Mathematics Grade 12 Term 2 June Past Papers and Memos

1. Q1 Algebra, equations and inequalities1.1.1 x(x−3)+2(x−3)=0 (2) 24 marks
2. Q2 Number patterns, sequences and series2.1 are the first three terms of a geometric sequence. 12 marks
3. Q3 Number patterns, sequences and series3.1 The following information of a quadratic pattern is given: 13 marks
4. Q4 Functions and graphsGiven the function 6 , where ������ ∈ ℝ 10 marks
5. Q5 Functions and graphsThe sketch below represents the graphs of f (x) = −2x +8x+10 and . A is the 15 marks
6. Q6 Functions and graphsThe graphs of y ==f (x) log x , −1 are drawn below. f passes through the point 8 marks
7. Q7 Finance, growth and decay7.1 Tom deposits R5 000 into a savings account. The interest rate is 9% p.a. compounded 14 marks
8. Q8 Differential calculus8.1 Determine , from first principles, if . (4) 15 marks
9. Q9 Functions and graphsGiven: f x = x −3x −9x−5. 16 marks
10. Q10 Functions and graphsGiven: h()x = −x +bx +cx, with P −−1; a turning point of h . The graph of h 7 marks
11. Q11 Probability and counting• P(A or B)’ = 0,2775 16 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, 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 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. Number the answers correctly according to the numbering system used in this question paper.
10. Write neatly and legibly.

1. Q1 StatisticsThe box and whisker plot below summarises the results obtained by CLASS A and 9 marks
2. Q2 StatisticsOn a particular day, 28 residents of a certain community went to a health care facility 10 marks
3. Q3 Analytical geometryIn the diagram below, MQ is parallel to the y-axis. PR is perpendicular to QS. N lies on QS. 22 marks
4. Q4 Analytical geometryIn the diagram below, O (1; q) is the centre of the circle. M is the midpoint of chord AB. EA 19 marks
5. Q5 TrigonometryIn the diagram below, sin = 5 where 90  180 and point S(a ; b) is in the 15 marks
6. Q6 TrigonometryGiven: 2sin3 A−sin 2AcosA =−4tan2A 13 marks
7. Q7 TrigonometryThe graph of f (x) = cosxis drawn in the interval of x−[ 90 ;270 ]. 13 marks
8. Q8 TrigonometryIn the diagram below, HC is the vertical pole mounted on the ground ACB. HC =3,5m, 10 marks
9. Q9 Euclidean geometryIn the diagram below, points A, B, C, D and E lie on the circumference of the circle. TAN 11 marks
10. Q10 Euclidean geometryIn the diagram below, ∆PQS and ∆PST are drawn. AB VS and ˆ . , 9 marks
11. Q11 Euclidean geometry11.1 In the diagram below, A = R , ˆ and ˆ . 19 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. 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 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 Algebra 27 marks
2. Q2 Sequences and Series 21 marks
3. Q3 Question 3 9 marks
4. Q4 Functions and Graphs 16 marks
5. Q5 Question 5 17 marks
6. Q6 Question 6 14 marks
7. Q7 Question 7 11 marks
8. Q8 Question 8 14 marks
9. Q9 Question 9 7 marks
10. Q10 Question 10 14 marks

Instructions to candidates

1. This question paper consists of 10 questions.
2. Answer ALL the questions.
3. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your 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 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. Number the answers correctly according to the numbering system used in this question paper.
10. Write neatly and legibly.

