Mathematics Grade 11 P2 November Mock 2026 QP (Eng)

Mock hlayiso mock exams Practice Series: Grade 11 Exam Preparation WWW.HLAYISO.COM NATIONAL SENIOR CERTIFICATE GRADE 11 MATHEMATICS P2 NOVEMBER EXAMINATION 2026 (MOCK) MARKS: 150 TIME: 3 hours This question paper consists of 9 pages, 1 information sheet and 2 answer sheets. 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 12 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. ANSWER SHEETS for QUESTIONS 2.1, 2.2 and 7.1 are attached at the end of this question paper. Write your name on the answer sheets and hand them 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 The number of push-ups that 15 Grade 11 learners completed in one minute during a fitness test is given below. The data is arranged in ascending order. 12 15 17 18 20 21 21 23 24 25 26 28 33 38 49 1.1 Calculate the mean number of push-ups. (2) 1.2 Write down the five-number summary of the data. (3) 1.3 Draw a box-and-whisker diagram to represent the data. (2) 1.4 Comment on the skewness of the data. (1) 1.5 Calculate the standard deviation of the data. (1) 1.6 How many learners completed a number of push-ups that lies within ONE standard deviation of the mean? (2) [11] QUESTION 2 The table below shows the time (in minutes) that 70 learners spent on social media on a particular day. TIME, t (IN MINUTES) NUMBER OF LEARNERS CUMULATIVE FREQUENCY 0 ≤ t < 30 6 30 ≤ t < 60 14 60 ≤ t < 90 22 90 ≤ t < 120 18 120 ≤ t < 150 7 150 ≤ t < 180 3 2.1 Complete the cumulative frequency column in the table on the ANSWER SHEET provided. (2) 2.2 Draw an ogive (cumulative frequency graph) of the data on the grid provided on the ANSWER SHEET. (3) 2.3 Use the ogive to estimate the median time spent on social media. (2) 2.4 Calculate the estimated mean time spent on social media. (3) [10] Copyright reserved Please turn over

Mathematics/P2 4 Hlayiso/Mock 2026 NSC Mock QUESTION 3 In the diagram, A(−2 ; 5), B(4 ; 7) and C(6 ; 1) are the vertices of △ABC. M is the midpoint of AC. y B(4 ; 7) A(−2 ; 5) M C(6 ; 1) x O 3.1 Calculate the length of AC. Leave your answer in simplest surd form. (2) 3.2 Prove that AB ⊥ BC. (3) 3.3 Determine the coordinates of M. (2) 3.4 Determine the equation of the line through B that is parallel to AC. Write your answer in the form y = mx + c. (3) 3.5 Calculate the size of BÂC. (4) 3.6 Determine the coordinates of D if ABCD, in that order, is a rectangle. (2) [16] QUESTION 4 P(−3 ; −2), Q(1 ; 6) and R(5 ; k) are points in a Cartesian plane. 4.1 Determine the value of k if P, Q and R are collinear. (3) 4.2 Calculate the size of the acute angle between line PQ and the line y = −x + 4. (4) 4.3 Determine the equation of the perpendicular bisector of PQ. (4) 4.4 The point T(t ; −1) is equidistant from P and Q. Calculate the value of t. (3) [14] Copyright reserved Please turn over

Mathematics/P2 5 Hlayiso/Mock 2026 NSC Mock QUESTION 5 5.1 Given: 5 sin θ + 3 = 0 and θ ∈ [90◦ ; 270◦ ] WITHOUT using a calculator and with the aid of a diagram, determine the value of: 5.1.1 tan θ (2) 5.1.2 sin(−θ ) + cos(180◦ − θ ) (3) sin(180◦ − x) . cos(−x) . tan(360◦ − x) 5.2 Simplify fully: (6) cos(90◦ + x) . sin(90◦ + x) 5.3 Determine the value of the following expression WITHOUT using a calculator: tan 135◦ . cos 300◦ ◦ + sin2 17◦ + sin2 73◦ (4) sin 330 1 5.4 Given the identity: − cos x = sin x . tan x cos x 5.4.1 Prove the identity. (3) 5.4.2 For which values of x in the interval 0◦ ≤ x ≤ 360◦ is the identity undefined? (2) [20] QUESTION 6 6.1 Determine the general solution of: 2 sin2 x − sin x − 1 = 0 (6) 6.2 Solve for x if tan(x − 20◦ ) = 1,5 and x ∈ [0◦ ; 360◦ ]. (4) [10] QUESTION 7 Given: f (x) = sin x and g(x) = cos 2x for x ∈ [−180◦ ; 180◦ ] 7.1 Sketch the graphs of f and g on the same system of axes on the grid provided on the ANSWER SHEET. Clearly show ALL intercepts with the axes, the coordinates of the turning points and the end points of each graph. (6) 7.2 Write down the period of g. (1) 7.3 The graphs of f and g intersect at x = −90◦ , x = 30◦ and x = 150◦ . Use your graphs to determine the values of x for which f (x) > g(x). (2) 7.4 Write down the range of h if h(x) = 3g(x) + 1. (2) [11] Copyright reserved Please turn over

