Grade 9 Mathematics Worksheet - Edupstairs

Grade 9 Mathematics Worksheet

Equations, expressions and factorization

Questions:

1.

a)

Simplify the expression f ? x ? ? 2 ? 3 ? 2 x ? ? 13 ? 3x ? 6 ?

b)

Solve the equation f ? x ? ? 2 x ? 3 if f (x) is as in (a) above

c)

Solve for x if 3 ? f ? x ? ? ? 2 x ? 3? if x is an integer and if f (x) is as in (a) above

d)

For which values of x will f ? 2 x ? ? ?1 ? if f (x) is as in (a) above

? x ? ? 4096

? x ?? x ?

3 4

e)

2.

3.

Solve for x :

6

2

Factorise the following:

a)

2 x2 ? 8

b)

2 x2 ? 14 x ? 36

c)

4x3 ? x

d)

8x3 ? 27

e)

4x ? 9

Simplify the following expressions:

a)

x2 ? x ? 6

9 ? x2

b

x? 3

x ?3

c)

2 x2 ? 2 x 2

?

x

x

Edupstairs Grade R - 9 Learning



Grade 9 Mathematics Worksheet

d)

e)

3

27x ?6

9 x2 y3

2

?

?2 1

3

18 x y

Edupstairs Grade R - 9 Learning



Grade 9 Mathematics Worksheet

Solution:

1.

a)

f ? x ? ? 2 ? 3 ? 2 x ? ? 13 ? 3x ? 6 ? ? 6 ? 4 x ? x ? 2 ? 4 ? 5 x

b)

f ? x ? ? 2 x ? 3 ? 4 ? 5 x.

? 7 x ? ?1

? x ? ? 17

c)

3 ? ? 4 ? 5 x ? ? ? 2 x ? 3?

?12 ? 15 x ? 2 x ? 3

??17 x ? ?9

? x ? 179

So the first value of x will be x = 1.

d)

4 ? 5 ? 2 x ? ? ?1

? 4 ? 10 x ? ?1

??10 x ? ?5

? x ? 12

e)

? x ? ? 4096 ? x

x

? x ?? x ?

a)

2x2 ? 8 ? 2( x2 ? 4) ? 2( x ? 2)( x ? 2)

b)

2x2 ? 14x ? 36 ? 2( x2 ? 7 x ?18) ? 2( x ? 9)( x ? 2)

c)

4x3 ? x ? x(4x2 ?1) ? x(2 x ? 1)(2 x ?1)

d)

8x3 ? 27 ? (2 x ? 3)(4 x2 ? 6 x ? 9)

e)

22x ? 32 ? (2x ? 3)(2x ? 3)

a)

x 2 ? x ? 6 ( x ? 2)( x ? 3) ( x ? 2)( x ? 3)

( x ? 2)

?

?

?

2

(3 ? x)(3 ? x) ?( x ? 3)(3 ? x) ?( x ? 3)

9? x

3 4

2.

3.

6

12

2

Edupstairs Grade R - 9 Learning

8

? 4096 ? x 4 ? 212 ? x ? ?23 ? ?8



Grade 9 Mathematics Worksheet

x? 3

x? 3

?

?

x ?3

( x ? 3)( x ? 3)

b)

c)

2 x 2 ? 2 x 2 2( x 2 ? x) x

? ?

? ? x 2 ? x or

x

x

x

2

1

d)

e)

1

x? 3

1

x( x ? 1)

1

3

x2

9 x2 y3

2 ( x 2 y3 ) ? ( x 2 y ?1 ) 2 3( x 4 y 2 ) ? 2(2) 3x 4 y 2 ? 4

?

?

? ?

?

2

3

6

6

18x ?2 y1 3

3

27 x ?6 ? (27 x ?6 ) 3 ? 27 3 x ?6? 3 ? 3x ?2 ?

Edupstairs Grade R - 9 Learning



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