Technical Mathematics Grade 12 Term 2 June Past Papers and Memos

1. Q1 1.1 Solve for ������������: 21 marks
2. Q2 ������������2−������������+1 8 marks
3. Q3 3.1 Simplify the following WITHOUT the use of a calculator: 21 marks
4. Q4 Given: 2 and ������������2 + ������������2 = 4 35 marks
5. Q5 5.1 Convert 17% per annum compounded quarterly to the effective annual interest rate. (3) 15 marks
6. Q6 Determine ( ) using FIRST PRINCIPLES. (5) 17 marks
7. Q7 7.1 BMA Construction has been assigned to build a tunne (lOE) and a bridge (EF) in a 15 marks
8. Q8 A rectangular garden has an existing wall as one of its borders. The area of the garden is 8 marks
9. Q9 9.1 Determine the following integrals: 10 marks

Instructions to candidates

1. This question paper consists of NINE questions.
2. Answer ALL the questions in the SPECIAL ANSWER BOOK provided.
3. Number the answers correctly according to the numbering system used in this question paper.
4. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining the answers.
5. Answers only will NOT necessarily be awarded full marks.
6. You may use an approved scientific calculator (non-programmable and non- graphical), unless stated otherwise.
7. If necessary, round off answers to TWO decimal places, unless stated otherwise.
8. Diagrams are NOT necessarily drawn to scale.
9. An information sheet with formulae is included at the end of the question paper.
10. Write neatly and legibly.

1. Q1 In the diagram below, trapezium ABCD is drawn with vertices A(‒ 6 ; 7); B(9 ; 4); 17 marks
2. Q2 2.1 The diagram below shows a circle, with the centre at the origin, with equation 8 marks
3. Q3 3.1 If 25sin������ = −7 and 0° < ������ < 270°, determine with the aid of a diagram, the 11 marks
4. Q4 4.1 Simplify: cot 180°+θ .sec 360°−θ 14 marks
5. Q5 Given the functions defined by ������(������) = tan3������ and ������(������) = sin6������ for ������ ∈ [0° ;90°] 12 marks
6. Q6 The diagram below represents a cross-section of a valley. The vertical heights, KR and 12 marks
7. Q7 In the diagram below, O is the centre of the circle. AB = 14 cm; OMP ⊥ AB with M on 7 marks
8. Q8 8.1 In the diagram below, AB is a diameter in the circle with centre O and DC║AB. 16 marks
9. Q9 9.1 The diagram below shows ∆DTR. DQ = 12 cm, DT = 0,3 m, SR = 36 cm, 16 marks
10. Q10 10.1 An enclosure is in the shape of a 72° sector of a circle with a radius of 80 m. 23 marks
11. Q11 11.1 A cylindrical concrete pipe has an inner diameter of 26 cm and an outer diameter of 14 marks

Instructions to candidates

1. This question paper consists of ELEVEN questions.
2. Answer ALL the questions in the SPECIAL ANSWER BOOK provided.
3. Clearly show ALL calculations, diagrams, graphs, et cetera which you have used in determining the answers.
4. Answers only will NOT necessarily be awarded full marks.
5. You may use an approved scientific calculator (non-programmable and non- graphical) unless stated otherwise.
6. If necessary, round off your answers to TWO decimal places, unless stated otherwise.
7. Diagrams are NOT necessarily drawn to scale.
8. An information sheet with formulae is included at the end of the question paper.
9. Write neatly and legibly.

1. Q1 Question 1 24 marks
2. Q2 Question 2 7 marks
3. Q3 Question 3 21 marks
4. Q4 Question 4 28 marks
5. Q5 Question 5 15 marks
6. Q6 Question 6 17 marks
7. Q7 Question 7 15 marks
8. Q8 Question 8 8 marks
9. Q9 Question 9 15 marks

Instructions to candidates

1. This question paper consists of NINE questions. Answer ALL the questions.
2. Clearly show ALL calculations, diagrams, graphs, et cetera which you have used in determining your answers.
3. You may use an approved scientific calculator (non-programmable and non-graphical) unless stated otherwise.
4. If necessary, answers should be rounded off to TWO decimal places, unless stated otherwise.
5. Number the answers correctly according to the numbering system used in this question paper.
6. Diagrams are NOT necessarily drawn to scale.
7. An information sheet with formulae is included at the end of the question paper.
8. Write neatly and legibly.

