Technical Mathematics Grade 11 P1 November Mock 2026 QP

Mock hlayiso mock exams Practice Series: Grade 11 Exam Preparation WWW.HLAYISO.COM NATIONAL SENIOR CERTIFICATE GRADE 11 TECHNICAL MATHEMATICS P1 NOVEMBER EXAMINATION 2026 (MOCK) MARKS: 150 TIME: 3 hours This question paper consists of 9 pages, a 2-page information sheet and an answer 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 EIGHT questions. 2. Answer ALL the questions. 3. Answer QUESTION 5.5 on the ANSWER SHEET provided. Write your name and the name of your school in the spaces provided on the ANSWER SHEET and hand it in with your ANSWER BOOK. 4. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your answers. 5. Answers only will NOT necessarily be awarded full marks. 6. An approved scientific calculator (non-programmable and non-graphical) may be used, unless stated otherwise. 7. If necessary, round off answers to TWO decimal places, unless stated otherwise. 8. Number the answers correctly according to the numbering system used in this question paper. 9. Diagrams are NOT necessarily drawn to scale. 10. An information sheet with formulae is included at the end of the question paper. 11. Write neatly and legibly. Copyright reserved Please turn over

Technical Mathematics/P1 3 Hlayiso/Mock 2026 NSC Mock QUESTION 1 1.1 Simplify the following WITHOUT using a calculator: 1 1.1.1 (3a2 b)0 + 8 3 (2) 3 √ x2 · x 1.1.2 (2) x−1 ( √ )2 1.1.3 2 5−1 (3) √ √ √ 1.1.4 50 + 18 − 8 (3) log3 81 − log2 18 1.1.5 (5) log 1 000 + log5 1 2x+2 − 2x 1.2 Simplify, WITHOUT using a calculator: (4) 3 · 2x−1 9x · 6x+1 1.3 Simplify, WITHOUT using a calculator: (4) 27x · 2x 1.4 Consider the binary numbers X = 1101012 and Y = 111012 . 1.4.1 Write X and Y as decimal numbers. (2) 1.4.2 Hence, or otherwise, determine X −Y as a binary number. (1) [26] QUESTION 2 2.1 Given: log 2 = a and log 3 = b Express each of the following in terms of a and b, WITHOUT using a calculator: 2.1.1 log 6 (2) 2.1.2 log 1,5 (3) 2.1.3 log 360 (4) Copyright reserved Please turn over

Technical Mathematics/P1 4 Hlayiso/Mock 2026 NSC Mock 2.2 Solve for x, WITHOUT using a calculator: 1 2.2.1 2x+1 = (3) 16 2.2.2 5x+1 + 5x = 150 (3) 2.2.3 log3 (2x − 1) = 2 (3) 2.2.4 log x + log(x − 3) = 1 (5) 2.3 Solve for x, correct to TWO decimal places: 3x = 20 (2) 2.4 The kinetic energy (E) of a moving object is given by the formula: 1 E = mv2 2 Where: E = kinetic energy (J) m = mass of the object (kg) v = speed of the object (m/s) 2.4.1 Make v the subject of the formula. (2) 2.4.2 Hence, calculate the speed of a trolley with a mass of 100 kg if its kinetic energy is 1 250 J. (2) [29] Copyright reserved Please turn over

Technical Mathematics/P1 5 Hlayiso/Mock 2026 NSC Mock QUESTION 3 3.1 Solve for x: 3.1.1 (2x − 3)(x + 4) = 0 (2) 3.1.2 3x2 − x − 5 = 0 (correct to TWO decimal places) (4) 3.1.3 x2 + 2x − 15 ≤ 0 (3) x 4 3.1.4 − =1, x ̸= 0 (4) 2 x 3.2 Solve for x and y simultaneously: y − 2x = 1 and x2 + y2 = 13 (6) 3.3 A rectangular steel plate is cut so that its length is 5 cm longer than its width, w (in cm). 3.3.1 Write down an expression, in terms of w, for the area of the plate. (1) 3.3.2 The area of the plate is 84 cm2 . Determine the length and the width of the plate. (4) 3.3.3 A circular hole with area A is drilled into the plate. The area of a circle is given by A = π r2 . Make r the subject of the formula. (2) [26] QUESTION 4 4.1 Determine the nature of the roots of 2x2 −7x+3 = 0 WITHOUT solving the equation. (3) √ 4± k−2 4.2 The roots of a quadratic equation are given by: x = k+3 Determine the value(s) of k for which the roots are: 4.2.1 Undefined (1) 4.2.2 Non-real (1) 4.2.3 Equal (1) 4.3 Determine the value(s) of p for which the equation x2 + px + 9 = 0 will have equal roots. (2) [8] Copyright reserved Please turn over

Technical Mathematics/P1 6 Hlayiso/Mock 2026 NSC Mock QUESTION 5 4 √ Given the functions defined by f (x) = − 2 and g(x) = 16 − x2 . x 5.1 Write down the equations of the asymptotes of f . (2) 5.2 Determine the x-intercept of f . (2) 5.3 Determine the x-intercepts of g. (2) 5.4 Write down the y-intercept of g. (1) 5.5 Sketch the graphs of f and g on the same set of axes on the ANSWER SHEET provided. Clearly indicate ALL the intercepts with the axes and the asymptotes. (6) 5.6 Write down the domain of g. (1) 5.7 Write down the range of g. (1) 5.8 Write down the range of f . (1) 5.9 Use your graph to determine the values of x for which f (x) > 0. (2) 5.10 Determine the x-coordinate of the point on f where f (x) = 2. (2) [20] Copyright reserved Please turn over

