4 Hence, determine, stating a reason, the size of SR̂Q. (2) [12] Copyright reserved Please turn over

Technical Mathematics/P2 7 Hlayiso/Mock 2026 NSC Mock QUESTION 7 7.1 Complete the following statement: The angle between a tangent to a circle and a chord drawn from the point of contact is equal to … (1) 7.2 In the diagram below, O is the centre of the circle and A, B and C are points on the circle. ECF is a tangent to the circle at C. Radii OB and OC are drawn. F ĈB = 48◦ and AĈE = 70◦ A O B 70◦ 48◦ E C F Determine, stating reasons, the size of: 7.2.1 BÂC (2) 7.2.2 AB̂C (2) 7.2.3 AĈB (2) 7.2.4 BÔC (2) 7.2.5 OĈB (2) Copyright reserved Please turn over

Technical Mathematics/P2 8 Hlayiso/Mock 2026 NSC Mock 7.3 Complete the following statement: Two tangents drawn to a circle from the same point outside the circle are … (1) 7.4 In the diagram below, 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 circle. Chords AB, AC and BC, and radii OA and OB are drawn. AP̂B = 50◦ A O 50◦ P C B Determine, stating reasons, the size of: 7.4.1 PÂB (2) 7.4.2 AĈB (2) 7.4.3 AÔB (2) 7.4.4 OÂB (2) [20] Copyright reserved Please turn over

Technical Mathematics/P2 9 Hlayiso/Mock 2026 NSC Mock QUESTION 8 8.1 Complete the following statement: The line drawn from the centre of a circle perpendicular to a chord … (1) 8.2 In the diagram below, O is the centre of the circle. AB is a chord of the circle with AB = 24 cm. OM ⊥ AB and OM produced meets the circle at C. MC = 8 cm. Let the radius of the circle be r. O A B M 8 cm C 8.2.1 Write down, with a reason, the length of AM. (2) 8.2.2 Write down the length of OM in terms of r. (1) 8.2.3 Hence, calculate the value of r. (4) 8.2.4 Write down the length of OM. (1) 8.2.5 Write down the length of the diameter of the circle. (1) [10] Copyright reserved Please turn over

Technical Mathematics/P2 10 Hlayiso/Mock 2026 NSC Mock QUESTION 9 9.1 A pulley with a diameter of 300 mm rotates at 450 revolutions per minute. 9.1.1 Determine the angular velocity of the pulley in radians per second. (3) 9.1.2 Determine the circumferential velocity of a point on the rim of the pulley in metres per second. (3) 9.2 A paved patio AOB has the shape of a sector of a circle with centre O, as shown below. The radius is 1,8 m and the central angle is 110◦ . A B 110◦ 1,8 m O 9.2.1 Convert 110◦ to radians. (2) 9.2.2 Calculate the length of arc AB. (2) 9.2.3 Calculate the area of the patio. (2) 9.2.4 Calculate the perimeter of the patio. (2) 9.3 The diagram below shows the circular cross-section of a stormwater pipe. The water surface KL is 1,2 m wide and the water is 0,4 m deep at the deepest point (h = 0,4 m). Calculate the diameter of the pipe. (4) 1,2 m K L h Copyright reserved Please turn over

Technical Mathematics/P2 11 Hlayiso/Mock 2026 NSC Mock 9.4 A gas tank consists of a cylinder with a hemisphere at each end, as shown below. The cylinder is 0,8 m long and the radius of the cylinder and the hemispheres is 0,15 m. The following formulae may be used: 0,15 m Volume of a cylinder = π r2 h 4 Volume of a sphere = π r3 3 Curved surface area of a cylinder = 2π rh 0,8 m Surface area of a sphere = 4π r2 1 m3 = 1 000 litres 9.4.1 Calculate the volume of the cylindrical part of the tank. (2) 9.4.2 Calculate the combined volume of the two hemispheres. (2) 9.4.3 Hence, determine the capacity of the tank in litres. (3) 9.4.4 Calculate the total external surface area of the tank. (4) [29] QUESTION 10 The diagram below shows a plot of land with one curved boundary. The straight boundary of 30 m is divided into 6 equal parts. The ordinates are 8 m; 10 m; 11 m; 12,5 m; 12 m; 10,5 m and 9 m respectively. 10 m 11 m 12,5 m 12 m 10,5 m 9m 8m 30 m 10.1 Write down the width of each equal part. (1) 10.2 Use the mid-ordinate rule to calculate the area of the plot. (4) [5] TOTAL: 150 Copyright reserved Please turn over

Technical Mathematics/P2 12 Hlayiso/Mock 2026 NSC Mock INFORMATION SHEET: TECHNICAL MATHEMATICS √ −b ± b2 − 4ac b 4ac − b2 x= x=− y= 2a 2a 4a a = b ⇔ x = loga b , a > 0 , a ̸= 1 and b > 0 x A = P(1 + ni) A = P(1 − ni) A = P(1 + i)n A = P(1 − i)n ( ) i m ieff = 1 + −1 m f (x + h) − f (x) f ′ (x) = lim h→0 h ∫ ∫ xn+1 k kxn dx = k · +C , n ̸= −1 dx = k · ln x +C , x>0 n+1 x ∫ anx k anx dx = k · +C , a>0 n ln a √ ( ) x2 + x1 y2 + y1 d = (x2 − x1 )2 + (y2 − y1 )2 M ; 2 2 y2 − y1 y = mx + c y − y1 = m(x − x1 ) m= tan θ = m x2 − x1 x2 y2 + =1 a2 b2 a b c In △ABC : = = a2 = b2 + c2 − 2bc · cos A sin A sin B sinC 1 Area of △ABC = ab · sinC 2 sin2 θ + cos2 θ = 1 1 + tan2 θ = sec2 θ 1 + cot2 θ = cosec2 θ Copyright reserved

Technical Mathematics/P2 13 Hlayiso/Mock 2026 NSC Mock π rad = 180◦ Angular velocity = ω = 2π n where n = rotation frequency Angular velocity = ω = 360◦ n where n = rotation frequency Circumferential velocity = v = π Dn where D = diameter and n = rotation frequency Circumferential velocity = v = ω r where ω = angular velocity and r = radius Arc length = s = rθ where r = radius and θ = central angle in radians rs Area of a sector = where r = radius and s = arc length 2 r2 θ Area of a sector = where r = radius and θ = central angle in radians 2 4h2 − 4dh + x2 = 0 where h = height of segment, d = diameter of circle and x = length of chord o1 + o2 AT = a (m1 + m2 + m3 + . . . + mn ) where a = width of equal parts, m1 = , 2 on = nth ordinate and n = number of ordinates OR ( ) o1 + on AT = a + o2 + o3 + . . . + on−1 where a = width of equal parts, on = nth ordinate and n 2 = number of ordinates Copyright reserved