Simplifying Equations

1.

 y = 4 x – 5

(a)

Find the value of x when y = 1

 x = …………………. (2)

(b)

(i)

Simplify pq + pq + pq

………………………… Simplify k 2 + k 2

(ii)

………………………... (2) (Total 4 marks)

2.

Simplify fully (i)

4

5

m  × m

…………………………….. (ii)

6

2

 p  ÷ p

……………………………… (iii)

5 x3 y × 2 xy8

………………………………

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(iv)

4k   8

2

k   8

…………………………….. (Total 5 marks)

3.

(a)

Simplify

5 p + 2q – 3 p – 3q

..................................... (2)

 y = 5 x – 3

(b)

Find the value of x when y = 4

 x = .............................. (2) (Total 4 marks)

4.

(a)

Simplify

4 x + 7 y + 2 x – 3 y

………………………… (2)

(b)

Simplify

2 pq + pq

………………………… (1)

(c)

Factorise 3t  – 12

………………………… (1)

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(d)

Expand and simplify 3(2 x – 1) – 2(2 x – 3)

………………………… (2) (Total 6 marks)

5.

(a)

Expand and simplify 3(2 x – 1) – 2(2 x – 3)

………………………… (2)

(b)

Factorise 2

 y  + y

………………………… (1) (Total 3 marks)

6.

(a)

Factorise 9 x2 – 6 x + 1

…………………………… (2)

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(b)

Simplify 6 x 2 9 x

2



7 x  3



6 x  1

…………………………… (3) (Total 5 marks)

7.

(a)

Solve

40 – x 3

 = 4 + x

 x = .................... (3)

(b)

Simplify fully

4 x 2  – 6 x 4 x 2  – 9

........................................ (3) (Total 6 marks)

8. 

Simplify

Khalid Mazhar Qureshi

4 x 2 2 x

2





9

5 x  3 www.edexcel-cie.com

..................................... (Total 3marks)

9.

(a)

Simplify

3

a



4

a

……………………. (1)

(b)

Simplify

3 x2 y



5 xy 3

……………………. (2)

(c)

Simplify

( x  1) 2  x  1

……………………. (1)

(d)

Factorise  x2 – 9

……………………. (1) (Total 5 marks)

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10. 

(a)

Simplify a3

4

a



…………………… (1)

(b)

Simplify 3 x2 y



5 xy 3

…………………… (2)

(c)

Simplify

( x  1) 2  x  1

…………………… (1)

(d)

Factorise

2

2

a  – 9b

…………………… (2) (Total 6 marks)

11.

Simplify fully (a)

(3 xy 2 ) 4 ……………………. (2)

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(b)

 x  x

2

2





3x

8 x  15

……………………. (3) (Total 5 marks)

12. 

Simplify

 x

2

2 x 2



9



6 x

……………………. (Total 3 marks)

13.

 y  4 x  5 (a)

Find the value of x when y = 1  x = …………………. (2)

(b)

Simplify  pq + pq + pq ………………………... (1) (Total 3 marks)

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14.

Simplify fully (i)

m

4



m

5

…………………………….. (ii)

 p

6



 p

2

……………………………… (iii)

q

2



q

q

6

3

……………………………… (iv)

5 x 3 y  2 xy 8

……………………………… 4k   8

2

(v)

k   8

…………………………….. (Total 6 marks)

15.

Simplify fully (i)

m4



m5

…………………………….. (ii)

 p

6



 p

2

………………………………

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(iii)

q

2



q

6

q3

……………………………… 4k   8

2

(iv)

k   8

…………………………….. (Total 4 marks)

16. 

(a)

Simplify 8 x + 5 y – 3 x + y

…………………………… (2)

(b)

Solve 2 x – 5 = 4

 x = …………………………… (2)

(c)

Factorise 3m + 15

…………………………… (1) (Total 5 marks)

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17. 

(a)

Simplify 12 y3 ÷ 3 y5

…………………………… (2)

(b)

Simplify 2w3 x2 × 3w4 x

…………………………… (2) (Total 4 marks)

18.

Simplify

5 x + 3 y  y + 2 x

…………………………………. (Total 2 marks)

19.

Simplify fully

5 x3 y4 × 7 xy2

…………………………… (Total 2 marks)

20. 

(a)

Simplify

q + q + q + q

……………………. (1)

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(b)

Simplify

7 x + 3 y + 2 x  2 y

……………………. (2) (Total 3 marks)

21. 

Simplify 2  x (5   x )

 x 2



25

…………………… (Total 2 marks)

22.

Simplify 3a + 5b + 6a – 2b

............................................... (Total 2 marks)

23.

(a)

Expand and simplify

(3 x + 2)(4 x + 1)

............................................ (2)

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(b)

Factorise completely

3 x2 + 6 xy

............................ (2) (Total 4 marks)

24.

Expand and simplify ( y + 5)( y + 3)

........................................ (Total 2 marks)

25.

(a)

Factorise completely

2( x – 5)2 + 3( x – 5)

................................ (2)

(b)

Simplify

3( y  4) 2 ( y  4)

................................ (1) (Total 3 marks)

26. 

(a)

Simplify  x + x + x

............................ (1)

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(b)

Simplify 2e × 3 f ............................ (1) (Total 2 marks)

27. 

Simplify 6 x + 3 y – x + 5 y

............................. (Total 2 marks)

28.

Expand and simplify ( x – 9)( x + 4)

................................ (Total 2 marks)

29. 

(a)

Simplify

d  + d  + d 

…………… (1)

(b)

Simplify

2c + 4c + c …………… (1)

(c)

Solve

 x + 7 = –3

 x = ……….. (1)

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(d)

Solve

5 y + 3 = 15

 y = ……….. (2) (Total 5 marks)

30.

Simplify fully

(3 xy2)4

…………………. (Total 2 marks)

Khalid Mazhar Qureshi

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