Technical Mathematics Grade 10 P1 November Mock 2026 QP

Mock hlayiso mock exams Practice Series: Grade 10 Exam Preparation WWW.HLAYISO.COM NATIONAL SENIOR CERTIFICATE GRADE 10 TECHNICAL MATHEMATICS P1 NOVEMBER EXAMINATION 2026 (MOCK) MARKS: 100 TIME: 2 hours This question paper consists of 6 pages and a 1-page diagram sheet. Copyright reserved Please turn over

Technical 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 SEVEN questions. 2. Answer ALL the questions. 3. Answer QUESTIONS 6.1 and 6.2 on the DIAGRAM SHEET provided. Write your name and class on the DIAGRAM SHEET and hand it in with your ANSWER BOOK. 4. Number the answers correctly according to the numbering system used in this question paper. 5. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your answers. 6. Answers only will NOT necessarily be awarded full marks. 7. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 8. If necessary, round off answers to TWO decimal places, unless stated otherwise. 9. Diagrams are NOT necessarily drawn to scale. 10. Write neatly and legibly. Copyright reserved Please turn over

Technical Mathematics/P1 3 Hlayiso/Mock 2026 NSC Mock QUESTION 1 √ 1.1 Between which TWO consecutive integers does 75 lie? (2) 1.2 State whether each of the following numbers is rational, irrational or non-real: √ 1.2.1 −9 (1) √ 1.2.2 12 (1) 1.3 Write 45 as a binary number. (2) 1.4 Determine the sum of 10112 and 1102 . Leave your answer in binary form. (2) 1.5 The thickness of a copper sheet used in a heat exchanger is 0,000 458 m. Write this thickness in scientific notation. (1) √ 1.6 Determine the product of (2 − i)(3 + 4i), where i = −1. Write your answer in the form a + bi. (3) [12] QUESTION 2 2.1 Determine the product and simplify: (2x − 3)(x + 5) − x(x − 1) (3) 2.2 Factorise the following expressions completely: 2.2.1 3x2 − 27 (2) 2.2.2 2x2 − 5x − 3 (2) 2.2.3 xy − 2y + 3x − 6 (2) 2.2.4 8m3 − 1 (2) x2 − 4 x+2 2.3 Simplify fully: ÷ (4) x +x−6 x+3 2 ( )2 2a3 b · 3a−2 2.4 Simplify, WITHOUT using a calculator: (3) 6a4 b [18] Copyright reserved Please turn over

Technical Mathematics/P1 4 Hlayiso/Mock 2026 NSC Mock QUESTION 3 3.1 Simplify, WITHOUT using a calculator: 5x+1 − 5x 3.1.1 (3) 4 · 5x 2x · 4x+1 3.1.2 (3) 8x 3.2 Logarithms 3.2.1 Write 25 = 32 in logarithmic form. (1) 3.2.2 Use the definition of a logarithm to determine, WITHOUT using a calculator, the value of: log3 81 + log 100 (2) [9] QUESTION 4 4.1 Solve for x: 4.1.1 x2 − x − 12 = 0 (3) x+1 x−2 4.1.2 − =2 (3) 2 3 1 4.1.3 3x+2 = (3) 9 4.2 Solve the following inequality and represent your answer on a number line: −3 ≤ 2x + 1 < 7 (3) 4.3 Solve for x and y simultaneously: x + 2y = 7 and 3x − y = 7 (4) 4.4 The final velocity (v) of a vehicle that accelerates uniformly is given by the formula: v = u + at Where: u = initial velocity (m/s) a = acceleration (m/s2 ) t = time (s) Make a the subject of the formula. (2) 4.5 An electrician cuts a 12 m length of electrical cable into TWO pieces. One piece is 2,4 m longer than the other piece. Determine the length of EACH piece. (3) [21] Copyright reserved Please turn over

Technical Mathematics/P1 5 Hlayiso/Mock 2026 NSC Mock QUESTION 5 5.1 Sipho invests R8 500 at a simple interest rate of 6,5% per annum. Calculate the amount in his account at the end of 3 years. (3) 5.2 Lindiwe invests R8 500 at 6,2% per annum, compounded annually, for 3 years. 5.2.1 Calculate the amount in Lindiwe’s account at the end of 3 years. (3) 5.2.2 Whose investment (Sipho’s or Lindiwe’s) is better after 3 years? Give a reason for your answer. (1) 5.3 A small engineering workshop buys a welding machine that costs R14 800. A deposit of 10% is paid in cash. The balance is paid off on a hire-purchase agreement at 16% per annum simple interest over 2 years, in equal monthly instalments. 5.3.1 Calculate the deposit. (1) 5.3.2 Calculate the total amount that must be repaid on the hire-purchase loan, including interest. (3) 5.3.3 Calculate the monthly instalment. (2) 5.4 A motor mechanic imports a diagnostic scanner from the USA for US$450. The exchange rate is US$1 = R18,40. Calculate the cost of the scanner in rand. (2) [15] QUESTION 6 Given the functions defined by f (x) = −x2 + 4 and g(x) = x + 2. 6.1 Complete the table on the DIAGRAM SHEET provided. (3) 6.2 Draw the graphs of f and g on the same set of axes on the DIAGRAM SHEET provided. Clearly show ALL the intercepts with the axes and the turning point. (5) 6.3 Write down: 6.3.1 The coordinates of the turning point of f (1) 6.3.2 The range of f (1) 6.3.3 The domain of g (1) 6.4 Use your graphs to determine the value(s) of x for which: 6.4.1 f (x) = g(x) (2) 6.4.2 f (x) > g(x) (2) [15] Copyright reserved Please turn over

Technical Mathematics/P1 6 Hlayiso/Mock 2026 NSC Mock QUESTION 7 k Sketched below are the graphs of the functions defined by f (x) = and g(x) = bx − 1. x • The graphs of f and g intersect at the point P(2 ; 3). • The graph of g passes through the origin. y g P(2 ; 3) f x O f 7.1 Determine the value of k. (2) 7.2 Determine the value of b. (2) 7.3 Write down the equation of the asymptote of g. (1) 7.4 Write down the range of f . (1) 7.5 Write down the range of g. (1) 7.6 The point Q(−3 ; y) lies on the graph of f . Determine the value of y. (1) 7.7 Write down the value(s) of x for which f (x) < 0. (1) 7.8 Write down the value(s) of x, where x > 0, for which g(x) > f (x). (1) [10] TOTAL: 100 Copyright reserved Please turn over

Technical Mathematics/P1 7 Hlayiso/Mock 2026 NSC Mock DIAGRAM SHEET NAME: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CLASS: . . . . . . . . . . . . . . . . QUESTION 6.1 x −3 −2 −1 0 1 2 3 f (x) g(x) QUESTION 6.2 y 5 4 3 2 1 x −4 −3 −2 −1 0 1 2 3 4 −1 −2 −3 −4 −5 Copyright reserved