Mathematics Grade 12 P2 NSC November Mock 2026 QP (Eng)

Mock hlayiso mock exams Practice Series: Grade 12 NSC Preparation WWW.HLAYISO.COM NATIONAL SENIOR CERTIFICATE GRADE 12 MATHEMATICS P2 MOCK EXAMINATION 2026 MARKS: 150 TIME: 3 hours This question paper consists of 10 pages and 1 information sheet. 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 11 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. An information sheet with formulae is included at the end of the question paper. 10. Write neatly and legibly. Copyright reserved Please turn over

Mathematics/P2 3 Hlayiso/Mock 2026 NSC Mock QUESTION 1 The number of hours that ten Grade 12 learners spent studying for a Mathematics test and the percentage that each learner obtained in the test are shown in the table below. NUMBER OF 2 3 4 5 6 7 8 9 10 12 HOURS (x) TEST 41 45 52 50 61 58 70 66 79 84 SCORE (%) (y) 1.1 Determine the equation of the least squares regression line. (3) 1.2 Predict the test score of a learner who studied for 11 hours. (2) 1.3 Write down the value of the correlation coefficient. (1) 1.4 Comment on the strength of the relationship between the number of hours spent studying and the test score. (1) 1.5 Explain why it would NOT be reliable to use the regression line to predict the test score of a learner who studied for 25 hours. (2) [9] QUESTION 2 2.1 The table below shows the time (in minutes) that 40 learners took to complete a puzzle. TIME, t (IN MINUTES) FREQUENCY 10 ≤ t < 20 4 20 ≤ t < 30 9 30 ≤ t < 40 14 40 ≤ t < 50 8 50 ≤ t < 60 5 2.1.1 Write down the modal class of the data. (1) 2.1.2 Calculate the estimated mean time taken to complete the puzzle. (3) 2.1.3 Draw an ogive (cumulative frequency graph) to represent the data. (3) 2.1.4 Use the ogive to estimate the number of learners who took longer than 45 minutes to complete the puzzle. (2) 2.2 The mean of a set of eight scores is 15 and the standard deviation is 2,5. Each score is increased by 4. Write down the new mean and the new standard deviation. (2) [11] Copyright reserved Please turn over

Mathematics/P2 4 Hlayiso/Mock 2026 NSC Mock QUESTION 3 In the diagram, A(−3 ; 4), B(5 ; 8) and C(1 ; −4) are the vertices of △ABC. M is the midpoint of BC. y B(5 ; 8) A(−3 ; 4) M x O C(1 ; −4) 3.1 Calculate the length of AB. Leave your answer in simplest surd form. (2) 3.2 Prove that AB ⊥ AC. (3) 3.3 Determine the coordinates of M. (2) 3.4 Give a reason why M is the centre of the circle passing through A, B and C. (1) 3.5 Determine the equation of the line through A that is parallel to BC. (3) 3.6 Calculate the size of AB̂C. (4) 3.7 Calculate the area of △ABC. (2) 3.8 Determine the coordinates of D if ABDC, in that order, is a square. (2) [19] Copyright reserved Please turn over

Mathematics/P2 5 Hlayiso/Mock 2026 NSC Mock QUESTION 4 In the diagram, the circle with centre M has equation x2 + y2 − 6x + 4y − 12 = 0. P(6 ; 2) is a point on the circle. The tangent to the circle at P cuts the y-axis at T. y T P(6 ; 2) x O M 4.1 Determine the coordinates of M and the length of the radius of the circle. (4) 4.2 Determine the equation of the tangent to the circle at P in the form y = mx + c. (4) 4.3 Calculate the length of PT. (3) 4.4 Calculate the size of the angle of inclination of the tangent PT. (2) 4.5 For which values of p will the line y = p NOT intersect the circle? (2) 4.6 Another circle with equation (x + 5)2 + (y − k)2 = 25 touches the given circle externally. Calculate the possible values of k. (4) [19] Copyright reserved Please turn over

Mathematics/P2 6 Hlayiso/Mock 2026 NSC Mock QUESTION 5 5.1 If sin 23◦ = p, express EACH of the following in terms of p, without using a calculator: 5.1.1 sin 203◦ (2) 5.1.2 cos 23◦ (2) 5.1.3 cos 46◦ (2) 5.2 Simplify fully, without using a calculator: sin(180◦ + x) . cos(90◦ − x) . tan(−x) (6) cos(360◦ − x) . sin(−x) [12] QUESTION 6 1 − cos 2x 6.1 Given the identity: = tan x sin 2x 6.1.1 Prove the identity. (4) 6.1.2 For which values of x in the interval 0◦ ≤ x ≤ 180◦ is the identity undefined? (2) 6.2 Determine the general solution of: cos 2x + 3 sin x = 2 (6) 6.3 √ − B) and cos(A + B) to show, without using a calculator, Use the expansions of cos(A 2 that cos 15◦ − cos 75◦ = . (3) 2 [15] QUESTION 7 Given: f (x) = sin 2x and g(x) = cos x for x ∈ [−180◦ ; 180◦ ] 7.1 Solve for x if f (x) = g(x) for x ∈ [−180◦ ; 180◦ ]. (4) 7.2 Sketch the graphs of f and g on the same system of axes for x ∈ [−180◦ ; 180◦ ]. Clearly show ALL intercepts with the axes and the coordinates of the turning points. (5) 7.3 Use your graphs to determine the values of x in the interval x ∈ [0◦ ; 180◦ ] for which f (x) ≥ g(x). (3) 7.4 Write down the range of h(x) = 2g(x) + 1. (2) [14] Copyright reserved Please turn over

