Mathematics Grade 12 P2 NSC November Prediction 2026 QP

Prediction hlayiso mock exams Practice Series: Grade 12 NSC Preparation WWW.HLAYISO.COM NATIONAL SENIOR CERTIFICATE GRADE 12 MATHEMATICS P2 PREDICTION EXAMINATION 2026 MARKS: 150 TIME: 3 hours This question paper consists of 12 pages, 1 information sheet and a SPECIAL ANSWER BOOK. Copyright reserved Please turn over

Mathematics/P2 2 Hlayiso/Prediction 2026 NSC Prediction 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 in the SPECIAL ANSWER BOOK provided. 3. Clearly show ALL calculations, diagrams, graphs, etc. which 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

Mathematics/P2 3 Hlayiso/Prediction 2026 NSC Prediction QUESTION 1 Ten Grade 12 learners were asked how much time (in hours) they spend on social media per day. Their marks (as a percentage) in a Mathematics test were also recorded. The information is given in the table and on the scatter plot below. TIME ON SOCIAL MEDIA PER DAY 0,5 1 1,5 2 2,5 3 4 4,5 5 6 (IN HOURS) (x) MARK 84 76 79 68 71 62 55 58 46 41 (AS A %) (y) SCATTER PLOT 90 80 Mark (as a %) 70 60 50 40 30 0 1 2 3 4 5 6 Time spent on social media per day (in hours) 1.1 Determine the equation of the least squares regression line for the data. (3) 1.2 Write down the correlation coefficient. (1) 1.3 Predict the mark of a learner who spends 3,5 hours per day on social media. (2) 1.4 Explain why the least squares regression line should NOT be used to predict the mark of a learner who spends 12 hours per day on social media. (1) 1.5 Write down the standard deviation of the marks. (1) 1.6 How many learners obtained a mark that was within ONE standard deviation of the mean mark? (3) [11] Copyright reserved Please turn over

Mathematics/P2 4 Hlayiso/Prediction 2026 NSC Prediction QUESTION 2 The amounts (in rand) that 80 customers spent at a spaza shop on a particular Saturday are summarised in the frequency table below. AMOUNT SPENT (IN RAND) NUMBER OF CUSTOMERS 0 < x ≤ 50 6 50 < x ≤ 100 14 100 < x ≤ 150 25 150 < x ≤ 200 18 200 < x ≤ 250 11 250 < x ≤ 300 6 2.1 Complete the cumulative frequency column in the table provided in the ANSWER BOOK. (2) 2.2 On the grid provided in the ANSWER BOOK, draw an ogive (cumulative frequency graph) to represent the data. (3) 2.3 Use the ogive to estimate the number of customers who spent more than R220. (2) 2.4 Calculate the estimated mean amount spent per customer. (2) [9] Copyright reserved Please turn over

Mathematics/P2 5 Hlayiso/Prediction 2026 NSC Prediction QUESTION 3 In the diagram, A(−3 ; 1), B(−1 ; −3) and C(5 ; 5) are the vertices of △ABC. BC cuts the x-axis at K. The angle of inclination of BC is θ . y C(5 ; 5) A(−3 ; 1) K θ x O B(−1 ; −3) 3.1 Prove that BÂC = 90◦ . (3) 3.2 Determine the equation of BC in the form y = mx + c. (3) 3.3 Calculate the size of θ . (2) 3.4 Calculate the size of AB̂C. (3) 3.5 Calculate the area of △ABC. (3) 3.6 Determine the equation of the circle that passes through A, B and C. Write your answer in the form (x − a)2 + (y − b)2 = r2 . (3) 3.7 E(k ; 3) is a point in the first quadrant such that AE = AB. Calculate the value of k. (3) [20] Copyright reserved Please turn over

Mathematics/P2 6 Hlayiso/Prediction 2026 NSC Prediction QUESTION 4 In the diagram, M is the centre of the circle having equation x2 + y2 + 2x − 4y − 40 = 0. P(2 ; 8) is a point on the circle. R(8 ; 2) is a point outside the circle and RK is a tangent to the circle at K. y P(2 ; 8) R(8 ; 2) M x O K 4.1 Determine the coordinates of M and the length of the radius of the circle. (3) 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 RK. (3) √ 4.4 Another circle, with centre N(k ; 6) and radius 5 units, touches the given circle externally. Calculate the possible values of k. (4) 4.5 Determine the equation of the other tangent to the given circle that is parallel to the tangent at P. (3) 4.6 For which values of p will the line y = − 12 x + p cut the given circle at two distinct points? (2) [19] Copyright reserved Please turn over

