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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