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Grade 12 Mathematics: Question Paper

DBE/May-June 2019
1. The first FOUR terms of a quadratic pattern are: 15 ; 29 ; 41 ; 51

1. Write down the value of the 5th term. (1) L1

2. Determine an expression for the nth term of the pattern in the form
Tn = an2 + bn + c. (4) L2

3. Determine the value of T27 . (2) L1

IEB/November 2019
2. The table below shows the number of passengers that were on a bus after every stop.

• 1st stop: 2, 2nd stop: 20, 3rd stop: 34, 4th stop: 44

The number of passengers on the bus after the n-th bus stop can be given by
Tn = an2 + bn + c.

1. Write down the number of passengers on the bus after the fifth stop. (1) L1

2. Determine a, b, and c. (4) L2

3. If it is given that Tn = an2 + bn + c., determine the maximum number of

passengers on the bus. (3) L2

4. Explain why the formula calculated in Question 2.3 does not work after the
eleventh stop. (3) L3

BISHOPS/SEPT 2016
3. A quadratic pattern has a second term equal to 1, a third term equal to −6, and a
fourth term equal to −14. Determine the general term. (5) L2

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WBHS/SEPT 2017
4. The p-th term of the first difference of a quadratic sequence is given by Tp = p2 − 3p.

1. Determine between which two consecutive terms of the quadratic sequence the
first difference is equal to 1450. (3) L3

2. The 40th term of the quadratic sequence is 2290. Calculate the value of c in
Tn = an2 + bn + c. (4) L3

WESTERFORD/SEPT 2016
5. A linear number pattern with a constant difference can be represented by the terms:
x + 3; 3x + 2; 6x − 1

1. Determine the value of x. (2) L1

2. Determine the value of T5 . (4) L2

6. Given the geometric sequence: 3; 2; k; ...

1. Write down the value of the common ratio. (1) L1

2. Calculate the value of k. (2) L2

128
3. Calculate the value of n if Tn = 729
. (4) L2

7. An arithmetic and geometric sequence have the same first term, 5. The common
difference and common ratio have the same value. The 5th term of the geometric
sequence is 80. Determine the first three terms of the arithmetic sequence. (5) L3

PLATINUM MATHEMATICS/GR12(BANK QUESTIONS)

8. Given the sequence: 3; 6; 9; ... ; 60

1. Determine the number of terms in the sequence. (3) L2

2. Determine the sum of the terms in the sequence. (3) L1

3. Determine the sum of all the natural numbers from 1 to 60 which are not
multiples of 3. (4) L3

9. Given: A set of natural numbers up to and including 900. If the multiples of 5 are
removed from the set, determine the sum of the remaining numbers. (7) L3

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DBE/November 2021
10. Given the geometric series: x + 90 + 81 + . . .

1. Calculate the value of x. (2) L2

2. Show that the sum of the first n terms is Sn = 1000((1 − (0.9)n ). (2) L2

3. Hence, or otherwise, calculate the sum to infinity. (2) L1

NHHS-JUNE 2016
11. Given the sequence: 7; 1; 7; 3; 7; 5 . . .

1. Determine the value of T17 . (1) L2

2. Determine the sum of the sequence from T9 up to and including T13 . (4) L2

12. The sum of 16 terms of an arithmetic series is 632, and the eleventh term is 47.
Determine the fifth term. (6) L3

DBE/November 2021
13. Consider the linear pattern: 5; 7; 9;

1. Determine T51 . (3) L1

2. Calculate the sum of the first 51 terms. (2) L2

5000
P
3. Write down the expansion of 2n + 3. Show only the first 3 terms and the last
n=1
term of the expansion. (3) L2
5000 5000
(−2n − 1). All working details
P P
4. Hence or otherwise, calculate (2n + 3) +
n=1 n=1
must be shown. (4) L3

NW/SEPT 2021
12
4( 21 )k−1
P
14. Consider the following:
k=3

1. Write down the first three terms of the series. (2) L1

2. Calculate the sum of the series. (3) L2

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IEB/November 2019
∞  n+2
P 1
15. Given: 4 2
n=2

1. Calculate the sum. (4) L2

2. Give a reason why the series converges. (1) L1

16. Determine for which value(s) of t the infinite series 2(t − 5) + 2(t − 5)2 + 2(t − 5)3
+ ..... will converge. (4) L2

MIND ACTION SERIES/GR12(NEW EDITION)