1. Q4 Mark out of 27 marks Mark out of 29 marks
2. Q8 Out of 11 marks Out of 14 marks
3. Q9 Mark out of 13 Mark out of 15

1. Q1 1.1.2 3x 2  6 x  1  0 (correct to TWO decimal places) (3) 25 marks
2. Q2 2.1 Given the arithmetic series: 5 + 7 + 9 + … + 93 18 marks
3. Q3 Given the quadratic sequence: 14 ; 9 ; 6 ; 5 ; … 9 marks
4. Q4 The graph of f ( x)   4 is drawn below. M is the point where the asymptotes of f 15 marks
5. Q5 The graph of f ( x)  a( x  p) 2  q is drawn below. C(– 1 ; 4) is the turning point of f 9 marks
6. Q6 The graphs of f ( x)  p x  q and g ( x)  mx  c are drawn below. A(3 ; 4) is the point 11 marks
7. Q7 7.1 John invests an amount of money in an account paying interest at a rate of 15% p.a., 13 marks
8. Q8 8.1 Determine f /(x) from first principles if it is given that f ( x)  x 2  2 (5) 17 marks
9. Q9 Given: f ( x)  x 3  6 x 2  9 x  4  ( x  4)( x  k ) 2 18 marks
10. Q10 10.1 A and B are mutually exclusive events. 8 marks
11. Q11 Consider the three-digit numbers from 501 up to 999. 7 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. which you have used in determining your 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 answers correct 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. 2025 Copyright reserved Please turn over Mathematics/P1 3 DBE/May/June 2025 SC/NSC Confidential

1. Q1 An insurance broker signed contracts with 15 people. The monthly premium (in rands) payabl 9 marks
2. Q2 The manager of a supermarket decided to do a survey on the number of items that a customer 10 marks
3. Q3 In the diagram below, ∆SRT is drawn where R lies on the x-axis and S lies to the left of R 21 marks
4. Q4 In the diagram, M is the centre of the circle having equation ( x  3) 2  y 2  25. E(–1 20 marks
5. Q5 5.1 If cos    where 180    360 , determine, without using a calculator, the 19 marks
6. Q6 6.1 Prove that 2 cos 2 (45  x)  1  sin 2 x . (4) 13 marks
7. Q7 In the diagram, the graphs of f ( x)  2 cos x  1 and g ( x)  sin 2 x are drawn for the 10 marks
8. Q8 In the diagram, A, B and C lie in the same horizontal plane with AB = AC. D is directly 8 marks
9. Q9 9.1 In the diagram, ∆DEF is drawn. Line GH intersects DF and EF at G and H 20 marks
10. Q10 10.1 In the diagram, ∆ABC and ∆PKL are drawn such that   P̂, B̂  K̂ and Ĉ  L̂. 20 marks

Instructions to candidates

1. This question paper consists of 10 questions.
2. Answer ALL the questions in the SPECIAL ANSWER BOOK provided.
3. Clearly show ALL calculations, diagrams, graphs, etc. which you have used in determining your 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 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. 2025 Copyright reserved Please turn over Mathematics/P2 3 DBE/May/June 2025 SC/NSC Confidential

1. Q1 Algebra, equations and inequalities1.1.2 2 (correct to TWO decimal places) (3) 25 marks
2. Q2 Number patterns, sequences and series2.1 Given the following arithmetic sequence: 2;−3;−8; ... 18 marks
3. Q3 Number patterns, sequences and seriesConsider the following quadratic number pattern: 3 ; 12 ; 33 ; . . . 7 marks
4. Q4 Functions and graphsThe diagram below shows the graphs of f (x) = 2 +1 and g(x)=a(x+2)2−8. 18 marks
5. Q5 Functions and graphsIn the diagram below, the graphs of f(x) = 3 and g(x) = −������ + 1 are given. 12 marks
6. Q6 Finance, growth and decay6.1 The purchase price of machinery bought by a company 5 years ago was R80 000. 13 marks
7. Q7 Differential calculus7.1 Determine , from first principles, if f ()x = 2 x . (4) 10 marks
8. Q8 Differential calculusGiven: f x =−x3+12x−16 20 marks
9. Q9 Differential calculusIn the diagram below, ABCD is a square with side length CD = 200 cm. PQRS is a rectangle 9 marks
10. Q10 Probability and counting10.1 Events A and B are independent events. It is further given that: 18 marks

Instructions to candidates

1. This question paper consists of 10 questions.
2. Answer ALL the questions.
3. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your 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 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. Number the answers correctly according to the numbering system used in this question paper.
10. Write neatly and legibly.

