Mathematics Grade 11 P1 November Mock Exam 2 2026 QP (Eng)

Mock hlayiso mock exams Practice Series: Grade 11 Exam Preparation WWW.HLAYISO.COM NATIONAL SENIOR CERTIFICATE GRADE 11 MATHEMATICS P1 NOVEMBER EXAMINATION 2026 (MOCK) MARKS: 150 TIME: 3 hours This question paper consists of 8 pages and 1 information sheet. Copyright reserved Please turn over

Mathematics/P1 2 Hlayiso/Mock 2026 NSC Mock INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of 9 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/P1 3 Hlayiso/Mock 2026 NSC Mock QUESTION 1 1.1 Solve for x: 1.1.1 x2 = 3x + 28 (2) 1.1.2 4x(x − 1) = 5 (correct to TWO decimal places) (4) 1.1.3 (x + 2)(5 − x) < 0 (3) √ 1.1.4 x− x+5 = 1 (4) 3 2 1.1.5 − =1 (x ̸= ±1) (4) x−1 x+1 1.2 Solve for x and y simultaneously: y + 3 = 2x x2 + xy = 6 (6) 1.3 Given: x2 − 2(k + 1)x + k2 + 5 = 0 Determine the values of k for which the equation has real roots. (4) [27] QUESTION 2 2.1 Simplify fully, WITHOUT using a calculator: 3x+1 . 15x−1 2.1.1 (4) 5x . 9x−1 5x+2 − 5x 2.1.2 (3) 4 . 5x+1 2.2 Solve for x: 5 2.2.1 3x 3 = 96 (3) 2.2.2 2x + 23−x = 6 (5) 1 1 2.3 Show, WITHOUT using a calculator, that √ −√ = 4. (4) 5−2 5+2 [19] Copyright reserved Please turn over

Mathematics/P1 4 Hlayiso/Mock 2026 NSC Mock QUESTION 3 3.1 Consider the linear number pattern: 47 ; 41 ; 35 ; . . . 3.1.1 Determine the general term, Tn , of the pattern. (2) 3.1.2 Determine the first negative term of the pattern and state its position in the pattern. (3) 3.2 In a school hall the chairs are arranged in rows. The first row has 18 chairs and every row after that has 4 more chairs than the row in front of it. 3.2.1 Determine a formula for the number of chairs in row n. (2) 3.2.2 The last row has 94 chairs. How many rows of chairs are there in the hall? (2) 3.2.3 Row k has three times as many chairs as row 3. Determine the value of k. (2) [11] QUESTION 4 4.1 The following quadratic number pattern is given: 40 ; 27 ; 18 ; 13 ; . . . 4.1.1 Determine the general term, Tn , of the pattern. (4) 4.1.2 Between which TWO consecutive terms of the pattern is the first difference equal to 107? (3) 4.1.3 Determine the smallest value of the terms of the pattern. Show ALL your working. (3) 4.2 The first four terms of a quadratic number pattern are: 2 ; p ; 20 ; 38 ; . . . Calculate the value of p. (4) [14] Copyright reserved Please turn over

Mathematics/P1 5 Hlayiso/Mock 2026 NSC Mock QUESTION 5 The graphs of f (x) = ax2 + bx + c and g(x) = x + 4 are drawn below. A and B(2 ; 0) are the x-intercepts of f and C(0 ; 8) is the y-intercept of f . D is the turning point of f . The graphs of f and g intersect at A and E. y D C(0 ; 8) g E A B(2 ; 0) x O f 5.1 Show that f (x) = −x2 − 2x + 8. (3) 5.2 Determine the coordinates of D. (2) 5.3 Write down the range of f . (1) 5.4 Determine the coordinates of E. (3) 5.5 Calculate the average gradient of f between D and B. (2) f (x) 5.6 For which values of x is ≤ 0? (2) g(x) 5.7 Calculate the maximum vertical distance between f and g between A and E. (3) 5.8 Determine the values of k for which f (x) = k will have two real roots that are opposite in sign. (2) [18] Copyright reserved Please turn over