1. Q1 1.1.2 x 7 x  9  8  0 (correct to TWO decimal places) (4) 21 marks
2. Q2 2.1 Given the equation: x 2  4  0 8 marks
3. Q3 3.1 Simplify the following without the use of a calculator: 22 marks
4. Q4 4.1 Given the function defined by h  x    4 26 marks
5. Q5 5.1 A mechanic bought a trolley jack for R10 063 and paid a deposit of R1 000. 14 marks
6. Q6 6.1 Given: f  x    8 x 22 marks
7. Q7 Given: f x    x 3  5 x 2  24 x 15 marks
8. Q8 The diagram below shows an open rectangular box with the following dimensions in 8 marks
9. Q9 9.1 Determine   5 x 9 dx. (2) 14 marks

Instructions to candidates

1. This question paper consists of NINE questions.
2. Answer ALL the questions in the SPECIAL ANSWER BOOK provided.
3. Number the answers correctly according to the numbering system used in this question paper.
4. Clearly show ALL calculations, diagrams, graphs, etc. that you have used in determining your answers.
5. Answers only will NOT necessarily be awarded full marks.
6. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise.
7. If necessary, round off answers to TWO decimal places, unless stated otherwise.
8. Diagrams are NOT necessarily drawn to scale.
9. An information sheet with formulae is included at the end of the question paper.
10. Write neatly and legibly. 2025 Copyright reserved Please turn over Technical Mathematics/P1 3 DBE/May/June 2025 SC/NSC Confidential

1. Q1 The diagram below shows RST with vertices R(2 ; 1), S(2 ; y) and T(x ; 5). 11 marks
2. Q2 2.1 In the diagram below, O is the centre of the circle KLM with vertices K(6 ; 2), 13 marks
3. Q3 3.1 Given: A  103 and B  52 16 marks
4. Q4 4.1.1 The reduction: cos 2 (180   )  ... (1) 12 marks
5. Q5 The graphs below represent the functions defined by f ( x)   2 cos x and g ( x)  cos 2 11 marks
6. Q6 The diagram below shows two triangles, NDE and CDN . 11 marks
7. Q7 In the diagram below, O is the centre of the circle DEF. 8 marks
8. Q8 8.1 In the diagram below, ABCD is a cyclic quadrilateral. 16 marks
9. Q9 In the diagram below, A, E and C are points on the circle. 14 marks
10. Q10 10.1 The picture below shows an industrial wood-sanding machine. The motor causes the 25 marks
11. Q11 11.1 The diagram below shows an irregular shape with one straight side of 72 cm, that is 13 marks

Instructions to candidates

1. This question paper consists of 11 questions.
2. Answer ALL the questions in the SPECIAL ANSWER BOOK provided.
3. Clearly show ALL calculations, diagrams, graphs, etc. that you used in determining your answers.
4. Answers only will NOT necessarily be awarded full marks.
5. If necessary, round off answers to TWO decimal places, unless stated otherwise.
6. Diagrams are NOT necessarily drawn to scale.
7. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise.
8. An information sheet with formulae is included at the end of the question paper.
9. Write neatly and legibly. 2025 Copyright reserved Please turn over Technical Mathematics/P2 3 DBE/May/June 2025 SC/NSC Confidential

1. Q1 Question 1 20 marks
2. Q2 Question 2 7 marks
3. Q3 Question 3 22 marks
4. Q4 Question 4 28 marks
5. Q5 Question 5 15 marks
6. Q6 Question 6 20 marks
7. Q7 Question 7 17 marks
8. Q8 Question 8 9 marks
9. Q9 Question 9 12 marks

1. Q1 Question 1 11 marks
2. Q2 Question 2 15 marks
3. Q3 Question 3 15 marks
4. Q4 Question 4 10 marks
5. Q5 Question 5 14 marks
6. Q6 Question 6 12 marks
7. Q7 Question 7 7 marks
8. Q8 Question 8 16 marks
9. Q9 Question 9 17 marks
10. Q10 Question 10 16 marks
11. Q11 Question 11 17 marks

1. Q1 Question 1 20 marks
2. Q2 Question 2 6 marks
3. Q3 Question 3 25 marks
4. Q4 Question 4 14 marks
5. Q6 Question 6 20 marks
6. Q7 Question 7 15 marks
7. Q8 Question 8 11 marks
8. Q9 Question 9 13 marks

1. Q1 Question 1 17 marks
2. Q2 Question 2 9 marks
3. Q3 Question 3 18 marks
4. Q4 Question 4 13 marks
5. Q5 Question 5 7 marks
6. Q6 Question 6 10 marks
7. Q7 Question 7 7 marks
8. Q8 Question 8 15 marks
9. Q9 Question 9 19 marks
10. Q10 Question 10 21 marks
11. Q11 Question 11 14 marks

1. Q1 Question 1 20 marks
2. Q2 Question 2 6 marks
3. Q3 Question 3 24 marks
4. Q4 Question 4 32 marks
5. Q5 Question 5 13 marks
6. Q6 Question 6 22 marks
7. Q7 Question 7 13 marks
8. Q8 Question 8 9 marks
9. Q9 Question 9 11 marks

1. Q1 Question 1 15 marks
2. Q2 Question 2 10 marks
3. Q3 Question 3 15 marks
4. Q4 Question 4 12 marks
5. Q5 Question 5 12 marks
6. Q6 Question 6 10 marks
7. Q7 Question 7 15 marks
8. Q8 Question 8 18 marks
9. Q9 Question 9 7 marks
10. Q10 Question 10 19 marks
11. Q11 Question 11 17 marks