A Level Maths PURE INTERMEDIATE, Exercises of Mathematics

A Level Maths Pure Intermediate questions

Typology: Exercises

2025/2026

Uploaded on 06/10/2026

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Questions
1. Differentiate:
y
=3
x
2+5
x
3
2. Solve:
2
x
27
x
15=0
3. Find:
1
3
(2
x
+5)
dx
4. Solve:
cos
x
=1
2
for
0
x
<360
.
5. Find the stationary points of:
y
=
x
36
x
2+9
x
6. Expand:
(
12
x
)
5
7. Solve:
8. Find the equation of the normal to:
y
=
x
2
at
x
=1
.
9. Given vectors
pf2

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Questions

  1. Differentiate:

y =

x

2 +^5 x^

3

  1. Solve:

2 x

2

− 7 x − 15 = 0

  1. Find: ∫ 1 3

( 2 x + 5 ) dx

  1. Solve: cos x =

for 0 ∘^ ≤ x < 360 ∘^.

  1. Find the stationary points of:

y = x

3

− 6 x

2

+ 9 x

  1. Expand:

( 1 − 2 x )

5

  1. Solve:

ln ( x )= 2

  1. Find the equation of the normal to:

y = x

2

at x = 1.

  1. Given vectors

a =

, b =

find 2 a − b.

  1. Find the sum of the first 20 terms of an arithmetic sequence with first term 7 and common difference 4.

Answers

x

3 +^15 x^

2

2.^ x^ =^5 ,^ −^

4. 60 ∘^ , 300 ∘

5. ( 1 , 4 )and ( 3 , 0 )

6. 1 − 10 x + 40 x

2

− 80 x

3

+ 80 x

4

− 32 x

5

8.^ y^ =

x +