Gr. 11 Mathematics
Term 2 - 2024
Paper 1
Total:150 marks Time:2 hours
Learner's name: ________________________________ Gr. 12: __________.
Instructions and information:
This paper consists of five questions, answer all the questions.
You may use a non-programmable and non-graphing calculator.
No Tip – Ex may be used
Show all the steps needed to arrive at the answer.
Good luck!!
Topics covered in this test:
Algebra and Equations
Series and Sequences
Quadratic Patterns
Functions and Graphs
Financial Mathematics
Calculus
Probability and Statistics
1|Page www.summariessa.co.za M a t h e m a ti c s
Grade 12 June Paper 1
,QUESTION 1
1.1 Solve for x :
2
1.1.1 x −16=0 (2)
3 7
1.1.2 - =0
x x+1
(4)
1.1.3 x=2+ √ 8−x (5)
2
1.1.4 3 x +5 x−20 ≥ 0 (3)
1.2 Solve simultaneously for x and y in: (6)
3 x+ 4 y =5
5 y−2 x=3
√
2
3 n +2 n
1.3 Simplify completely, WITHOUT the use of a calculator: 2
(4)
n + 6 n+5
[17]
QUESTION 2
y y y
Given the following geometric series: y + + + + …
2 4 8
2.1.1 Determine the value of r , the common ratio, in term of y (1)
2.1.2 Determine the values of y for which this series converges. (2)
2.1.3 If y=5 , determine the sum of the series to 10 terms. (3)
2.2 Calculate
2|Page www.summariessa.co.za M a t h e m a ti c s
Grade 12 June Paper 1
, ( )
4
1
∑ 5
k (3)
k =1
2.3 The sum of the first n terms of an arithmetic series is given by: Sn=2n 2+3 n
2.3.1 Calculate the sum of the first 12 terms. (2)
2.3.2 Calculate the value of T 12 (2)
2.3.3 If the first term of this series is 9, which term in the series will have a value
of 225? (4)
[11]
QUESTION 3
3.1 Consider the following quadratic number pattern: 120 ; 88 ; z ; 44 ; . . .
3.1 Determine the value of z . (2)
3.2 If z=64 determine the general term of the number pattern in the form
2
T n=a n +bn+ c (4)
3.3 Detemine T 20 (1)
3.4 Which term in the number pattern will be equal to 1 500. (4)
[11]
QUESTION 4
The graph of g ( x )=a ()
1 x
3
+7 passes through point E (-2 ; 10).
4.1 Calculate the value of a (3)
4.2 Calculate the coordinates of the y−¿ intercept of g (2)
()
x
1
4.3 Consider: h ( x )=
3
3|Page www.summariessa.co.za M a t h e m a ti c s
Grade 12 June Paper 1
Term 2 - 2024
Paper 1
Total:150 marks Time:2 hours
Learner's name: ________________________________ Gr. 12: __________.
Instructions and information:
This paper consists of five questions, answer all the questions.
You may use a non-programmable and non-graphing calculator.
No Tip – Ex may be used
Show all the steps needed to arrive at the answer.
Good luck!!
Topics covered in this test:
Algebra and Equations
Series and Sequences
Quadratic Patterns
Functions and Graphs
Financial Mathematics
Calculus
Probability and Statistics
1|Page www.summariessa.co.za M a t h e m a ti c s
Grade 12 June Paper 1
,QUESTION 1
1.1 Solve for x :
2
1.1.1 x −16=0 (2)
3 7
1.1.2 - =0
x x+1
(4)
1.1.3 x=2+ √ 8−x (5)
2
1.1.4 3 x +5 x−20 ≥ 0 (3)
1.2 Solve simultaneously for x and y in: (6)
3 x+ 4 y =5
5 y−2 x=3
√
2
3 n +2 n
1.3 Simplify completely, WITHOUT the use of a calculator: 2
(4)
n + 6 n+5
[17]
QUESTION 2
y y y
Given the following geometric series: y + + + + …
2 4 8
2.1.1 Determine the value of r , the common ratio, in term of y (1)
2.1.2 Determine the values of y for which this series converges. (2)
2.1.3 If y=5 , determine the sum of the series to 10 terms. (3)
2.2 Calculate
2|Page www.summariessa.co.za M a t h e m a ti c s
Grade 12 June Paper 1
, ( )
4
1
∑ 5
k (3)
k =1
2.3 The sum of the first n terms of an arithmetic series is given by: Sn=2n 2+3 n
2.3.1 Calculate the sum of the first 12 terms. (2)
2.3.2 Calculate the value of T 12 (2)
2.3.3 If the first term of this series is 9, which term in the series will have a value
of 225? (4)
[11]
QUESTION 3
3.1 Consider the following quadratic number pattern: 120 ; 88 ; z ; 44 ; . . .
3.1 Determine the value of z . (2)
3.2 If z=64 determine the general term of the number pattern in the form
2
T n=a n +bn+ c (4)
3.3 Detemine T 20 (1)
3.4 Which term in the number pattern will be equal to 1 500. (4)
[11]
QUESTION 4
The graph of g ( x )=a ()
1 x
3
+7 passes through point E (-2 ; 10).
4.1 Calculate the value of a (3)
4.2 Calculate the coordinates of the y−¿ intercept of g (2)
()
x
1
4.3 Consider: h ( x )=
3
3|Page www.summariessa.co.za M a t h e m a ti c s
Grade 12 June Paper 1
