Technical Mathematics Grade 11 P2 2026 QP (Eng)

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 12 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(−3 ; −1), B(5 ; 3) and C(−1 ; 5). α is the angle of inclination of the line AC. y C(−1 ; 5) B(5 ; 3) α x O A(−3 ; −1) Determine: 1.1 The gradient of AB (2) 1.2 The length of AB (leave your answer in simplest surd form) (3) 1.3 The coordinates of M, the midpoint of AB (2) 1.4 The equation of the line that passes through M and is perpendicular to AB, in the form y = mx + c (3) 1.5 Show that C lies on the line in QUESTION 1.4 and hence explain why △ABC is isosceles. (3) 1.6 The size of α (2) 1.7 The size of CÂB (3) 1.8 The area of △ABC (4) √ 1.9 E(x ; −3) is a point such that BE = 2 13 units and x < 5. Calculate the value of x. (4) [26] Copyright reserved Please turn over

Technical Mathematics/P2 4 Hlayiso/Mock 2026 NSC Mock QUESTION 2 2.1 Given: A = 48,6◦ and B = 117,3◦ Use a calculator to determine the value of: 2.1.1 tan(2A − B) (2) sec B 2.1.2 (3) cot2 A 2.2 Given: 17 cos θ − 8 = 0 and sin θ < 0 With the aid of a sketch and WITHOUT using a calculator, determine the value of: 2.2.1 tan θ (3) 2.2.2 8 tan θ − 17 sin θ (3) 2.3 Solve for θ , correct to ONE decimal place: 4 cot θ + 7 = 2 for θ ∈ [0◦ ; 360◦ ] (4) [15] QUESTION 3 sin(360◦ − x) · tan(180◦ + x) 3.1 Simplify: (6) cos(180◦ + x) · tan 225◦ cos x 3.2 Prove that: − tan x = sec x (4) 1 − sin x [10] QUESTION 4 Given the functions defined by f (x) = 2 cos x and g(x) = sin(x − 30◦ ) 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 period of g. (1) 4.3 Write down the range of f . (2) 4.4 Use your graphs to determine the values of x for which f (x) · g(x) > 0. (3) [12] Copyright reserved Please turn over

Technical Mathematics/P2 5 Hlayiso/Mock 2026 NSC Mock QUESTION 5 The diagram below shows the triangular frame PQR of a roof truss. PR is the horizontal tie beam and QS is a vertical support with S on PR. • PQ = 4,2 m and QR = 5,6 m • PQ̂R = 105◦ Q 105◦ 4,2 m 5,6 m P S R 5.1 Calculate the length of the tie beam PR. (3) 5.2 Calculate the size of QP̂R. (3) 5.3 Calculate the area of △PQR. (2) 5.4 Hence, or otherwise, calculate the length of the vertical support QS. (3) [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 exterior angle of a cyclic quadrilateral is equal to … (1) 6.2 In the diagram below, O is the centre of the circle and A, B, C and D are points on the circle. ABCD is a cyclic quadrilateral and DC is produced to E. Chord AC and radii OA and OC are drawn. AÔC = 124◦ and DÂB = 95◦ B E A C 124◦ O D Determine, stating reasons, the size of: 6.2.1 AD̂C (2) 6.2.2 AB̂C (2) 6.2.3 OÂC (3) 6.2.4 BĈE (2) 6.2.5 BÂC, if it is further given that AD = DC (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 tangent to a circle is perpendicular to the … at the point of contact. (1) 7.2 In the diagram below, O is the centre of the circle and A, B, C and D are points on the circle. BC is a diameter. SAT is a tangent to the circle at A and meets BC produced at T . Chords AB, AC, AD and DB, and radius OA are drawn. CÂT = 32◦ S A 32◦ B T O C D Determine, stating reasons, the size of: 7.2.1 AB̂C (2) 7.2.2 BÂC (2) 7.2.3 T̂ (3) 7.2.4 AD̂B (2) 7.3 Prove that △TAC ||| △T BA. (4) Copyright reserved Please turn over

Technical Mathematics/P2 8 Hlayiso/Mock 2026 NSC Mock 7.4 In the diagram below, O is the centre of the circle. KM and KN are tangents to the circle at M and N. P is a point on the minor arc MN. Chords MN, MP and NP, and radii OM and ON are drawn. M K̂N = 64◦ M P O 64◦ K N 7.4.1 Prove that KMON is a cyclic quadrilateral. (3) 7.4.2 Determine, stating reasons, the size of M P̂N. (3) [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 and CD are parallel chords on opposite sides of O. F lies on AB and E lies on CD such that F, O and E are on a straight line with OF ⊥ AB and OE ⊥ CD. AB = 48 cm, CD = 40 cm and FE = 22 cm. Let OF = x. F A B O C D E 8.2.1 Write down, with a reason, the length of AF. (2) 8.2.2 Write down the length of OE in terms of x. (1) 8.2.3 By writing OA2 and OC2 in terms of x, show that x = 7. (4) 8.2.4 Hence, calculate the radius of the circle. (2) [10] Copyright reserved Please turn over

Technical Mathematics/P2 10 Hlayiso/Mock 2026 NSC Mock QUESTION 9 9.1 The wheels of a car have a diameter of 0,64 m. The car travels at a constant speed of 72 km/h without the wheels slipping. 72 km/h 0,64 m 9.1.1 Convert 72 km/h to metres per second. (2) 9.1.2 Calculate the rotational frequency of a wheel in revolutions per second. (3) 9.1.3 Calculate the angular velocity of a wheel in radians per second. (2) 9.1.4 How many complete revolutions does a wheel make in 5 minutes? (2) 9.2 A garden sprinkler waters a region OPQ in the shape of a sector of a circle with centre O, as shown below. The radius is 3 m and the area watered is 6,75 m2 . P Q θ 3m O 9.2.1 Calculate the central angle θ in radians. (3) 9.2.2 Convert θ to degrees. (2) 9.2.3 Calculate the length of arc PQ. (2) Copyright reserved Please turn over

Technical Mathematics/P2 11 Hlayiso/Mock 2026 NSC Mock 9.3 The diagram below shows the circular cross-section of a service tunnel with a diameter of 2 m. The flat floor KL of the tunnel is a chord that is 1,6 m wide. Calculate the height h of the tunnel from the middle of the floor to the highest point of the roof. (5) h K L 1,6 m 9.4 A closed rectangular water tank is 1,2 m long, 0,8 m wide and 0,75 m high, as shown below. The following formulae may be used: Volume of a rectangular prism = l × b × h Total surface area of a rectangular prism 0,75 m = 2(lb + lh + bh) 0,8 m 1 m3 = 1 000 litres 1,2 m 9.4.1 Calculate the capacity of the tank in litres. (3) 9.4.2 A workshop makes 6 of these tanks from sheet metal that costs R185,50 per m2 . Calculate the cost of the sheet metal needed for the 6 tanks. (Ignore overlaps and waste.) (5) [29] Copyright reserved Please turn over

Technical Mathematics/P2 12 Hlayiso/Mock 2026 NSC Mock QUESTION 10 The diagram below shows an irregular plot with an area of 294 m2 . The straight boundary of 36 m is divided into 6 equal parts. The ordinates are 6 m; 7,5 m; 8 m; y m; 9 m; 8,5 m and 7 m respectively. 6m 7,5 m 8m y 9m 8,5 m 7m 36 m 10.1 Write down the width of each equal part. (1) 10.2 Use the mid-ordinate rule to calculate the value of y. (4) [5] TOTAL: 150 Copyright reserved Please turn over

Technical Mathematics/P2 13 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 14 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