Free Printable Year 9 Algebra Review

1.

Simplify the expression:

12a² +4 +3a² -2

a)

15a² + 2

b)

15a - 2

c)

15a² - 2

d)

9a² +2

2.

Evaluate: 5k + 7 + 2p when k = 10 and p = -3

a)

63

b)

60

c)

55

d)

51

3.

Solve for p: 10p - 5 = -2p + 19

a)

-4

b)

-2

c)

2

d)

24

4.

Cross multiply and solve for x: $\frac{x\ +\ 2}{8}=\frac{5}{2}$

a)

10

b)

18

c)

6

d)

3

5.

Simplify the exponential expression.

a)

2x⁶y¹²

b)

2x⁵y⁷

c)

8x⁶y¹²

d)

8x⁵y⁷

6.

4⁰=

a)

0

b)

1

c)

4

d)

-4

7.

Rachel and Sharon are splitting up their Pokemon cards. Rachel has 4 fewer than 3 times as many as Sharon. Together they have 100 cards. Which equation could be used to solve for how many cards Sharon had originally? Let n = number of cards that Sharon had.

a)

n + (3n - 4) = 100

b)

n - (3n - 4) = 100

c)

n + (4 - 3n) = 100

d)

4 - 3n = 100

8.

What is the value of 27^⅓?

a)

27

b)

9

c)

3

d)

1/3

9.

Solve for h.
V = πr²h

a)

h = V/(πr²)

b)

h = V - πr²

c)

h = πr²V

d)

h = V + πr²

10.

Amy needs to get at least a 70 to pass the class. Which of these inequalities show the grades Amy can get?

a)

x < 70

b)

x > 70

c)

x ≤ 70

d)

x ≥ 70

11.

Solve.
2x + 8 > 4x + 6

a)

x < 1

b)

x > 1

c)

x < 2

d)

x > 2

12.

Solve the system. What is the value of x?
2x + 3y = 13
x - 2y = 3

a)

x = 1

b)

x = 3

c)

x = -2

d)

x = 5

13.

10, 8, 6, 4, ...
a_n =

a)

10n + 2

b)

10n - 2

c)

-2n + 10

d)

-2n + 12

14.

(x + 7)(x - 2) =

a)

x² + 9x - 14

b)

x² + 5x - 14

c)

x² + 5x + 9

d)

x² + 7x - 2

15.

What is the Greatest Common Factor: 8x³ + 6x² ?

Factorise completely.

a)

GCF = 8x; $8x\left(x^2+6x\right)$

b)

GCF = 2x²; $2x^2\left(4x+3\right)$

c)

GCF = 4x²; $4x^2\left(2x+2\right)$

d)

GCF = 2x³; $2x^3\left(4+3x^{-1}\right)$

16.

Factor.
x² + 11x + 18

a)

(x + 11)(x + 18)

b)

(x + 5)(x + 6)

c)

(x + 3)(x + 6)

d)

(x + 9)(x + 2)

17.

Which inequality is represented by the number line shown?

a)

n > -12

b)

n < -12

c)

n ≥ -12

d)

n ≤ -12

18.

Which compound inequality is represented by the number line shown?

a)

-6 < x < 0

b)

-6 < x ≤ 0

c)

-6 ≤ x ≤ 0

d)

-6 ≤ x < 0

19.

Simplify the following expression:
$3x+2x+3y-7y$

a)

$5x+10y$

b)

$5x+4y$

c)

$5x-4y$

d)

$5x-10y$

20.

Simplify the expression: $3x^2\times5xy$

a)

$8\times2+y$

b)

$15x^3y$

c)

$3x^2+5xy$

d)

$3\times25xy$

21.

Simplify these expressions:

6x⁵y²z ÷ 12x²y⁵z³

a)

HUH????

b)

2x⁷y⁷z³

c)

x³ / 2y³z²

d)

2x³y³z²

22.

Expand these expressions:

4(3 + 2a + 3b)

a)

12 + 2a + 3b

b)

12 + 8a + 3b

c)

12 + 8a + 12b

d)

32ab

23.

Students mailed invitations to a play to 414 parents. Each student mailed 18 invitations. If x equals the number of students who mailed invitations, which equation best shows the number of invitations that were mailed?

a)

x + 18 = 414

b)

x ÷ 18 = 414

c)

18 ÷ x = 414

d)

18x = 414

24.

Solve for x:
3(5x + 10) + 10 = 6x - (x + 10)

a)

3

b)

-3

c)

-5

d)

5

25.

Simplify:

a)

4(x+5)/3(x+5)

b)

4/3

c)

3/4

d)

x+5

26.

Simplify the algebraic fraction.

a)

1/a

b)

8a/9

c)

9/8a

d)

9a/8

27.

a)

A

b)

B

c)

C

d)

D

28.

a)

3c

b)

9b/4a

c)

4a

d)

2c/b

29.

What is the nth term for the sequence

4, 9, 14, 19, 24, ....

a)

5n+1

b)

n+5

c)

5n-1

d)

5n+4

30.

Find an expression for the nth term of the sequence

98, 94, 90, ....

a)

-4n+94

b)

-4n+102

c)

-4n

d)

4n+94

31.

Find the nth term for the following sequence:

-8, -5, -2, 1, 4, ...

a)

-3n - 5

b)

-8n + 3

c)

3n - 11

d)

-3n + 5

32.

Find the inverse of the function
f(x) = 3x − 5

a)

f^-1(x)=3x +5

b)

f^-1(x)=(x+5)/3

c)

f^-1(x)=3y-5

d)

f^-1(x)=3y+5

33.

What's the name of the inverse of g(x)?

a)

f(x)

b)

f^-1(x)

c)

y

d)

g^-1(x)

34.

$f\left(x\right)=\frac{x-2}{6}$
Find $f^{-1}\left(x\right)$

a)

$\frac{x-6}{2}$

b)

$6x+2$

c)

$2x+6$

d)

$6\left(x+2\right)$

35.

$f\left(x\right)=\frac{6x}{5}+3$
Find $f^{-1}\left(x\right)$

a)

$\frac{5x-3}{6}$

b)

$\frac{5\left(x-3\right)}{6}$

c)

$\frac{5x}{6}-3$

d)

$\frac{5x}{6}+3$

36.

$f\left(x\right)=\frac{3x+10}{7}$
Find $f^{-1}\left(x\right)$

a)

$7x-\frac{10}{3}$

b)

$\frac{7x}{3}-10$

c)

$\frac{7\left(x-10\right)}{3}$

d)

$\frac{7x-10}{3}$

37.

Given
f(x)= 2x² + 5x - 17, find f(-1).

a)

f(-1) = -20

b)

f(-1) = -24

38.

Find f(x) if x=-2.

a)

f(x)=9

b)

f(x)=-15

c)

f(x)=-9

d)

f(x)=21

39.

a)

1/16

b)

1/9

c)

1/3

d)

1/27

40.

Solve:

3x + 5y = 4

4x - 5y = -18

a)

x = -2

y = 2

b)

x = -2

y = -2

c)

x = 2

y = -2

d)

x = 2

y = 2

Year 9 Algebra Review

Total questions: 40

Worksheet time: 1hrs 20mins

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