1. Q1 StatisticsThe maximum daily temperatures in Bloemfontein for the first 11 days in January were 12 marks
2. Q2 StatisticsIn a certain school, the analysis of mathematics matric results in percentages were represented 8 marks
3. Q3 Analytical geometryIn the diagram below, A (–2 ; p), B( –4 ; 0), C(–1 ; –3) and D(4 ; –1) are the vertices of a trapezium. 18 marks
4. Q4 Analytical geometryIn the diagram below, a circle with centre C 3;–1 and a radius of 10 units is drawn. PQR and PT 23 marks
5. Q5 Euclidean geometryIf sin14 = p, without using a calculator, determine the values of the following in terms 29 marks
6. Q6 Trigonometry6.1 Sketch the graphs of f (x) =3sin x and g(x) = tan 2 x in the interval of 12 marks
7. Q7 TrigonometryIn the diagram below, PQ is a vertical pole having height h metres. R, Q and T are three points 9 marks
8. Q8 Analytical geometryIn the diagram below, the circle having centre O, passes through U, T, S and V. PUK is a tangent 17 marks
9. Q9 Euclidean geometry9.1 In ∆ABC below, M is a point on AB and N is a point on AC, such that MN || BC. 12 marks
10. Q10 Euclidean geometryIn the diagram below, A, B, C and D are points on the circumference of the circle. PC and QC 10 marks

Instructions to candidates

1. This question paper consists of 10 questions.
2. Answer ALL the questions in the SPECIAL ANSWER BOOK provided.
3. Clearly show ALL calculations, diagrams, graphs, etc. 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 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.
8. Write neatly and legibly.

1. Q1 Algebra, equations and inequalities1.1.2 x−50+ = (correct to TWO decimal places) (4) 24 marks
2. Q2 Number patterns, sequences and seriesGiven the following geometric series: 24 2 17 marks
3. Q3 Number patterns, sequences and seriesConsider the following quadratic number pattern: 95 ; 72 ; y ; 32 ; . . . 11 marks
4. Q4 Functions and graphsThe diagram below shows the graphs of f (x) = 5 +q and g(x)=5x2 +10x+3. 19 marks
5. Q5 Functions and graphsh(x) = ax; a 0 and a 1  13 marks
6. Q6 Finance, growth and decay6.1 A school bought computers for R980 000. The value of the computers depreciates 13 marks
7. Q7 Differential calculus7.1 Determine , from first principles, if . (4) 11 marks
8. Q8 Functions and graphsGiven: 32 . A, and are the 20 marks
9. Q9 A large cruise ship uses fuel at a cost of 4x rand per hour, where x is the speed of the ship 8 marks
10. Q10 Probability and counting10.1 Events A and B are mutually exclusive. It is further given that: 14 marks

Instructions to candidates

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

1. Q1 StatisticsBetween 05:00 and 06:00 on New Year’s Day, 11 minibus taxis were stopped at a 8 marks
2. Q2 StatisticsWorking dads help working moms with housework. 12 marks
3. Q3 Analytical geometry3.1 The straight-line y = 3x − 3 is perpendicular to the straight line which cuts the 21 marks
4. Q4 Analytical geometryIn the diagram below, circle x + y = 16 intersects the straight-line PQ, which is defined by 18 marks
5. Q5 TrigonometryIf 5cos������ − 3 = 0 ; 180 < ������ < 360 and 17sin������ = 8 ; 90 < ������ < 270 , 28 marks
6. Q6 TrigonometryIn the diagram below, the function ������ x = tan������ − 1 is drawn for the interval [−180 ;180 ]. 12 marks
7. Q7 TrigonometryIn the figure below, OA is a vertical tower and the points K and T are in the same 11 marks
8. Q8 Analytical geometry8.1 In the diagram below, O is the centre of the circle passing through A, B and C. 17 marks
9. Q9 Euclidean geometryRefer to the diagram below. O is the centre of the circle. E, F, G and H are on the 6 marks
10. Q10 Euclidean geometryIn the diagram below, ED is a tangent to the circle passing through A, C and E. F is the 17 marks

