Technical Mathematics Grade 10 P1 2026 QP (Eng)

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 7 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 Consider the following numbers: √ √ −25 π 3 ; 64 ; ; 0,3̇ Which ONE of the numbers above is: 1.1.1 Irrational (1) 1.1.2 Non-real (1) √ 1.2 Between which TWO consecutive integers does − 40 lie? (2) 1.3 Determine the product of 1011012 and 112 . Leave your answer in binary form. (3) 1.4 A roll of fibre-optic cable is 2,5 × 103 m long. It is cut into short connector pieces, each 5 × 10−2 m long. Determine, WITHOUT using a calculator, how many pieces can be cut from the roll. Write your answer in scientific notation. (2) √ 1.5 Simplify (3 − 2i)2 , where i = −1. Write your answer in the form a + bi. (3) [12] QUESTION 2 2.1 Determine the product and simplify: (x − 3)(x2 + 3x + 9) − x(x − 2)2 (4) 2.2 Factorise the following expressions completely: 2.2.1 2x4 − 32 (3) 2.2.2 3x2 + 5x − 12 (2) 2.2.3 x3 − 2x2 − 9x + 18 (3) 2.2.4 27 + 8a3 (2) 2 8 2.3 Simplify fully: − 2 (4) x−2 x −4 [18] Copyright reserved Please turn over

Technical Mathematics/P1 4 Hlayiso/Mock 2026 NSC Mock QUESTION 3 3.1 Simplify, WITHOUT using a calculator: 6x+1 · 2x−1 3.1.1 (4) 12x 2x+2 − 2x 3.1.2 (3) 3 · 2x−1 √ ( )2 64a6 · 2a−1 3 3.2 Simplify, WITHOUT using a calculator: (2) [9] QUESTION 4 4.1 Solve for x: 15 4.1.1 x−2 = , x ̸= 0 (3) x 4.1.2 3 · 2x+1 = 96 (3) 4.2 Solve the following inequality and represent your answer on a number line: 3 − 2x −1 < ≤3 (4) 5 4.3 A school’s electrical workshop buys supplies from a hardware store. One order of 4 light switches and 3 plugs costs R174. A second order of 2 light switches and 5 plugs costs R164. Let the price of ONE light switch be x rand and the price of ONE plug be y rand. Set up a pair of equations and solve them simultaneously to determine the price of ONE light switch and ONE plug. (5) 4.4 The power dissipated in a resistor is given by the formula: V2 P= R Where: P = power (W) V = voltage (V) R = resistance (Ω) Make V the subject of the formula. (2) 4.5 A delivery van leaves a depot at 07:00 and travels along a straight road at a constant speed of 80 km/h. At 07:30 a motorcyclist leaves the same depot and follows the van along the same road at a constant speed of 100 km/h. At what time will the motorcyclist catch up with the van? (4) [21] Copyright reserved Please turn over

Technical Mathematics/P1 5 Hlayiso/Mock 2026 NSC Mock QUESTION 5 5.1 Determine how much money Ayanda must invest now at 7,5% per annum, compounded annually, so that the investment grows to R20 000 after 4 years. (3) 5.2 The graph below shows the value of Thandi’s savings over a period of time. The interest rate stays the same over the whole period. Value (in rand) R6 600 R5 000 Time (in years) 0 1 2 3 4 5 6 5.2.1 Write down the amount that Thandi invested at the start. (1) 5.2.2 Is the interest earned on Thandi’s savings simple or compound interest? Give a reason for your answer. (2) 5.2.3 Hence, calculate the annual interest rate. (3) 5.3 A panel-beating business buys an air compressor with a cash price of R12 600. A cash deposit of 15% is paid. The balance is financed by a hire-purchase agreement at 14% per annum simple interest. The loan is repaid in equal monthly instalments over 18 months. 5.3.1 Calculate the amount of the loan. (2) 5.3.2 Calculate the monthly instalment. (3) 5.3.3 Calculate the total amount that the business will pay for the compressor. (1) [15] Copyright reserved Please turn over

Technical Mathematics/P1 6 Hlayiso/Mock 2026 NSC Mock QUESTION 6 ( )x 4 1 Given the functions defined by f (x) = − and g(x) = − 2. x 2 6.1 Complete the tables on the DIAGRAM SHEET provided. (3) 6.2 Sketch 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 asymptotes. (5) 6.3 Write down: 6.3.1 The equation of the asymptote of g (1) 6.3.2 The range of g (1) 6.3.3 The domain of f (1) 6.4 Determine, algebraically, the x-intercept of g. (2) 6.5 Use your graphs to determine the values of x, where x < 0, for which f (x) > g(x). (2) [15] Copyright reserved Please turn over

Technical Mathematics/P1 7 Hlayiso/Mock 2026 NSC Mock QUESTION 7 Sketched below are the graphs of the functions defined by f (x) = ax2 + q and g(x) = mx + c. • A and B(2 ; 0) are the x-intercepts of f , and C(0 ; −8) is the turning point of f . • The graph of g passes through B and has a y-intercept at D(0 ; 4). • The graphs of f and g intersect at B and at E. y E f D(0 ; 4) x A O B(2 ; 0) g C(0 ; −8) 7.1 Write down the value of q. (1) 7.2 Determine the value of a. (2) 7.3 Determine the equation of g. (2) 7.4 Determine, algebraically, the coordinates of E. (3) 7.5 Write down the range of f . (1) 7.6 Write down the length of CD. (1) [10] TOTAL: 100 Copyright reserved Please turn over

Technical Mathematics/P1 8 Hlayiso/Mock 2026 NSC Mock DIAGRAM SHEET NAME: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CLASS: . . . . . . . . . . . . . . . . QUESTION 6.1 x −4 −2 −1 1 2 4 f (x) x −3 −2 −1 0 1 2 g(x) QUESTION 6.2 y 7 6 5 4 3 2 1 x −5 −4 −3 −2 −1 0 1 2 3 4 5 −1 −2 −3 −4 −5 −6 Copyright reserved