Mathematics/P1 6 Hlayiso/Mock 2026 NSC Mock QUESTION 6 a The graph of f (x) = + q is drawn below. The asymptotes of f intersect at P(3 ; −1). The x+ p graph of f cuts the x-axis at K(1 ; 0). y f K(1 ; 0) O x P(3 ; −1) f 6.1 Write down the values of p and q. (2) 6.2 Show that a = −2. (2) 6.3 Determine the coordinates of the y-intercept of f . (1) 6.4 Determine the equation of the axis of symmetry of f that has a negative gradient. (2) 6.5 K is reflected in the axis of symmetry in QUESTION 6.4 to give K′ . Write down the coordinates of K′ . (2) 6.6 For which values of x is f (x) ≤ 0 ? (2) −2 6.7 Describe, in words, the transformation of f to g if g(x) = + 3. (2) x+1 [13] Copyright reserved Please turn over

Mathematics/P1 7 Hlayiso/Mock 2026 NSC Mock QUESTION 7 ( )x 1 7.1 Given: g(x) = 2 −6 3 7.1.1 Write down the equation of the asymptote of g. (1) 7.1.2 Calculate the coordinates of the intercepts of g with the axes. (3) 7.1.3 Sketch the graph of g. Clearly show the asymptote and the intercepts with the axes. (3) 7.1.4 Use your graph to write down the values of x for which g(x) ≥ 0. (1) 7.1.5 Determine the value of x for which g(x) = 12. (2) 7.1.6 The graph of h is obtained by reflecting g in the y-axis. Write down the equation of h. (1) 7.2 The graph of p(x) = a . bx + q has a horizontal asymptote y = 2 and passes through the points (0 ; 5) and (1 ; 8). Determine the values of a, b and q. (3) [14] QUESTION 8 8.1 A delivery bakkie was bought for R380 000. After 4 years its book value was R190 000. Calculate the annual rate of depreciation if the reducing-balance method was used. (3) 8.2 A bank offers an effective interest rate of 8,5% p.a. Calculate the equivalent nominal interest rate per annum, compounded monthly. (3) 8.3 Sizwe has R12 000 to invest for 4 years. He considers two options: Option A: 9,2% p.a. simple interest Option B: 8,4% p.a. compounded quarterly Which option should Sizwe choose? Show calculations to support your answer. (4) 8.4 Lerato deposited R25 000 into a savings account. One year after the initial deposit she deposited a further R8 000, and four years after the initial deposit she withdrew Rx from the account. For the first 3 years the account earned interest at 8% p.a., compounded monthly. Thereafter the interest rate changed to 9% p.a., compounded half-yearly. Six years after the initial deposit the balance in the account was R46 418,61. Calculate the value of x, the amount that Lerato withdrew. (5) [15] Copyright reserved Please turn over

Mathematics/P1 8 Hlayiso/Mock 2026 NSC Mock QUESTION 9 9.1 The two-way table below shows how 200 Grade 10 and Grade 11 learners at a school travel to school. Taxi Walk Total Grade 10 48 a 80 Grade 11 b 50 c Total 118 82 200 9.1.1 Write down the values of a, b and c. (2) 9.1.2 Are the events ‘being in Grade 10’ and ‘walking to school’ mutually exclusive? Give a reason for your answer. (2) 9.1.3 Are the events ‘being in Grade 11’ and ‘travelling by taxi’ independent? Show calculations to support your answer. (4) 9.2 A and B are independent events. It is given that P(A) = 0,6 and P(A or B) = 0,8. 9.2.1 Calculate P(B). (3) 9.2.2 Draw a Venn diagram to represent the probabilities of events A and B. (2) 9.3 Sipho travels to school by bus or by taxi. The probability that he takes the bus on any day is 0,6. If he takes the bus, the probability that he arrives late is 0,15. If he takes a taxi, the probability that he arrives late is 0,25. 9.3.1 Draw a tree diagram to represent the information. Show the probabilities associated with each branch as well as the outcomes. (3) 9.3.2 Calculate the probability that Sipho arrives late on a randomly chosen day. (3) [19] TOTAL: 150 Copyright reserved Please turn over

Mathematics/P1 9 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