17. Given the geometric series: 3 + 2 + x + . . .

1. Calculate the value of x. (1) L2

2. Write this infinite geometric series in sigma notation. (2) L2

KZN/June 2021
∞
P
18. Consider the geometric series where Tn = 27and S6 = 26. Calculate the value of
n=1
the constant ratio r. (4) L3

IEB/November 2020
∞ 10
k
22i
P P
19. Determine the smallest value of k for which 2i
+ > 1000000. for K
i=1 i=1
∈Z (5)L3

NHHS/SEPT 2014
p−1
20. Consider the geometric series: 2p−1
+ (p − 1) + (p − 1)(2p − 1) + . . .

1. Determine the common ratio r in terms of p. (3) L1

2. For which value(s) of p will the series converge? (2) L2

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MIND ACTION SERIES/GR12(NEW EDITION)

21. The sum of the first n terms of a series is given by Sn = 2n2 + 4n.

1. Calculate the sum of the first 200 terms. (2) L1

2. Calculate the value of the value of 100th term. (3) L2

3. How many terms must be added for the sum to be 4230. (3) L2

22. For a certain series Sn = 64 − 64( 21 )n

225
1. How many terms must be added for the sum to equal 4
? (3) L2

2. Determine the value of T4 . (3) L2

3. Show that Tn = 26−n . (4) L2

4. If 2n = p, determine the value of S6−n − S6+n in terms of p. (3) L2

23. A certain quadratic pattern has the following features: T1 = p, T2 = 18,

T1 = 4T1 and T3 + T2 = 10. Determine the value of p. (5) L3

KZN June 2021

24. Consider the sequence: −11; 2sin3x;15. Determine the values of x for which the
sequence will be arithmetic x ∈ [0◦ ; 90◦ ]. (4)L3

25. In a geometric sequence, the third term is 5p + 1, the fifth term is 4, and the
seventh term is 1. Determine the value of p. (3) L2
26. If the sum of the first n terms of the following geometric series is greater than 300,
determine the smallest value of n 49 + 42 + 36 + 2177
+ .... (5) L3

MIND ACTION SERIES/GR12(NEW EDITION)

27. Jacob wrote 12 Maths tests. For the first test, he scored 32% However, on each
successive test, his score was 1.05 times more than the preceding one. In answering the
questions which follow, give all answers correct to two decimal places.

1. Write down the first 3 test scores as a sequence. (2) L1

2. What was Jacob’s percentage for his last (twelfth) test? (3) L2

3. What was the total of all his tests? (2) L2

4. Find his average percentage for the 12 tests. (2) L1

28. The 1st, 2nd, and 3rd terms of a geometric progression are the 1st, 9th, and 21st
terms, respectively, of an arithmetic progression. Determine the value of the common
ratio r where r ̸= 1. (7)L3

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RBHS/SEPT 2015
29. Consider the geometric progression: 13 ; 23 ; 43 . . .

1. Determine the general term. (2) L2

2. Calculate the sum of the first 8 terms. (3) L1

21
2(k − 1).
P
30. Calculate: (3) L2
k=1

1 1 1
31. If b−a ; 2b ; b−c form an arithmetic sequence, prove that a, bandc are in grometric
sequence. (5) L3

RBHS/SEPT 2016
32. Given that a convergent geometric series has a first term a and S∞ = p where p > 0.

1. Show that a ∈ (0, 2p). (5) L2

2. Determine the value of the constant ratio when a = p4 . (3) L2

KZN/SEPT 2021
5 7 ∞
3(2)k−1 = ( 1 )j−2 .
P P P
33. Evaluate: (4y + 3p) + 3
(4) L2
p=1 k=4 j=1

WESTERFORD/SEPT 2014
34. Parents of a new born baby decide they will save for the child’s future. They decide
to save one cent this month when the baby has just been born, then two cents next
month and so on, doubling the amount every month. How old will the child be when
they have saved a total of R1 000 000, if they keep saving in this way? Give you answer
correct to the nearest whole number.. (4) L2

NW/SEPT 2021
35. Consider the series: cos θ + sin 2θ + 4 sin2 θ cos θ . . ..

1. Prove that it is a geometric series. (4) L2

2. Calculate for which values of θ it will be a converging series. (3) L2