Technical Mathematics Grade 12 Term 4 November Past Papers and Memos

1. Q1 Question 1 20 marks
2. Q2 Question 2 8 marks
3. Q3 Question 3 24 marks
4. Q4 Question 4 24 marks
5. Q5 Question 5 15 marks
6. Q6 Question 6 20 marks
7. Q7 Question 7 16 marks
8. Q8 Question 8 8 marks
9. Q9 Question 9 15 marks

1. Q1 Question 1 14 marks
2. Q2 Question 2 12 marks
3. Q3 Question 3 13 marks
4. Q4 Question 4 13 marks
5. Q5 Question 5 11 marks
6. Q6 Question 6 12 marks
7. Q7 Question 7 8 marks
8. Q8 Question 8 22 marks
9. Q9 Question 9 8 marks
10. Q10 Question 10 20 marks
11. Q11 Question 11 17 marks

1. Q1 1.1.2 3x 2 + x = 6 + 5x (correct to TWO decimal places) (4) 22 marks
2. Q2 2.1 Given: x = . Determine the numerical value(s) of p if x is: 7 marks
3. Q3 3.1 Simplify the following, showing ALL calculations, where applicable: 22 marks
4. Q4 4.1 Given functions f and h defined by f ( x) = 3 x − 1 and h ( x) = 25 − x 2 25 marks
5. Q5 5.1 The annual effective interest rate charged by a financial institution is 9,1%. Calcula 17 marks
6. Q6 6.1 Given: f (x ) = 9 x − 6 21 marks
7. Q7 The graph of function f, defined by f (x ) = x 3 + x 2 − 32 x − 60 , is drawn below. 15 marks
8. Q8 A company manufactures x bottle caps weekly and makes a profit of P rands. The relationshi 7 marks
9. Q9 9.1 Determine the following integrals: 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. Copyright reserved Please turn over Technical Mathematics/P1 3 DBE/2025 NSC Exemplar Confidential

1. Q1 ∆ PQR is reghoekig by punt P. Hoekpunte P , Q en R (6 ; ) is gegee. PQ is 16 marks
2. Q2 2.1 Die diagram hieronder verwys na ʼn sirkel met vergelyking . Die 10 marks
3. Q3 3.1 In die diagram hieronder word S( ; −3) en OS = 5 gegee.
4. Q4 ( ° (). °( )∙° ) ( ° ) [10] 14 marks
5. Q7 In die diagram hieronder, is O die middelpunt van die sirkel. AB = 24 cm; M is die 12 marks
6. Q9 9.1 In die onderstaande diagram is PV = 24 cm; VR = 22 cm en ST = 12 cm. PQ║VS en 12 marks
7. Q10 ʼn Buiteband, van ʼn motor wat op die snelweg ry, het ʼn gemiddelde rotasie van 1 500 rpm. Die 15 marks
8. Q11 11.1 Die prent en diagram hieronder verteenwoordig ʼn suurlemoen wat in die helfte gesny 18 marks

Instructions to candidates

1. Hierdie vraestel bestaan uit ELF vrae.
2. Beantwoord AL die vrae in die SPESIALE ANTWOORDEBOEK wat verskaf word.
3. Toon duidelik ALLE berekeninge, diagramme, grafieke, ensovoorts wat jy gebruik het om die antwoorde te bepaal.
4. Slegs antwoorde sal NIE noodwendig volpunte toegeken word NIE.
5. Jy mag ʼn goedgekeurde wetenskaplike sakrekenaar (nieprogrammeerbaar en niegrafies) gebruik, tensy anders vermeld.
6. Indien nodig, rond jou antwoorde tot TWEE desimale plekke af, tensy anders vermeld.
7. Diagramme is NIE noodwendig volgens skaal geteken NIE.
8. ʼn Inligtingsblad met formules is aan die einde van die vraestel ingesluit.
9. Skryf netjies en leesbaar. TEGNIESE WISKUNDE V2 3

1. Q1 Question 1 23 marks
2. Q2 Question 2 6 marks
3. Q3 Question 3 19 marks
4. Q4 Question 4 26 marks
5. Q5 Question 5 14 marks
6. Q6 Question 6 23 marks
7. Q7 Question 7 18 marks
8. Q8 Question 8 8 marks
9. Q9 Question 9 150 marks

1. Q1 Question 1 14 marks
2. Q2 Question 2 10 marks
3. Q3 Question 3 14 marks
4. Q4 Question 4 15 marks
5. Q5 Question 5 11 marks
6. Q6 Question 6 9 marks
7. Q7 Question 7 6 marks
8. Q8 Question 8 26 marks
9. Q9 Question 9 7 marks
10. Q10 Question 10 20 marks
11. Q11 Question 11 18 marks

1. Q1 Question 1 20 marks
2. Q2 Question 2 6 marks
3. Q3 Question 3 24 marks
4. Q4 Question 4 26 marks
5. Q5 Question 5 15 marks
6. Q6 Question 6 21 marks
7. Q7 Question 7 15 marks
8. Q8 Question 8 9 marks
9. Q9 Question 9 14 marks

1. Q1 Question 1 22 marks
2. Q2 Question 2 5 marks
3. Q3 Question 3 25 marks
4. Q4 Question 4 24 marks
5. Q5 Question 5 15 marks
6. Q6 Question 6 21 marks
7. Q7 Question 7 17 marks
8. Q8 Question 8 8 marks
9. Q9 Question 9 13 marks

1. Q1 Question 1 24 marks
2. Q2 Question 2 7 marks
3. Q3 Question 3 22 marks
4. Q4 Question 4 27 marks
5. Q5 Question 5 16 marks
6. Q6 Question 6 15 marks
7. Q7 Question 7 14 marks
8. Q8 Question 8 12 marks
9. Q9 Question 9 13 marks