Mathematics/P2 6 Hlayiso/Mock 2026 NSC Mock QUESTION 8 ABCD is a quadrilateral-shaped vegetable garden at a community centre. The diagonal AC divides the garden into two triangular beds. AB = 12 m, AC = 9 m, AD = 7 m, BÂC = 58◦ and CÂD = 40◦ . D 7m 40◦ A C 9m 58◦ 12 m B 8.1 Calculate the length of BC. (3) 8.2 Calculate the size of AB̂C. (3) 8.3 Calculate the area of the garden ABCD. (3) [9] QUESTION 9 A farmer’s grain silo consists of a closed cylinder with a cone-shaped roof, as shown in the diagram. The radius of the cylinder and of the cone is 3 m. The height of the cylinder is 10 m and the perpendicular height of the cone is 4 m. 4m s 3m 10 m Volume of a cylinder = π r2 h Volume of a cone = 13 π r2 h Curved surface area of a cone = π rs 9.1 Calculate the slant height, s, of the roof. (2) 9.2 Calculate the total volume of the silo. (3) 9.3 The outside of the roof will be painted. Calculate the curved surface area of the roof. (2) [7] Copyright reserved Please turn over

Mathematics/P2 7 Hlayiso/Mock 2026 NSC Mock Give reasons for your statements in QUESTIONS 10, 11 and 12. QUESTION 10 10.1 In the diagram, O is the centre of the circle and A, B and C are points on the circle. A O B C Use the diagram to prove the theorem which states that the angle subtended by an arc at the centre of a circle is double the size of the angle subtended by the same arc at the circle, that is, prove that BÔC = 2 BÂC. (5) 10.2 In the diagram, O is the centre of the circle and ABCD is a cyclic quadrilateral. AB = BC. OA, OC and AC are drawn. D̂ = 64◦ . D 64◦ O 1 A C B Calculate, with reasons, the size of: 10.2.1 Ô1 (2) 10.2.2 AB̂C (2) 10.2.3 OÂC (3) 10.2.4 BÂC (2) [14] Copyright reserved Please turn over

Mathematics/P2 8 Hlayiso/Mock 2026 NSC Mock QUESTION 11 11.1 In the diagram, O is the centre of the circle. AB is a chord of length 24 units and OM ⊥ AB with M on AB. The radius of the circle is 13 units. OM is produced to meet the circle at N. AN is drawn. O A B M N Calculate, with reasons, the length of: 11.1.1 OM (4) 11.1.2 AN (4) 11.2 In the diagram, PAT is a tangent to the circle at A. A, D, B and C are points on the circle. AC = BC and TÂC = 70◦ . Chords AB, BC, AD and DB are drawn. C B 70◦ D P A T Calculate, with reasons, the size of: 11.2.1 AB̂C (2) 11.2.2 BÂC (2) 11.2.3 PÂB (2) 11.2.4 AD̂B (2) [16] Copyright reserved Please turn over

Mathematics/P2 9 Hlayiso/Mock 2026 NSC Mock QUESTION 12 In the diagram, A, B and C are points on the circle. TAS is a tangent to the circle at A. D is a point on AB and E is a point on AC such that DE ∥ TS. TÂB = x. T A S x D E C B 12.1 Name, with reasons, TWO other angles equal to x. (4) 12.2 Prove that DBCE is a cyclic quadrilateral. (3) 12.3 Prove that AÊD = AB̂C. (2) 12.4 If it is further given that AD̂E = AÊD, prove that AB = AC. (3) [12] TOTAL: 150 Copyright reserved Please turn over

Mathematics/P2 10 Hlayiso/Mock 2026 NSC Mock INFORMATION SHEET: MATHEMATICS GRADE 11 √ −b ± b2 − 4ac x= 2a A = P(1 + ni) A = P(1 − ni) A = P(1 − i)n A = P(1 + i)n √ ( ) x 1 + x2 y 1 + y2 d = (x2 − x1 )2 + (y2 − y1 )2 M ; 2 2 y2 − y1 y = mx + c y − y1 = m(x − x1 ) m= m = tan θ x2 − x1 a b c In △ABC : = = sin A sin B sinC a2 = b2 + c2 − 2bc. cos A area △ABC = 12 ab. sinC 2 ∑x ∑ni=1 (xi − x̄) x̄ = σ2 = 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 1 NAME: QUESTION 2.1 TIME, t (IN MINUTES) NUMBER OF LEARNERS CUMULATIVE FREQUENCY 0 ≤ t < 30 6 30 ≤ t < 60 14 60 ≤ t < 90 22 90 ≤ t < 120 18 120 ≤ t < 150 7 150 ≤ t < 180 3 QUESTION 2.2 Time spent on social media 70 60 50 Cumulative frequency 40 30 20 10 t 0 30 60 90 120 150 180 Time (in minutes) Copyright reserved

Mathematics/P2 12 Hlayiso/Mock 2026 NSC Mock ANSWER SHEET 2 NAME: QUESTION 7.1 y 1.5 1 0.5 x −180◦ −150◦ −120◦ −90◦ −60◦ −30◦ 0◦ 30◦ 60◦ 90◦ 120◦ 150◦ 180◦ −0.5 −1 −1.5 Copyright reserved