Instructions to candidates

1. This question paper consists of 10 questions.
2. Answer ALL the questions in the SPECIAL ANSWER BOOK provided.
3. Clearly show ALL calculations, diagrams, graphs, etc. 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 answers to TWO decimal places, unless stated otherwise.
7. Write neatly and legibly. 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 Algebra, equations and inequalities1.1 Solve for x, in each of the following: 24 marks
2. Q2 Number patterns, sequences and series2.1 Given the geometric sequence: 9 ; 9 ;18 ; ... ; 2304 19 marks
3. Q3 Number patterns, sequences and seriesThe following figure represents a pattern of shaded triangles placed on a white rectangular 8 marks
4. Q4 Functions and graphs4.1 Write down the domain of f. (2) 13 marks
5. Q5 Functions and graphsf (x) = 2(x+1)2 −8 and g(x)= 16 marks
6. Q6 Finance, growth and decay6.1 How long must R50 000 be invested, in order for it to double at an interest rate of 13 marks
7. Q7 Differential calculus7.1 Determine  from first principles if f (x) = −2x + x . 12 marks
8. Q8 Functions and graphsThe sketch below represents the functions 32 . 19 marks
9. Q9 Differential calculusIn the figure below, ABE has a base of length x metres. 10 marks
10. Q10 Probability and counting10.1 In a survey, 1 530 people were asked if they had ever broken a limb. The results of 16 marks

Instructions to candidates

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

1. Q1 1.1 Solve for x, in each of the following: 24 marks
2. Q2 Sequences and Series2.1 Given the geometric sequence: 9 ; 9 ;18 ; ... ; 2304 19 marks
3. Q3 The figure below represents a pattern of shaded triangles placed on a white rectangular board. 8 marks
4. Q4 Analytical Geometry4.1 Write down the domain of f . (2) 13 marks
5. Q5 Functions and GraphsThe graphs of f (x)  2(x1) 8 and g(x) are represented in the sketch below. 16 marks
6. Q6 Finance6.1 For how long must R50 000 be invested, so that it can double, at an interest rate of 13 marks
7. Q7 fx() f (x)  2x  x 12 marks
8. Q8 Analytical GeometryThe sketch below represents the functions f x  x bx cxd and g(x)  axq . 19 marks
9. Q9 In the figure below, ABE has a base of x metres. 10 marks
10. Q10 10.1 In a survey, 1 530 people were asked whether they had ever broken a limb. The 16 marks

Instructions to candidates

1. This question paper consists of 10 questions. Answer ALL the questions.
2. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your answers.
3. Answers only will not necessarily be awarded full marks. m
4. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. co . cs
5. If necessary, round-off answers to TWO decimal places, unless stated otherwise. i s
6. Diagrams are NOT necessarily drawn to scale. hy p
7. An information sheet, with formulae, is included at the end of the question paper. e r o
8. Number the answers correctly according to the numbering system used in this question paper. m n
9. Write neatly and legibly. t a s m ro f d de a lo n w do P.T.O. MATHEMATICS 3 (PAPER 1) 06/22

1. Q1 StatisticsThe box and whisker diagrams below show the Mathematics results of class A and class B 5 marks
2. Q2 StatisticsA group of 30 pupils was asked to complete an obstacle course at their Grade 11 camp. The 8 marks
3. Q3 StatisticsConsider the following set of four positive whole numbers and their frequency. 6 marks
4. Q4 Analytical geometryIn the diagram below, the coordinates of A −4;5 ,C −1;−4 and B(4;1) are the vertices 24 marks
5. Q5 Analytical geometryIn the figure below, M is the common centre of two circles. The larger circle has equation 16 marks
6. Q6 Trigonometry6.1 If cos26 = . Determine the following in terms of ������. 24 marks
7. Q7 TrigonometryGiven: f ������ = sin ������ − 30 and g ������ = cos3������. 17 marks
8. Q8 TrigonometryRefer to the figure shown below. PQRS forms a straight road with TQ another road that 9 marks
9. Q9 Euclidean geometry9.1 Complete the statement: The angle at the ... is equal to two times the angle at the 15 marks
10. Q10 Euclidean geometryIn the diagram below, P, Q and R are points on a circle. YR bisects PRQ with Y on PQ. 9 marks
11. Q11 Euclidean geometry11.1 In the diagram below D and E are points on sides AB and AC of ∆ ������������������ such that 17 marks