Mathematics/P2 7 Hlayiso/Mock 2026 NSC Mock QUESTION 8 In the diagram, AB is a vertical cellphone tower of height h metres. B, C and D lie in the same horizontal plane. The angle of elevation from C to the top of the tower, A, is α . BĈD = x and BD̂C = y. A h B α x y D C 8.1 Express BC in terms of h and α . (2) h sin x 8.2 Hence, show that BD = (2) tan α . sin y 8.3 Calculate the length of BD if h = 30 m, α = 40◦ , x = 65◦ and y = 50◦ . (2) [6] Give reasons for your statements in QUESTIONS 9, 10 and 11. QUESTION 9 9.1 In the diagram, O is the centre of the circle and ABCD is a cyclic quadrilateral. A D O B C Use the diagram to prove the theorem which states that the opposite angles of a cyclic quadrilateral are supplementary, that is, prove that  + Ĉ = 180◦ . (5) Copyright reserved Please turn over

Mathematics/P2 8 Hlayiso/Mock 2026 NSC Mock 9.2 In the diagram, O is the centre of the circle and AB is a diameter. C is a point on the circle. The tangent to the circle at C meets BA produced at T. AB̂C = 28◦ . C 28◦ T B A O Calculate, with reasons, the size of: 9.2.1 AĈB (2) 9.2.2 TĈA (2) 9.2.3 T̂ (3) [12] Copyright reserved Please turn over

Mathematics/P2 9 Hlayiso/Mock 2026 NSC Mock QUESTION 10 10.1 In the diagram, △ABC is drawn with D on AB and E on AC such that DE ∥ BC. A D E B C Use the diagram to prove the theorem which states that a line drawn parallel to one side of a triangle divides the other two sides proportionally, that is, prove that: AD AE = (6) DB EC 10.2 In the diagram, D and E are points on sides AB and AC of △ABC respectively, such that DE ∥ BC. F is a point on BC and AF cuts DE at G. AD : DB = 3 : 2, BF = 10 units and BC = 30 units. A G D E B C F Calculate, with reasons: AE 10.2.1 (2) EC 10.2.2 The length of DG (3) 10.2.3 The length of GE (3) Area of △ADE 10.2.4 (3) Area of △ABC [17] Copyright reserved Please turn over

Mathematics/P2 10 Hlayiso/Mock 2026 NSC Mock QUESTION 11 In the diagram, PT is a tangent to the circle at T. PAB is a secant of the circle with A between P and B. C is a point on the circle such that TC ∥ PB. TA, TB and CB are drawn. T C P A B 11.1 Prove that △PTA ||| △PBT. (4) 11.2 Hence, show that PT2 = PA . PB. (1) 11.3 If PA = 4 units and AB = 5 units, calculate the length of PT. (2) 11.4 Prove that PT̂A = CT̂B. (3) 11.5 Prove that TA = CB. (4) Area of △PTA 11.6 Use the information in QUESTION 11.3 to calculate the value of (2) Area of △PBT [16] TOTAL: 150 Copyright reserved Please turn over

Mathematics/P2 11 Hlayiso/Mock 2026 NSC Mock INFORMATION SHEET √ −b ± b2 − 4ac x= 2a A = P(1 + ni) A = P(1 − ni) A = P(1 − i)n A = P(1 + i)n n[ ] Tn = a + (n − 1)d Sn = 2a + (n − 1)d 2 a (r − 1) n a Tn = ar n−1 Sn = ; r ̸= 1 S∞ = ; −1 < r < 1 r−1 1−r x [(1 + i)n − 1] x [1 − (1 + i)−n ] F= P= i i f (x + h) − f (x) f ′ (x) = lim h→0 h √ ( ) x1 + x2 y1 + y2 d = (x2 − x1 ) + (y2 − y1 ) 2 2 M ; 2 2 y2 − y1 y = mx + c y − y1 = m(x − x1 ) m= m = tan θ x2 − x1 (x − a)2 + (y − b)2 = r2 a b c In △ABC : = = a2 = b2 + c2 − 2bc. cos A sin A sin B sinC area △ABC = 12 ab. sinC sin(α + β ) = sin α . cos β + cos α . sin β sin(α − β ) = sin α . cos β − cos α . sin β cos(α + β ) = cos α . cos β − sin α . sin β cos(α − β ) = cos α . cos β + sin α . sin β   cos α − sin α 2 2 cos 2α = 1 − 2 sin2 α sin 2α = 2 sin α . cos α   2 cos2 α − 1 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) ∑(x − x̄)(y − ȳ) ŷ = a + bx b= ∑(x − x̄)2 Copyright reserved