Mathematics/P2 7 Hlayiso/Prediction 2026 NSC Prediction QUESTION 5 5.1 In the diagram, P(a ; −8) is a point in the Cartesian plane such that OP = 17 units. The reflex angle between OP and the positive x-axis is θ . y θ x O P(a ; −8) Without using a calculator, determine: 5.1.1 The value of a (2) 5.1.2 cos 2θ (3) 5.1.3 sin(θ + 30◦ ) (3) 5.2 Given: sin 34◦ = m Without using a calculator, express EACH of the following in terms of m: 5.2.1 cos 236◦ (2) 5.2.2 cos 68◦ (2) 5.3 Simplify the following expression to a single trigonometric ratio: 2 sin(x − 180◦ ). cos(−x) (6) sin(360◦ − x). cos(90◦ + x) + cos(180◦ + x). sin(90◦ − x) [18] QUESTION 6 sin 2x − sin x 6.1 Given: = tan x 1 + cos 2x − cos x 6.1.1 Prove the identity. (4) 6.1.2 For which values of x in the interval x ∈ [0◦ ; 360◦ ] is the identity undefined? (2) 6.2 Determine the general solution of: sin 3x. cos x − cos 3x. sin x = cos x (6) [12] Copyright reserved Please turn over

Mathematics/P2 8 Hlayiso/Prediction 2026 NSC Prediction QUESTION 7 In the diagram, the graph of f (x) = sin(x + 30◦ ) is drawn for the interval x ∈ [−180◦ ; 180◦ ]. y f 1 0,5 x −180◦ −150◦ −120◦ −90◦ −60◦ −30◦ 0 30◦ 60◦ 90◦ 120◦ 150◦ 180◦ −0,5 −1 7.1 Write down the period of g(x) = cos 2x. (1) 7.2 On the same system of axes provided in the ANSWER BOOK, draw the graph of g(x) = cos 2x for the interval x ∈ [−180◦ ; 180◦ ]. Clearly show ALL the intercepts with the axes and the coordinates of the turning points. (3) 7.3 Determine, without using a calculator, the values of x in the interval x ∈ [−180◦ ; 180◦ ] for which f (x) = g(x). (4) 7.4 Use the graphs to determine the values of x in the interval x ∈ [0◦ ; 180◦ ] for which f (x) > g(x). (2) 7.5 The graph of f is translated 120◦ to the right to form the graph of h. Determine the equation of h in its simplest form. (2) [12] Copyright reserved Please turn over

Mathematics/P2 9 Hlayiso/Prediction 2026 NSC Prediction QUESTION 8 In the diagram, AB is a vertical tower. B, C and D are points in the same horizontal plane. The angle of elevation of A from C is y. BĈD = x, BD̂C = 90◦ + x and CD = d metres. A B y x C d D d. cos x. tan y 8.1 Show that AB = (5) cos 2x 8.2 Calculate the height of the tower if d = 25 m, x = 20◦ and y = 35◦ . (2) 8.3 Calculate the area of △BCD. (2) [9] Copyright reserved Please turn over

Mathematics/P2 10 Hlayiso/Prediction 2026 NSC Prediction 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. A, B and C lie on the circle. DCE is a tangent to the circle at C. Chords AB, BC and AC and radii OB and OC are drawn. BĈE = 32◦ . A O B 32◦ D C E 9.1.1 Write down, with a reason, the size of BÂC. (2) 9.1.2 Calculate, with reasons, the size of OĈB. (3) 9.2 In the diagram, O is the centre of the circle. A, B, C and D lie on the circle such that AB = AD. DC is produced to E. OB, OD and BD are drawn. BÔD = 136◦ . A O 136◦ B D C E Calculate, with reasons, the size of: 9.2.1 BÂD (2) 9.2.2 BĈD (2) 9.2.3 AB̂D (2) 9.2.4 BĈE (2) [13] Copyright reserved Please turn over

Mathematics/P2 11 Hlayiso/Prediction 2026 NSC Prediction QUESTION 10 10.1 In the diagram, △ABC and △DEF are drawn such that  = D̂, B̂ = Ê and Ĉ = F̂. D A B C E F Use the diagram to prove the theorem which states that if two triangles are equiangular, then the corresponding sides are in proportion, that is, prove that: AB AC = (6) DE DF 10.2 In the diagram, ABC is a triangle. D, E and F are points on AB, AC and BC respectively such that DE ∥ BC and EF ∥ AB. AD : DB = 2 : 3 and DE = 8 units. A 8 D E B F C AE 10.2.1 Write down, with a reason, the value of . (2) EC 10.2.2 Calculate, with reasons, the length of BC. (3) area of △ADE 10.2.3 Calculate the value of (2) area of △ABC [13] Copyright reserved Please turn over

Mathematics/P2 12 Hlayiso/Prediction 2026 NSC Prediction QUESTION 11 In the diagram, P, Q and R lie on the circle. KPL is a tangent to the circle at P. S and T are points on the chords PQ and PR respectively such that ST ∥ KL. Let KP̂Q = x. K P L x S T Q R 11.1 Name, with reasons, TWO other angles that are each equal to x. (4) 11.2 Prove that QSTR is a cyclic quadrilateral. (2) 11.3 Prove that △PST ||| △PRQ. (3) 11.4 Hence, prove that PS.PQ = PT.PR. (2) 11.5 If PS = 4 units, SQ = 5 units and PT = 3 units, calculate the length of TR. (3) [14] TOTAL: 150 Copyright reserved Please turn over

Mathematics/P2 13 Hlayiso/Prediction 2026 NSC Prediction 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