Instructions to candidates

1. This question paper consists of ELEVEN questions. Answer ALL the questions in the SPECIAL ANSWER BOOK provided.
2. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your answer.
3. You may use an approved scientific calculator (non-programmable and non- graphical), unless stated otherwise.
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. Number the answers correctly according to the numbering system used in this question paper.
8. An information sheet with formulae is included at the end of the question paper.
9. Write neatly and legibly.

1. Q1 Analytical geometryIn the diagram below, A −1;4 , B 2;−2 and C −4;1 are three points in a 24 marks
2. Q2 Analytical geometryIn the diagram, QP and QR are the tangents to the circle from Q 2;−3 . 21 marks
3. Q3 Euclidean geometry3.1 If cos35 = p, without using a calculator, determine the following in terms of p. 22 marks
4. Q4 Euclidean geometry4.1 Prove that: 2 sin( x + 45) −sin(90− x)+cos180 = sin x −1 (5) 16 marks
5. Q5 Trigonometryf (x) =1+sin(x−30) g(x) = d cosx 8 marks
6. Q6 Euclidean geometryIn the diagram, AB is a diameter of circle ABC. AB is produced to a point D so that 12 marks
7. Q7 Euclidean geometryIn the diagram, ABCD is a cyclic quadrilateral. PAQ is a tangent to circle at A. 9 marks
8. Q8 Euclidean geometry8.1 In the diagram, O is the centre of circle ABD. F is a point on chord AB such that 20 marks
9. Q9 Euclidean geometryIn the diagram, ABC is drawn. D is a point on AB and E is point on AC such that 6 marks
10. Q10 Euclidean geometryIn the diagram, two circles PSL and PQR touch internally at P. K and L are the 12 marks

Instructions to candidates

1. This question paper consists of 10 questions.
2. Answer ALL the questions in the SPECIAL ANSWER BOOK provided.
3. Clearly show ALL calculations, diagrams, graphs, etc. which you have used in determining your answers.
4. Answers only will NOT necessarily be awarded full marks.
5. You may use an approved scientific calculator (non-programmable and m non-graphical), unless stated otherwise. co . s
6. If necessary, round off answers correct to TWO decimal places, unless stated otherwise. ic ys
7. Diagrams are NOT necessarily drawn to scale. h p e
8. An information sheet with formulae is included at the end of the question paper. r o
9. Write neatly and legibly. m n t a s m ro f d de a lo n w do Mathematics/P2 3 NW/June 2022 NSC

1. Q1 Question 1 26 marks
2. Q2 Sequences and Series 16 marks
3. Q3 Question 3 11 marks
4. Q4 Question 4 9 marks
5. Q5 Question 5 12 marks
6. Q6 Question 6 14 marks
7. Q7 Question 7 15 marks
8. Q8 Question 8 11 marks
9. Q9 Question 9 23 marks
10. Q10 Question 10 13 marks

1. Q1 Statistics 12 marks
2. Q2 Statistics 21 marks
3. Q4 Euclidean Geometry 20 marks
4. Q5 Trigonometry 18 marks
5. Q6 Trigonometry 12 marks
6. Q7 Question 7
7. Q8 Trigonometry 8 marks
8. Q9 Euclidean Geometry 16 marks
9. Q10 Question 10 25 marks

