A Level Mathematics
k k k
AQA – OCR k k
Paper 2 – Pure Mathematics & Mechanics
k k k k k k k
Set 1 k
Name ………………………………………………
Date ………………………………………………
2k hoursk allowed
Calculatork Paperk
Maximumk Mark:k 100
,Sectionk Ak –k Purek Mathematics
Questionk 1
Thek functionk 𝑓k isk definedk by
𝑓(𝑥) k =
k 3
k +k 3−𝑥 k ,k k 𝑥 ∈ ℝ
k k
(i) Usingk setk notation,k statek thek rangek ofk 𝑓
…………………………………………………………………………………………………………………………………………….
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(2)
(ii) Usingk setk notation,k statek thek domaink ofk 𝑓−1
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(1)
(iii) Findk ank expressionk fork 𝑓−1
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(3)
, Thek functionk 𝑔k isk definedk by
𝑔(𝑥) =
k k 3+
k k √𝑥 k ,k k (𝑥 ∈ ℝ ∶ 𝑥 > 0)
k k k k k k
(iv) Findk ank expressionk fork 𝑔𝑓(𝑥)
…………………………………………………………………………………………………………………………………………….
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(1)
(v) Solvek thek equationk 𝑔𝑓(𝑥)k = 5,
k k givingk yourk answerk ink ank exactk form.
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(3)
(Totalk 10k Marks)
k k k
AQA – OCR k k
Paper 2 – Pure Mathematics & Mechanics
k k k k k k k
Set 1 k
Name ………………………………………………
Date ………………………………………………
2k hoursk allowed
Calculatork Paperk
Maximumk Mark:k 100
,Sectionk Ak –k Purek Mathematics
Questionk 1
Thek functionk 𝑓k isk definedk by
𝑓(𝑥) k =
k 3
k +k 3−𝑥 k ,k k 𝑥 ∈ ℝ
k k
(i) Usingk setk notation,k statek thek rangek ofk 𝑓
…………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………….
(2)
(ii) Usingk setk notation,k statek thek domaink ofk 𝑓−1
…………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………….
(1)
(iii) Findk ank expressionk fork 𝑓−1
…………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………….
(3)
, Thek functionk 𝑔k isk definedk by
𝑔(𝑥) =
k k 3+
k k √𝑥 k ,k k (𝑥 ∈ ℝ ∶ 𝑥 > 0)
k k k k k k
(iv) Findk ank expressionk fork 𝑔𝑓(𝑥)
…………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………….
(1)
(v) Solvek thek equationk 𝑔𝑓(𝑥)k = 5,
k k givingk yourk answerk ink ank exactk form.
…………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………….
…………………………………………………………………………………………………………………………………………….
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(3)
(Totalk 10k Marks)
