Technical Mathematics Grade 12 P1 NSC November Mock 2026 QP

Mock hlayiso mock exams Practice Series: Grade 12 NSC Preparation WWW.HLAYISO.COM NATIONAL SENIOR CERTIFICATE GRADE 12 TECHNICAL MATHEMATICS P1 MOCK EXAMINATION 2026 MARKS: 150 TIME: 3 hours This question paper consists of 8 pages, a 2-page information sheet and 2 answer sheets. 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 NINE questions. 2. Answer ALL the questions. 3. Answer QUESTION 3.4.3 and QUESTION 4.1.4 on the ANSWER SHEETS provided. Write your centre number and examination number in the spaces provided on the ANSWER SHEETS and hand in the ANSWER SHEETS 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, etc. 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. 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 Solve for x: 1.1.1 x(3x + 8) = 0 (2) 1.1.2 2x(x − 3) = 4 (correct to TWO decimal places) (4) 1.1.3 x2 − 2x − 8 > 0 (3) 1.2 Given: 2x + y = 5 and xy − 2 = 0 1.2.1 Make y the subject of the equation 2x + y = 5. (1) 1.2.2 Hence, solve for x and y simultaneously. (5) 1.3 The power (P) dissipated in an electric heating element is given by the formula: V2 P= R Where: P = power (W) V = potential difference (V) R = resistance (Ω) 1.3.1 Make V the subject of the formula. (2) 1.3.2 Hence, calculate the numerical value of V if P = 60 W and R = 240 Ω. (2) 1.4 Express 45 as a binary number. (1) 1.5 Evaluate 1011012 + 11102 and leave your answer as a binary number. (2) [22] QUESTION 2 2.1 Given: 2x2 − 3x + 5 = 0 2.1.1 Determine the numerical value of the discriminant of the equation. (2) 2.1.2 Hence, describe the nature of the roots of the equation. (1) 2.2 Determine the numerical value(s) of p for which the equation 2x2 − px + 8 = 0 will have equal roots. (3) √ −3 ± 2p − 4 2.3 Given: x = . Determine the numerical value(s) of p if x is: p+1 2.3.1 Undefined (1) 2.3.2 Non-real (1) [8] Copyright reserved Please turn over

Technical Mathematics/P1 4 Hlayiso/Mock 2026 NSC Mock QUESTION 3 3.1 Simplify the following, showing ALL calculations, where applicable: √3 3.1.1 8x6 (1) 2x+2 · 4x 3.1.2 (3) 8x · 2 √ 3.1.3 log 8 + log 125 − log3 9 + log2 2 (4) 3.2 Solve for x: log2 (x + 2) + log2 (x − 2) = 5 (4) 3.3 Solve for x: 3x+1 − 3x = 54 (3) 3.4 Given the complex number: z = (1 + 2i)(i − 2) 3.4.1 Express z in the form a + bi. (2) 3.4.2 Write down z̄ (the conjugate of z). (1) 3.4.3 Represent z as an Argand diagram on the complex plane provided on the ANSWER SHEET. (2) 3.4.4 Express z in the form r cis θ (θ in degrees). (4) [24] QUESTION 4 4.1 Given functions f and g defined by f (x) = x2 − 2x − 3 and g(x) = x + 1. 4.1.1 Write down the y-intercept of f . (1) 4.1.2 Determine the x-intercepts of f . (2) 4.1.3 Determine the coordinates of the turning point of f . (3) 4.1.4 Draw sketch graphs of f and g on the same set of axes provided on the ANSWER SHEET. Clearly indicate ALL the intercepts with the axes and the turning point. (5) 4.1.5 Write down the range of f . (1) 4.1.6 Use your graphs to determine the values of x for which f (x) < 0. (2) Copyright reserved Please turn over

Technical Mathematics/P1 5 Hlayiso/Mock 2026 NSC Mock a 4.2 The graphs below represent functions h and k defined by h(x) = + q and k(x) = x bx + q. • h and k have the same horizontal asymptote, y = −2. • P(−1 ; 2) is a point on h and R(2 ; 7) is a point on k. • B is the x-intercept of h. y k R(2 ; 7) P(−1 ; 2) B x O h k y = −2 h 4.2.1 Write down the equations of the asymptotes of h. (2) 4.2.2 Determine the numerical value of a. (2) 4.2.3 Determine the numerical value of b. (2) 4.2.4 Determine the coordinates of B. (2) 4.2.5 Write down the range of k. (1) 4.2.6 Write down the domain of h. (1) [24] Copyright reserved Please turn over

