Mathematics Grade 10 P1 November Mock Exam 2 2026 QP (Eng)

Mock hlayiso mock exams Practice Series: Grade 10 Exam Preparation WWW.HLAYISO.COM NATIONAL SENIOR CERTIFICATE GRADE 10 MATHEMATICS P1 NOVEMBER EXAMINATION 2026 (MOCK) MARKS: 100 TIME: 2 hours This question paper consists of 7 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 8 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 Simplify fully: 1.1.1 (3x − 2)2 − (x + 4)(x − 4) (2) 3 x − 10 1.1.2 − 2 (4) x+2 x −4 6x+1 . 2x+1 1.1.3 (3) 12x . 3 1 1.2 If a − = 3, determine, WITHOUT solving for a, the value of: a 1 1.2.1 a2 + (2) a2 1 1.2.2 a4 + (1) a4 1.3 Factorise fully: 1.3.1 3x3 − 12x (2) 1.3.2 25 − x2 + 6xy − 9y2 (3) [17] QUESTION 2 2.1 Solve for x: 2.1.1 x(3x − 1) = 10 (3) 2.1.2 2x+2 + 2x = 40 (3) 2x + 1 x − 2 2.2 Given: − <2 3 2 2.2.1 Solve for x. (3) 2.2.2 Write down the largest integer that satisfies the inequality. (1) 2.3 The Grade 10 learners at a school in Mthatha sold braai packs at R45 each and boerewors rolls at R25 each at a fundraising day. They sold 160 items altogether and collected R5 200. Let x be the number of braai packs and y the number of boerewors rolls sold. Set up a pair of equations and solve them simultaneously to determine how many of each item were sold. (4) [14] Copyright reserved Please turn over

Mathematics/P1 4 Hlayiso/Mock 2026 NSC Mock QUESTION 3 3.1 The first three terms of a linear number pattern are: 5x − 1 ; 3x + 4 ; 4x − 3 ; . . . 3.1.1 Show that x = 4. (3) 3.1.2 Hence, determine the general term, Tn , of the pattern. (2) 3.1.3 Which term of the pattern is equal to −131? (2) 3.1.4 Determine the value of the first term of the pattern that is negative. (2) 3.2 A learner writes the word LIMPOPO over and over again, without spaces: LIMPOPOLIMPOPOLIMPOPOLIMPOPO … 3.2.1 Which letter will be in the 250th position? (2) 3.2.2 How many times will the letter O appear in the first 250 letters? (2) [13] QUESTION 4 4.1 Nomsa buys a laptop with a cash price of R14 500 on hire purchase. The conditions of the agreement are: • A deposit of 15% of the cash price must be paid. • Simple interest of 18% p.a. is charged on the balance. • The loan must be paid off in equal monthly instalments over 2 years. • A compulsory insurance premium of R85 per month is added to each instalment. 4.1.1 Calculate the balance owing after Nomsa has paid the deposit. (2) 4.1.2 Calculate Nomsa’s total monthly payment. (4) 4.2 Sizwe will spend 4 nights in a hotel in New York that charges $135 per night. Calculate the total cost of his stay in rand if the exchange rate is $1 = R17,85. (2) 4.3 An amount of money was invested 5 years ago at 9% p.a. interest, compounded annually. The investment is now worth R23 000. Calculate the amount that was invested. (3) [11] Copyright reserved Please turn over

Mathematics/P1 5 Hlayiso/Mock 2026 NSC Mock QUESTION 5 a The graphs of f (x) = + q and g(x) = mx + c are drawn below. x • The asymptotes of f are the y-axis and the line y = −2. • P(4 ; −1) is a point on f . • A is the x-intercept of f . The graph of g passes through A and C(0 ; −4). • The graphs of f and g intersect at A and E. y f g O A x P(4 ; −1) y = −2 f C(0 ; −4) E 5.1 Write down the value of q. (1) 5.2 Show that a = 4. (2) 5.3 Calculate the coordinates of A. (2) 5.4 Determine the equation of g. (2) 5.5 Calculate the coordinates of E. (4) 5.6 For which values of x is f (x) ≥ g(x) ? (3) 5.7 The graph of k is obtained by reflecting the graph of f in the x-axis. Write down the equation of k. (1) [15] Copyright reserved Please turn over

Mathematics/P1 6 Hlayiso/Mock 2026 NSC Mock QUESTION 6 1 Given: p(x) = x2 − 2 2 6.1 Calculate the x-intercepts of p. (2) 6.2 Sketch the graph of p. Clearly show the turning point and the intercepts with the axes. (2) 6.3 Write down the range of p. (1) 6.4 For which values of k will the equation p(x) = k have NO real solutions? (1) 6.5 Determine the equation of the straight line that passes through the turning point of p and the positive x-intercept of p. (2) [8] QUESTION 7 Given: h(x) = −2x + 4 7.1 Write down the range of h. (1) 7.2 Calculate the coordinates of the x-intercept of h. (2) 7.3 Sketch the graph of h. Clearly show the asymptote and the intercepts with the axes. (3) 7.4 For which values of x is h(x) > 3 ? (1) [7] Copyright reserved Please turn over

Mathematics/P1 7 Hlayiso/Mock 2026 NSC Mock QUESTION 8 8.1 Events A and B are such that P(A) = 0,45, P(B) = 0,3 and P(A and B) = 0,12. 8.1.1 Calculate P(A or B). (2) 8.1.2 Draw a Venn diagram to represent the probabilities of ALL the regions in the sample space. (3) 8.1.3 Are events A and B mutually exclusive? Give a reason for your answer. (1) 8.2 A group of 50 learners in Polokwane was asked whether they use TikTok (T) or WhatsApp (W). • 28 learners use TikTok. • 22 learners use WhatsApp. • 7 learners use neither TikTok nor WhatsApp. 8.2.1 Calculate the number of learners who use BOTH TikTok and WhatsApp. (2) 8.2.2 Draw a Venn diagram to represent the information above. (3) 8.2.3 Calculate the probability that a learner, chosen at random, uses exactly ONE of the two apps. (2) 8.3 C and D are complementary events and P(C) = 2P(D). Determine P(D). (2) [15] TOTAL: 100 Copyright reserved Please turn over

Mathematics/P1 8 Hlayiso/Mock 2026 NSC Mock INFORMATION SHEET: MATHEMATICS GRADE 10 A = P(1 + ni) A = P(1 − ni) A = P(1 − i)n A = P(1 + i)n √ ( ) x1 + x2 y1 + y2 d = (x2 − x1 )2 + (y2 − y1 )2 M ; 2 2 y2 − y1 y = mx + c m= x2 − x1 ∑x ∑ fx x̄ = x̄ = n n n(A) P(A) = P(A or B) = P(A) + P(B) − P(A and B) n(S) Copyright reserved