Technical Mathematics/P1 7 Hlayiso/Mock 2026 NSC Mock QUESTION 6 The sketch below represents the graph of the function f defined by f (x) = bx − 9. • The graph passes through the point P(1 ; −6). • C is the y-intercept and E is the x-intercept of f . y f O x E P(1 ; −6) C 6.1 Write down the equation of the asymptote of f . (1) 6.2 Determine the numerical value of b. (2) 6.3 Determine the coordinates of C. (2) 6.4 Determine the coordinates of E. (2) 6.5 Write down the range of f . (1) 6.6 The graph of f is reflected about the x-axis to form the graph of g. Write down the equation of g. (2) 6.7 Use the graph to write down the values of x for which f (x) < 0. (1) [11] Copyright reserved Please turn over

Technical Mathematics/P1 8 Hlayiso/Mock 2026 NSC Mock QUESTION 7 The sketch below represents the graphs of the functions f and g defined by f (x) = −x2 + 2x + 8 and g(x) = x + 2. • A and D are the x-intercepts of f . • C is the turning point of f . • The graphs of f and g intersect at A and B. y C g B A D x O f 7.1 Determine the coordinates of A and D. (3) 7.2 Determine the coordinates of the turning point, C. (3) 7.3 Determine the coordinates of B. (3) 7.4 Use the graphs to determine the values of x for which f (x) ≥ g(x). (2) 7.5 Write down the range of f . (1) 7.6 The graph of f is shifted 3 units down to form the graph of h. Write down the coordinates of the turning point of h. (1) [13] Copyright reserved Please turn over

Technical Mathematics/P1 9 Hlayiso/Mock 2026 NSC Mock QUESTION 8 8.1 Thandi invested R12 000 at a simple interest rate of 7,5% per annum. Calculate the amount in the account at the end of 4 years. (3) 8.2 Determine the effective annual interest rate if the nominal interest rate is 9% per annum, compounded quarterly. (3) 8.3 A minibus taxi depreciates at a rate of 12% per annum on the reducing-balance method. After 5 years its book value is R210 000. Determine the price of the taxi when it was new. (3) 8.4 Lerato deposits R40 000 into a savings account that pays interest at 8% per annum, compounded monthly. • At the end of the 2nd year she withdraws R10 000 to pay for a welding course. • The interest rate then changes to 9% per annum, compounded half-yearly, for the remaining time. 8.4.1 Calculate the amount in the account at the end of the 2nd year, BEFORE the withdrawal. (3) 8.4.2 Calculate the amount in the account at the end of the 5th year. (5) [17] TOTAL: 150 Copyright reserved Please turn over

Technical Mathematics/P1 10 Hlayiso/Mock 2026 NSC Mock INFORMATION SHEET: TECHNICAL MATHEMATICS √ −b ± b2 − 4ac b 4ac − b2 x= x=− y= 2a 2a 4a a = b ⇔ x = loga b , a > 0 , a ̸= 1 and b > 0 x A = P(1 + ni) A = P(1 − ni) A = P(1 + i)n A = P(1 − i)n ( ) i m ieff = 1 + −1 m f (x + h) − f (x) f ′ (x) = lim h→0 h ∫ ∫ xn+1 k kxn dx = k · +C , n ̸= −1 dx = k · ln x +C , x>0 n+1 x ∫ anx k anx dx = k · +C , a>0 n ln a √ ( ) x2 + x1 y2 + y1 d = (x2 − x1 )2 + (y2 − y1 )2 M ; 2 2 y2 − y1 y = mx + c y − y1 = m(x − x1 ) m= tan θ = m x2 − x1 x2 y2 + =1 a2 b2 a b c In △ABC : = = a2 = b2 + c2 − 2bc · cos A sin A sin B sinC 1 Area of △ABC = ab · sinC 2 sin2 θ + cos2 θ = 1 1 + tan2 θ = sec2 θ 1 + cot2 θ = cosec2 θ Copyright reserved

Technical Mathematics/P1 11 Hlayiso/Mock 2026 NSC Mock π rad = 180◦ Angular velocity = ω = 2π n where n = rotation frequency Angular velocity = ω = 360◦ n where n = rotation frequency Circumferential velocity = v = π Dn where D = diameter and n = rotation frequency Circumferential velocity = v = ω r where ω = angular velocity and r = radius Arc length = s = rθ where r = radius and θ = central angle in radians rs Area of a sector = where r = radius and s = arc length 2 r2 θ Area of a sector = where r = radius and θ = central angle in radians 2 4h2 − 4dh + x2 = 0 where h = height of segment, d = diameter of circle and x = length of chord o1 + o2 AT = a (m1 + m2 + m3 + . . . + mn ) where a = width of equal parts, m1 = , 2 on = nth ordinate and n = number of ordinates OR ( ) o1 + on AT = a + o2 + o3 + . . . + on−1 where a = width of equal parts, on = nth ordinate and n 2 = number of ordinates Copyright reserved

Technical Mathematics/P1 12 Hlayiso/Mock 2026 NSC Mock ANSWER SHEET NAME AND SURNAME: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SCHOOL: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . QUESTION 5.5 y 6 4 2 x −6 −4 −2 0 2 4 6 −2 −4 −6 Copyright reserved