1. Q1 Analytical geometryIn the diagram below, the circle centred at E 3;1 passes through pointP 5; −5 . 18 marks
2. Q2 Functions and graphs������(������) = ( ) 12 marks
3. Q3 Analytical geometry3.1 Given: ������ ������ = 2.2 −1 8 marks
4. Q4 Differential calculus4.1 From first principles, determine ������′(������) if ������(������) = 4������2 − ������. (5) 8 marks
5. Q5 Functions and graphsThe sketch below shows the graph of ������′(������) where ������(������) = ������3 + ������������2 + 24������ + ������. A(2;0) is an x- 15 marks
6. Q6 Finance, growth and decay6.1 If a car valued at R255 000 depreciates on a reducing balance method at an 7 marks
7. Q7 Number patterns, sequences and seriesIn the diagram below, B, C and D are three points on the same horizontal plane such that 7 marks

Instructions to candidates

1. This question paper consists of 7 questions.
2. Answer ALL questions.
3. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your answers.
4. Answers only will not necessarily be awarded full marks.
5. An approved scientific calculator (non-programmable and non-graphical) may be used, unless stated otherwise.
6. If necessary, answers should be rounded off to TWO decimal places, unless stated otherwise.
7. Diagrams are NOT necessarily drawn to scale.
8. Number the answers correctly according to the numbering system used in this question paper. Write neatly and legibly. Mathematics 3 June 2021 Practice NSC

1. Q1 Question 1 24 marks
2. Q2 Question 2 17 marks
3. Q3 Question 3 9 marks
4. Q4 Functions and Graphs 10 marks
5. Q5 Question 5 18 marks
6. Q6 Question 6 8 marks
7. Q7 Finance 13 marks
8. Q8 Question 8 12 marks
9. Q9 Question 9 11 marks
10. Q10 Question 10 13 marks
11. Q11 Question 11 15 marks

1. Q1 Question 1 14 marks
2. Q2 Statistics 9 marks
3. Q3 Analytical Geometry 19 marks
4. Q4 Trigonometry 20 marks
5. Q5 Trigonometry 18 marks
6. Q6 Trigonometry 13 marks
7. Q7 Trigonometry 9 marks
8. Q8 Question 8 16 marks
9. Q9 Euclidean Geometry 17 marks
10. Q10 Question 10 15 marks

1. Q1 1.1 100 ; 124 AA✓✓answers (2) 11 marks
2. Q2 2. ������ + ������������ = ������������ → ������ A✓equation (1) 7 marks
3. Q3 Functions and Graphs3.1 ������ A✓equation (1) 14 marks
4. Q4 Euclidean Geometry4.1 Draw AP = DE and AQ = DF ✓S Construction (or could be 23 marks
5. Q5 5.1 Let AE = 2a therefore EB = 3a ✓S ✓R (2) 10 marks
6. Q6 ������������������ ������������ =������������������ ������ ������������ 17 marks
7. Q7 7.1 ������ − ������������������ ������ ������ 18 marks

1. Q1 Sequences and Series1.1 The following geometric sequence is given: 10; 5; 2,5;1,25;...
2. Q2 Euclidean Geometry2.1 In the diagram below, PQR is given such that QT = 3 units, TV = 5 units,
3. Q3 In the diagram below, reflex and P has coordinates −5;−12 . 50 marks

Instructions to candidates

1. This question paper consists of THREE questions. Answer all the questions.
2. Clearly show all calculations you have used in determining your answers.
3. Write neatly and legibly.
4. Give all your answers to TWO decimal places, except stated otherwise.
5. Diagrams are NOT necessarily drawn to scale. 2021 TERM 1 ORTID MATHEMATICS CONTROLLED TEST GRADE 12

1. Q1 Sequences and SeriesGiven the sequence –5; 4; 21; 46; …… 8 marks
2. Q2 2.1 m 32(2)5−i 500 7 marks
3. Q3 Sequences and Series2x; x+1; 6−x; . . . are the first three (3) terms of an arithmetic sequence. 6 marks
4. Q4 TrigonometryThe sum of the first n terms of a series is given by : S = n(14−4n) 19 marks
5. Q7 Euclidean Geometry7.1 In the diagram below, O is the centre of the circle and P is a point on the 18 marks
6. Q8 8.1 Calculate the following without using calculator: 18 marks