Technical Mathematics/P1 6 Hlayiso/Mock 2026 NSC Mock QUESTION 5 5.1 A farmer bought a tractor for R480 000. The tractor depreciates at a rate of 12% per annum on the reducing-balance method. Calculate the value of the tractor at the end of 5 years. (3) 5.2 A bank offers a nominal interest rate of 9,6% per annum, compounded monthly. Calculate the annual effective interest rate. (3) 5.3 The number of learners registered on an online study platform grew from 12 000 to 20 000 over a period of 6 years. Determine the annual compound growth rate. (4) 5.4 Sipho invested R25 000 in a savings account that offered an interest rate of 8% per annum, compounded quarterly. • At the end of 2 years the interest rate changed to 9% per annum, compounded monthly. • The interest rate then remained unchanged for the remaining years. • Sipho deposited an additional R5 000 into the account at the end of the 3rd year. Determine the amount of money in the account at the end of the 5th year. (5) [15] QUESTION 6 6.1 Determine f ′ (x) from FIRST PRINCIPLES if f (x) = 2x2 − 3. (5) 6.2 Determine: dy 6.2.1 if y = 5x4 − 3x + 8 (2) dx 6 √ 6.2.2 f ′ (x) if f (x) = 2 − 3 x (3) x [ 2 ] x −9 6.2.3 Dx (3) x+3 6.3 Given: g(x) = x3 − 4x 6.3.1 Determine g′ (x). (1) 6.3.2 Hence, determine the gradient of the tangent to g at x = 1. (1) 6.3.3 Determine the equation of the tangent to g at x = 1 in the form y = mx + c. (3) 6.3.4 Determine the x-coordinates of the points on g at which the tangents to g are parallel to the line y = 8x + 1. (2) [20] Copyright reserved Please turn over

Technical Mathematics/P1 7 Hlayiso/Mock 2026 NSC Mock QUESTION 7 The graph of function f , defined by f (x) = x3 − 3x2 − 9x + 27, is drawn below. • A and B are the x-intercepts of f and C is the y-intercept of f . • D and B are the turning points of f . y D C f A x O B 7.1 Write down the coordinates of C. (1) 7.2 Show that (x + 3) is a factor of f (x). (2) 7.3 Hence, determine the coordinates of A and B. (3) 7.4 Determine the coordinates of the turning points D and B. (5) 7.5 Use the graph to determine the values of x for which f is decreasing. (2) 7.6 Determine the gradient of the tangent to f at point C. (1) [14] QUESTION 8 A pump fills a reservoir on a farm. The volume of water, V (in kilolitres), in the reservoir t hours after the pump is switched on, is given by: V (t) = −t 3 + 6t 2 + 15t + 200 , 0≤t ≤8 Determine: 8.1 The volume of water in the reservoir when the pump is switched on (1) 8.2 V ′ (t) (2) 8.3 The rate at which the volume of water is changing 2 hours after the pump is switched on (2) 8.4 The maximum volume of water in the reservoir (3) [8] Copyright reserved Please turn over

Technical Mathematics/P1 8 Hlayiso/Mock 2026 NSC Mock QUESTION 9 9.1 Determine the following integrals: ∫ 3 9.1.1 dx (2) x ∫ 9.1.2 (2x − 1)2 dx (3) ∫ ( ) √ 9.1.3 x + 2x dx (3) 9.2 The sketch below shows the graph of f defined by f (x) = −x2 + 2x + 3. • A and B are the x-intercepts of f . • The shaded area is bounded by the graph of f and the x-axis between A and B. y x A O B f 9.2.1 Determine the x-coordinates of A and B. (2) 9.2.2 Calculate the area of the shaded region. (5) [15] TOTAL: 150 Copyright reserved Please turn over

Technical Mathematics/P1 9 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 10 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 11 Hlayiso/Mock 2026 NSC Mock ANSWER SHEET CENTRE NUMBER EXAMINATION NUMBER QUESTION 3.4.3 Im 6 4 2 −6 −4 −2 Re 0 2 4 6 −2 −4 −6 Copyright reserved

Technical Mathematics/P1 12 Hlayiso/Mock 2026 NSC Mock ANSWER SHEET CENTRE NUMBER EXAMINATION NUMBER QUESTION 4.1.4 y x 0 Copyright reserved