Download 12 AS Test 2

CORNELIUS GORESEB HIGH SCHOOL
MATHEMATICS ~ Sequences, Series and Binomial Theorem
TEST 2
10 June 2021
GRADE: 12 AS
MARKS: 25
NAME: ………………………………………………
1. The first 2 terms of a convergent geometric series are 𝑥 and 6 respectively. The sum to
infinity is 25.
Determine the possible non-zero values of 𝑥.
Answer: ……………………………………….[5]
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2. Given that
∑𝑛𝑟=1 3(2 ) =378
Find the value of 𝑛.
Answer: ……………………………………….[5]
3. (a) In the expansion of (3𝑥 − 4)4 , find the coefficient of 𝑥.
Answer: ……………………………………….[3]
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(b) Find the first four terms in the expansion in ascending powers of 𝑥 of
(3 + 2𝑥²)10 .
Answer: ……………………………………….[4]
(c) Find the coefficient of 𝑥³ in the expansions
1 15
(3𝑥² + 𝑥) .
Answer: ……………………………………….[3]
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4. The expansion of (𝑎 + 𝑥)(1 − 3𝑥) in ascending powers of 𝑥 is 4 − 95𝑥 + 𝑝𝑥 2 + ⋯,
where 𝑎 and 𝑝 are constants and 𝑛 is a positive integer. Find the values of 𝑎 , 𝑛 and 𝑝.
Answer: 𝑎 = ………… 𝑛 = …………. 𝑝 = ……………[5]
……………………………………..end……………………………………………..
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