1. Q1 Algebra, equations and inequalities1.1.2 , correct to TWO decimal places. (4) 25 marks
2. Q2 Number patterns, sequences and seriesThe first four terms of a quadratic sequence are 8 marks
3. Q3 Number patterns, sequences and seriesare the first four terms of an arithmetic sequence. 8 marks
4. Q4 Number patterns, sequences and seriesis the general term of a geometric sequence. 11 marks
5. Q5 Functions and graphsis a point on the graph of f. The asymptotes to the graph intersects at 10 marks
6. Q6 Functions and graphsand are sketched below. f intersects the axes at A, 15 marks
7. Q7 Functions and graphs7.1 Write down the domain of h. (1) 10 marks
8. Q8 Finance, growth and decay8.1 Melissa invests a fixed amount of money at an interest rate of 9,45 % p.a. compounded (3) 12 marks
9. Q9 Differential calculus9.1 Determine the derivative of f, using first principle, if (5) 12 marks
10. Q10 Differential calculusGiven : is a cubic function. A( – 1 ; 0), B and C are the x- intercepts . D 18 marks
11. Q11 Differential calculusA right circular cone has a slant height(s) of 12 cm as shown in the figure below. 9 marks
12. Q12 Probability and countingAt a school, 240 grade 11 learners data are represented below: 12 marks

Instructions to candidates

1. This question paper consists of 12 questions.
2. Answer ALL questions.
3. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your answers.
4. Answers only will not necessarily be awarded full marks.
5. An approved scientific calculator (non-programmable and non-graphical) may be used, unless stated otherwise.
6. If necessary, answers should be rounded off to TWO decimal places, unless stated otherwise.
7. Diagrams are NOT necessarily drawn to scale.
8. Number the answers correctly according to the numbering system used in this question paper. Write neatly and legibly. Mathematics 3 June Common Test 2020 NSC

1. Q1 Question 1 27 marks
2. Q2 Sequences and Series 15 marks
3. Q3 Question 3 9 marks
4. Q4 Question 4 11 marks
5. Q5 Question 5 20 marks
6. Q6 Finance 15 marks
7. Q7 Question 7 12 marks
8. Q8 Question 8 14 marks
9. Q9 Question 9 12 marks
10. Q10 Question 10 7 marks
11. Q11 Question 11 8 marks

1. Q1 Statistics 11 marks
2. Q2 Question 2 23 marks
3. Q4 Euclidean Geometry 17 marks
4. Q5 Trigonometry 13 marks
5. Q7 Trigonometry 9 marks
6. Q8 Analytical Geometry 15 marks
7. Q9 Euclidean Geometry 14 marks
8. Q10 Question 10 21 marks

1. Q1 Question 1 23 marks
2. Q2 Sequences and Series 15 marks
3. Q3 Question 3 11 marks
4. Q4 Question 4 9 marks
5. Q5 Question 5 12 marks
6. Q6 Question 6 11 marks
7. Q7 Question 7 13 marks
8. Q8 Question 8 16 marks
9. Q9 Question 9 17 marks
10. Q10 Question 10 8 marks
11. Q11 Question 11 15 marks

1. Q1 Algebra, equations and inequalities 26 marks
2. Q2 Number patterns, sequences and series 14 marks
3. Q3 Number patterns, sequences and series 11 marks
4. Q4 Functions and graphs 21 marks
5. Q5 Functions and graphs 12 marks
6. Q6 Finance, growth and decay 16 marks
7. Q7 Differential calculus 12 marks
8. Q8 Functions and graphs 13 marks
9. Q9 Differential calculus 9 marks
10. Q10 Probability and counting 10 marks
11. Q11 Probability and counting 6 marks

1. Q1 Statistics 12 marks
2. Q2 Question 2 9 marks
3. Q3 Trigonometry 18 marks
4. Q4 Analytical Geometry 21 marks
5. Q5 Trigonometry 18 marks
6. Q6 Trigonometry 13 marks
7. Q7 Trigonometry 9 marks
8. Q8 Euclidean Geometry 18 marks
9. Q9 Euclidean Geometry 13 marks
10. Q10 Question 10 19 marks