Mathematics Grade 10 P1 November Mock 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 WITHOUT √ using a calculator, determine between which TWO consecutive integers 58 lies. (2) 1.2 Simplify fully: 1.2.1 (2x − 3)(x2 + x − 4) (3) x2 − 9 2x − 4 1.2.2 × (4) x +x−6 2 x−3 3x+2 − 3x 1.2.3 (3) 4 . 3x−1 1.3 Factorise fully: 1.3.1 2x2 + x − 15 (2) 1.3.2 x3 − 27 + 2x − 6 (3) [17] QUESTION 2 2.1 Solve for x: 2.1.1 3x2 = 5x + 2 (3) 2.1.2 5x+1 = 0,04 (3) 2.2 Solve for x and represent your solution on a number line: −4 < 2 − 3x ≤ 11 (4) 2.3 Solve for x and y simultaneously: 3x + 2y = 7 and x − 4y = 14 (4) [14] Copyright reserved Please turn over

Mathematics/P1 4 Hlayiso/Mock 2026 NSC Mock QUESTION 3 3.1 Consider the linear number pattern: 5 ; 9 ; 13 ; 17 ; . . . 3.1.1 Write down the next TWO terms of the pattern. (1) 3.1.2 Determine the general term, Tn , of the pattern. (2) 3.1.3 Calculate the value of the 40th term. (2) 3.1.4 Which term of the pattern is equal to 297? (2) 3.2 Matches are used to build the pattern of squares below. Diagram 1 Diagram 2 Diagram 3 3.2.1 How many matches are needed to build Diagram 5? (1) 3.2.2 Determine a formula for the number of matches, Tn , needed to build Diagram n. (2) 3.2.3 Thabo has a box of 150 matches. Determine the number of the largest diagram that he can build completely, and how many matches will be left over. (3) [13] QUESTION 4 4.1 Lerato wants to invest R12 000 for 4 years. She has two options: Option A: 8,5% p.a. simple interest Option B: 7,8% p.a. interest, compounded annually 4.1.1 Calculate the value of her investment after 4 years if she chooses Option A. (2) 4.1.2 Calculate the value of her investment after 4 years if she chooses Option B. (2) 4.1.3 Which option should Lerato choose? Give a reason for your answer. (1) 4.2 The cash price of a fridge is R9 600. Sipho buys the fridge on hire purchase. He pays a 10% deposit and the balance is paid off over 3 years at a simple interest rate of 14% p.a. Calculate Sipho’s monthly instalment. (4) 4.3 A 2-litre bottle of milk costs R32,99 in 2026. Calculate what the same bottle of milk is expected to cost in 2030 if the average rate of inflation is 5,2% p.a. (2) [11] Copyright reserved Please turn over

Mathematics/P1 5 Hlayiso/Mock 2026 NSC Mock QUESTION 5 The graphs of f (x) = ax2 + q and g(x) = mx + c are drawn below. A(4 ; 0) and C are the x-intercepts of f . B is the turning point of f and lies on the y-axis at (0 ; 8). The graph of g passes through A and D(0 ; 4). The graphs of f and g intersect at A and E. y B(0 ; 8) E D(0 ; 4) C A(4 ; 0) x O g f 5.1 Show that a = − 12 and q = 8. (3) 5.2 Determine the equation of g. (2) 5.3 Calculate the coordinates of E. (4) 5.4 Write down the range of f . (1) 5.5 For which values of x is f increasing? (1) 5.6 For which values of x is f (x) ≥ g(x) ? (2) 5.7 The graph of f is translated 3 units downwards to form the graph of h. 5.7.1 Write down the equation of h. (1) 5.7.2 Write down the range of h. (1) [15] Copyright reserved Please turn over

Mathematics/P1 6 Hlayiso/Mock 2026 NSC Mock QUESTION 6 6 Given: f (x) = +2 x 6.1 Write down the equations of the asymptotes of f . (2) 6.2 Calculate the coordinates of the x-intercept of f . (2) 6.3 Sketch the graph of f . Clearly show the asymptotes and the intercept(s) with the axes. (3) 6.4 Write down the domain of f . (1) [8] QUESTION 7 The graph of g(x) = bx + q is drawn below. The graph cuts the y-axis at (0 ; −2) and passes through the point P(2 ; 6). The line y = −3 is the asymptote of g. y g P(2 ; 6) O x (0 ; −2) y = −3 7.1 Write down the value of q. (1) 7.2 Show that b = 3. (2) 7.3 Calculate the coordinates of the x-intercept of g. (2) 7.4 Write down the range of g. (1) 7.5 The graph of h is obtained by reflecting the graph of g in the y-axis. Write down the equation of h. (1) [7] Copyright reserved Please turn over

Mathematics/P1 7 Hlayiso/Mock 2026 NSC Mock QUESTION 8 8.1 A and B are two events such that: P(A) = 0,35 ; P(B) = 0,4 and P(A or B) = 0,75. 8.1.1 Show, by calculation, that events A and B are mutually exclusive. (2) 8.1.2 Are events A and B complementary? Give a reason for your answer. (2) 8.2 120 Grade 10 learners at a school in Soweto were asked whether they take part in team sport (T) and whether they sing in the school choir (C). • 70 learners take part in team sport. • 45 learners sing in the choir. • x learners take part in team sport AND sing in the choir. • 25 learners do neither of the two activities. 8.2.1 Draw a Venn diagram to represent the information above in terms of x. (3) 8.2.2 Show that x = 20. (2) 8.2.3 Calculate the probability that a learner, chosen at random: (a) Takes part in team sport only (2) (b) Does NOT sing in the choir (2) 8.3 A spinner with coloured sections was spun 80 times. It landed on red 28 times. 8.3.1 Determine the relative frequency of the spinner landing on red. (1) 8.3.2 Predict how many times the spinner will land on red if it is spun 200 times. (1) [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