GCSEMathsOCRHigherExam Questions6. AlgebraFactorising

Factorising (OCR GCSE Maths: Higher): Exam Questions

Exam code: J560

2 hours45 questions
Easy
Medium
Hard
1
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Factorise      y squared space minus space 2 y

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2
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Factorise        n squared space minus space 7 n

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3
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Factorise          x to the power of 2 space end exponent plus space 7 x

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4
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Factorise             6 thin space plus thin space 9 x

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5
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Factorise          3 e squared plus 5 e

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6
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Factorise        3 x plus 6

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7a
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Simplify      3 a space cross times space 5 b space cross times space 2 c

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7b
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Factorise             3 y space plus space 6

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8
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Factorise        y squared space plus space 27 y

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9
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Tenzin is given this question.

Factorise fully.

2 x squared plus 6 x

Here is his answer.

2 x squared plus 6 x equals x open parentheses 2 x plus 6 close parentheses

Explain why Tenzin’s answer is not correct.

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10
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Factorise.

x2 - xy

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11
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Factorise fully  8 p squared space – space 2 p

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1
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Factorise                 x squared plus 3 x minus 10

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2
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Factorise               y squared minus 10 y space plus 16

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3a
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i) Factorise                x squared space minus 12 x space plus space 27

[2]

ii) Solve the equation          x squared space minus 12 x space plus space 27 space equals space 0

[1]

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3b
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Factorise     

                y squared space minus 100

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4
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Factorise

                 y squared space plus space 7 y space plus space 6

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5
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Factorise  x to the power of 2 space end exponent plus space 3 x space minus 4

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6
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Factorise         x squared space minus space 49

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7a
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Factorise fully

      8 a squared space plus space 12 a

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7b
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Factorise         y squared space minus space y space minus 2

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8
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Factorise

                   e squared space plus space e space minus 12

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9
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Factorise fully       3 x y squared space minus space 6 x y

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10a
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Factorise              6 m space minus space 9

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10b
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Factorise fully       2 x squared y space plus space 4 x y squared

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11a
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Simplify fully      fraction numerator n to the power of 7 space cross times space n cubed over denominator n to the power of 6 end fraction

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11b
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Expand and simplify      x open parentheses x space minus space 2 close parentheses space plus space 2 x open parentheses x space plus space 3 close parentheses

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11c
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Factorise   5 y space minus space 15

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11d
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Factorise fully      18 a b space plus space 27 a b squared

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12
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Factorise completely          8 x to the power of 2 space end exponent plus space 4 x y

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13
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Factorise completely         6 y squared space minus space 9 x y

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14
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Factorise fully          9 x squared space minus space 6 x y

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15
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Factorise   y squared minus 2 y minus 35

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16
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Factorise  x squared space – space 11 x space plus space 24

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17
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Circle the factor of  x squared minus 5 x

x minus 1

negative 5 x

x minus 5

5 x

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18
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Factorise x squared space – space 64 Circle your answer.

left parenthesis x space plus space 8 right parenthesis squared

left parenthesis x space – space 8 right parenthesis squared

left parenthesis x space plus space 8 right parenthesis left parenthesis x space – space 8 right parenthesis

x left parenthesis x space – space 64 right parenthesis

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1
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Factorise fully       20 x squared space minus space 5

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2a
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Factorise           y squared space minus space 16

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2b
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Factorise         2 p squared space minus space p space minus 10

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3
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Factorise          4 x squared space minus space 9

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4a
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Factorise        a squared space minus space b squared

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4b
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Hence, or otherwise, simplify fully open parentheses x squared plus 4 close parentheses squared space minus space open parentheses x squared space minus space 2 close parentheses squared

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5
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i) Factorise. x squared space – space 43 squared

[1]

ii) Calculate. 57 squared space – space 43 squared

[2]

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6
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Factorise fully  15 b to the power of 5 space c space minus space 35 b cubed space c to the power of 9

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7
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Factorise fully   15 y to the power of 4 space plus space 20 u y cubed

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8
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 Factorise fully  25 a to the power of 4 c to the power of 7 d space plus space 45 a to the power of 9 c cubed h

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9
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Factorise fully 2 e squared – space 18

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10
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Factorise  4 c squared space – space 9 d squared

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11
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Factorise  6 y squared space – space y space – space 5

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12
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Factorise  3 x to the power of 2 space end exponent plus space 11 x space – space 20

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13
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Factorise fully     144 minus 4 x squared

How did you do?

14a
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Factorise   5 x squared plus 6 x minus 8

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14b
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Simplify fully  fraction numerator x squared plus 9 x plus 14 over denominator x squared minus 4 end fraction

How did you do?

15a
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Here is an identity.

x squared space – space y squared space equals space left parenthesis x space plus space y right parenthesis left parenthesis x space – space y right parenthesis

Use the identity to work out the value of  193 squared minus 7 squared.

You must show your working.

How did you do?

15b
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Factorise  100 a to the power of 2 space end exponent – space 81 b squared

How did you do?

16
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Factorise   3 x squared space plus space 14 x space plus space 8

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