Mathematics Grade 11 P1 November Mock 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 (x − 3)(2x + 1) = 0 (2) 1.1.2 2x2 − 7x = 3 (correct to TWO decimal places) (4) 1.1.3 x(x + 3) ≤ 10 (3) √ 1.1.4 2x + 7 − x = 2 (4) 1.2 Solve for x and y simultaneously: x−y+2 = 0 2x2 − xy + y2 = 8 (6) 1.3 Given: 2x2 + (p + 2)x + p = 0 Show that the roots of the equation are real and rational for all rational values of p. (4) 1.4 The length of a rectangular poster is 3 cm more than its breadth. The diagonal of the poster is 15 cm long. Calculate the breadth of the poster. (4) [27] QUESTION 2 2.1 Simplify fully, WITHOUT using a calculator: 2x+2 . 6x−1 2.1.1 (4) 12x . 3−1 √ √ 50 + 98 2.1.2 √ (3) 8 2.2 Solve for x: 3 2.2.1 x 2 = 27 (3) 2.2.2 2x+2 − 2x = 48 (3) √ 2.2.3 x−5 x+4 = 0 (4) 2.3 If 32x = 5, determine the value of 9x+1 without using a calculator. (2) [19] Copyright reserved Please turn over

Mathematics/P1 4 Hlayiso/Mock 2026 NSC Mock QUESTION 3 3.1 Consider the linear number pattern: 7 ; 3 ; −1 ; −5 ; . . . 3.1.1 Write down the next term of the pattern. (1) 3.1.2 Determine the general term, Tn , of the pattern. (2) 3.1.3 Which term of the pattern is equal to −233 ? (2) 3.2 The first three terms of a linear number pattern are: x ; 2x + 3 ; 5x ; . . . Calculate the value of x. (3) 3.3 The first term of a linear number pattern is 8 and the 20th term is 103. Determine the 50th term of the pattern. (3) [11] QUESTION 4 4.1 The following quadratic number pattern is given: −1 ; 4 ; 13 ; 26 ; . . . 4.1.1 Write down the next term of the pattern. (1) 4.1.2 Determine the general term, Tn , of the pattern. (4) 4.1.3 Which term of the pattern is equal to 1 768 ? (3) 4.1.4 Between which TWO consecutive terms of the quadratic pattern will the difference be 161? (3) 4.2 The first and third terms of a quadratic number pattern are 5 and 25 respectively. The second difference of the pattern is 6. Calculate the value of the second term. (3) [14] Copyright reserved Please turn over

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

Mathematics/P1 6 Hlayiso/Mock 2026 NSC Mock QUESTION 6 6 Given: f (x) = −2 x+1 6.1 Write down the equations of the asymptotes of f . (2) 6.2 Calculate the coordinates of the intercepts of f with the axes. (3) 6.3 Sketch the graph of f . Clearly show the asymptotes and the intercepts with the axes. (3) 6.4 Determine the equation of the axis of symmetry of f that has a positive gradient. (2) 6.5 Use your graph to determine the values of x for which f (x) ≥ 4. (2) 6.6 The graph of f is translated 3 units to the right to form the graph of h. Write down the equation of h. (1) [13] QUESTION 7 7.1 Given: f (x) = 2x+1 − 8 7.1.1 Write down the range of f . (1) 7.1.2 Calculate the coordinates of the intercepts of f with the axes. (3) 7.1.3 Sketch the graph of f . Clearly show the asymptote and the intercepts with the axes. (3) 7.1.4 The graph of g is obtained by reflecting f in the x-axis. Write down the equation of g. (1) 7.1.5 Calculate the average gradient of f between x = −1 and x = 2. (3) ( )x 7.2 The graph of k(x) = a 21 + q has a y-intercept of −1 and passes through the point (−1 ; 1). Determine the values of a and q. (3) [14] Copyright reserved Please turn over

Mathematics/P1 7 Hlayiso/Mock 2026 NSC Mock QUESTION 8 8.1 A school bought a tablet for R8 500. The tablet depreciates at 18% p.a. on the reducing-balance method. Calculate the value of the tablet after 4 years. (3) 8.2 Calculate the effective annual interest rate if interest is charged at 9,6% p.a., compounded monthly. (3) 8.3 An investment of R15 000 grew to R22 000 after 5 years. Interest was compounded annually. Calculate the annual interest rate of the investment. (3) 8.4 Naledi invested R40 000 in a savings account. Two years after the initial deposit she withdrew R10 000 and four years after the initial deposit she deposited a further R5 000. For the first 3 years interest was earned at 7,5% p.a., compounded quarterly. Thereafter the interest rate changed to 8,2% p.a., compounded monthly. Calculate the amount in the account 6 years after the initial deposit. (6) [15] Copyright reserved Please turn over

Mathematics/P1 8 Hlayiso/Mock 2026 NSC Mock QUESTION 9 9.1 For two events, A and B, it is given that: P(A) = 0,45 P(B) = 0,3 P(A and B) = 0,135 9.1.1 Are events A and B mutually exclusive? Give a reason for your answer. (2) 9.1.2 Show, by calculation, whether events A and B are independent. (2) 9.1.3 Calculate P(A or B). (2) 9.2 A survey was conducted among 100 Grade 11 learners about the messaging and social media apps they use: TikTok (T), WhatsApp (W) and Instagram (I). • 50 learners use TikTok, 70 use WhatsApp and 35 use Instagram. • 30 learners use TikTok and WhatsApp. • 20 learners use WhatsApp and Instagram. • 15 learners use TikTok and Instagram. • x learners use all three apps. • 5 learners do not use any of the three apps. 9.2.1 Draw a Venn diagram to represent the information above in terms of x. (3) 9.2.2 Show that x = 5. (2) 9.2.3 Calculate the probability that a learner, chosen at random, uses exactly TWO of the apps. (2) 9.3 A bag contains 5 red sweets and 3 blue sweets. Thandi takes a sweet out of the bag at random and eats it. She then takes a second sweet out of the bag at random. 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 both sweets are of the same colour. (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