Technical Mathematics Grade 11 P1 2026 QP (Eng)

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: ( )− 2 27 3 1.1.1 + 160,75 (3) 8 18x · 4x+1 1.1.2 (4) 24x · 3x−1 (√ √ )2 3 + 12 1.1.3 √ (3) 27 √ 1 log2 8 + log3 27 1.1.4 (5) log 0,01 × log4 2 2 log 6 − log 4 − log 0,9 1.2 Prove, WITHOUT using a calculator, that: √ =2 (5) log 10 1.3 Consider the binary numbers 11012 and 1012 . 1.3.1 Calculate 11012 × 1012 . Leave your answer as a binary number and show ALL working. (2) 1.3.2 Convert your answer to QUESTION 1.3.1 to a decimal number, WITHOUT using a calculator. (2) 1.4 A copper wire used in a transformer coil has a circular cross-section with a diameter of 0,5 mm. Use the formula A = π r2 to calculate the cross-sectional area of the wire in m2 . Give your answer in scientific notation, correct to TWO decimal places. (2) [26] QUESTION 2 5x+1 − 5x−1 2.1 Show, WITHOUT using a calculator, that: = 2,4 (4) 2 · 5x 2.2 Solve for x, WITHOUT using a calculator: 3 2.2.1 2x 2 − 54 = 0 (3) 2.2.2 22x − 6 · 2x + 8 = 0 (5) √ 2.2.3 x+7−x = 1 (5) 2.2.4 log2 (x + 2) + log2 (x − 5) = 3 (6) Copyright reserved Please turn over

Technical Mathematics/P1 4 Hlayiso/Mock 2026 NSC Mock 2.3 Solve for x, correct to TWO decimal places: 5x−1 = 40 (2) 2.4 The period of a simple pendulum, used to time a mechanical clock, is given by: √ L T = 2π g Where: T = period of one complete swing (s) L = length of the pendulum (m) g = gravitational acceleration (m/s2 ) 2.4.1 Make L the subject of the formula. (2) 2.4.2 Hence, calculate the length of a pendulum with a period of 1,8 s if g = 9,8 m/s2 . (2) [29] QUESTION 3 3.1 Solve for x: 3.1.1 x(2x + 1) = 15 (3) 3 3.1.2 2x − =4, x ̸= 0 (correct to TWO decimal places) (4) x 3.1.3 6 + x − x2 < 0 and represent the solution on a number line (4) 3.2 Solve for x and y simultaneously: 3x + y = 5 and x2 + xy + y2 = 7 (6) Copyright reserved Please turn over

Technical Mathematics/P1 5 Hlayiso/Mock 2026 NSC Mock 3.3 A closed cylindrical water tank is made from sheet metal. The total outer surface area (A) of the tank is given by: A = 2π r2 + 2π rh where r is the radius and h is the height of the tank, both in metres. 3.3.1 Make h the subject of the formula. (2) 3.3.2 Calculate the height of a tank with a radius of 0,4 m that uses 4,5 m2 of sheet metal. (3) 3.3.3 A second tank must have a height of 1,2 m and must use exactly 6 m2 of sheet metal. Calculate the radius of this tank. (4) [26] QUESTION 4 4.1 Determine the nature of the roots of 4x2 = 12x − 9 WITHOUT solving the equation. (3) 4.2 Determine the value(s) of k for which the equation kx2 − 6x + 3 = 0 will have real roots. (3) 4.3 Show that the roots of x2 − (p + 1)x + p = 0 are real and rational for ALL real values of p. (2) [8] Copyright reserved Please turn over

Technical Mathematics/P1 6 Hlayiso/Mock 2026 NSC Mock QUESTION 5 ( )x 3 1 Given the functions defined by f (x) = − + 1 and g(x) = − 2. x 2 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 coordinates of the x- and y-intercepts of g. (3) 5.4 Write down the equation of the asymptote 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 Determine the equation of the axis of symmetry of f that has a negative gradient. (2) 5.7 Write down the range of g. (1) 5.8 Use your graph to determine the values of x for which f (x) ≤ 0. (2) 5.9 The graph of g is reflected about the y-axis to form the graph of h. Write down the equation of h in the form h(x) = ax + q. (1) [20] Copyright reserved Please turn over

Technical Mathematics/P1 7 Hlayiso/Mock 2026 NSC Mock QUESTION 6 √ The sketch below represents the graphs of the semicircle g(x) = − r2 − x2 and the straight line h. • The semicircle passes through the point P(−3 ; −4). • A and B are the x-intercepts and C is the y-intercept of g. • The line h passes through B and C. y h A O x B P(−3 ; −4) g C 6.1 Determine the equation of g. (2) 6.2 Write down the coordinates of A, B and C. (2) 6.3 Determine the equation of h. (2) 6.4 Write down the range of g. (1) 6.5 Use the graphs to determine the values of x for which g(x) ≥ h(x). (2) 6.6 Calculate the length of BC. (2) [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) = ax2 + bx + c and g(x) = 2x − 10. • T (2 ; −9) is the turning point of f and C(0 ; −5) is the y-intercept of f . • A and D are the x-intercepts of f . • The graphs of f and g intersect at D and E. y f g A O D x C(0 ; −5) E T (2 ; −9) 7.1 Determine the values of a, b and c. (3) 7.2 Determine the coordinates of A and D. (3) 7.3 Determine the coordinates of E. (3) 7.4 Use the graphs to determine the values of x for which f (x) < g(x). (2) 7.5 Determine the values of k for which f (x) + k = 0 will have NO real roots. (2) [13] Copyright reserved Please turn over

Technical Mathematics/P1 9 Hlayiso/Mock 2026 NSC Mock QUESTION 8 8.1 Sipho buys an air compressor for his panel-beating business on hire purchase. The cash price of the compressor is R8 400. He pays a 10% deposit and repays the balance in equal monthly instalments over 2 years. Simple interest is charged at 12,5% per annum on the balance. 8.1.1 Calculate the deposit that Sipho pays. (1) 8.1.2 Calculate Sipho’s monthly instalment. (3) 8.2 A 3D printer bought for R45 000 has a book value of R18 000 after 6 years. Depreciation is calculated on the reducing-balance method. Calculate the annual rate of depreciation. (3) 8.3 Calculate how many years it will take for R20 000 to grow to R35 000 if it is invested at 7,5% per annum, compounded monthly. (3) 8.4 Nomvula invests R60 000 in an account that pays interest at 9,6% per annum, compounded monthly. • At the end of the 3rd year she deposits a further R15 000 into the account, and the interest rate changes to 10% per annum, compounded quarterly. • At the end of the 4th year she withdraws R8 000 to buy tools. 8.4.1 Calculate the effective annual interest rate for the first 3 years. (2) 8.4.2 Calculate the amount in the account at the end of the 6th 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