Free Printable Surds

1.

Simplify fully:
√32

a)

4√8

b)

16√2

c)

4√2

d)

4√4

2.

Simplify fully:
√120

a)

4√30

b)

2√30

c)

12√10

d)

6√10

3.

Simplify fully:
√32 + 5√32

a)

6√32

b)

24√8

c)

24√2

d)

6√8

4.

Simplify fully:
2√45 - 5√45 + 9√16

a)

-9√5 + 36

b)

-3√45 + 144

c)

6√16

d)

6√106

5.

Rationalise the Denominator:
³/_√5

a)

³^√5/₅

b)

³^√5/₂₅

c)

^√5/₅

d)

^√5/3

6.

Rationalise the Denominator:
^{(3 + √4)}/_√2

a)

^5√2/₂

b)

^{(3√2 +√8)}/₂

c)

^{(3√2 +√8)}/4

d)

^{(3√2 +}^√3⁾/₂

7.

Which one would you multiply by to rationalise this denominator:
^√5/_{(√2 - 1)}

a)

(√2 - 1)

b)

√2

c)

√2 + 1

d)

√5

8.

Which one would you multiply by to rationalise this denominator:
⁷/_3√6

a)

√6

b)

3√6

c)

2√3

d)

3 - √6

9.

$2√32-√50+√98$

a)

$√2$

b)

$10√2$

c)

$56√2$

d)

$700√2$

10.

| x - 4 | < 7

a)

x < - 3 or x > 11

b)

3 < x < 11

c)

- 3 < x < 11

d)

x < 3 or x > 11

11.

| 9 - 2x | > 1

a)

x < - 4 or x > 5

b)

4 < x < 5

c)

x < - 4

d)

x < 4 or x > 5

12.

Which function is represented in the graph?

a)

$f\left(x\right)=\left|x\right|$

b)

$f\left(x\right)=\left|x+2\right|+1$

c)

$f\left(x\right)=\left|x-2\right|$

d)

$f\left(x\right)=\left|x-2\right|+1$

13.

y=|x+1|−4

a)

A

b)

B

c)

C

d)

y=D

14.

y=|x−3|

a)

A

b)

B

c)

C

d)

D

15.

y=|x+2|+1

a)

A

b)

B

c)

C

d)

D

16.

y=|x|−2

a)

A

b)

B

c)

C

d)

D

17.

a)

(-2,2)

b)

$\left(-\infty,\ -2\right)\cup\left(2,\ \infty\right)$

c)

[-2,2]

d)

$\left(\infty,\ -2\right)\cup\left(2,\ -\infty\right)$

18.

Solve for x:
$\frac{3x-7}{x+2}>1$

a)

$\left(-2,\ \frac{9}{2}\right)$

b)

$\left(-\infty,-2\right)\cup\left(\frac{9}{2},\ \infty\right)$

c)

$\left(-\infty,-2\right)\cup\left(\frac{7}{3},\ \infty\right)$

d)

$\left(-2,\ \frac{7}{3}\right)$

19.

Solve:

2x² + 5x ≥ 12

a)

[-4, 1.5]

b)

(−∞, -4) U (1.5, ∞)

c)

(−∞, -4] U [1.5, ∞)

d)

no solution

20.

6x² - 54 ≤ 0

a)

-3 ≤ x ≤ 3

b)

x ≤ -3 or x ≥ 3

c)

-3 < x < 3

d)

x < -3 or x > 3

21.

2x² + 9x - 143 < 0

a)

-11 < x < 6.5

b)

-11 ≤ x ≤ 6.5

c)

no solution

d)

all reals

22.

Solve:
6x+10>5x-12

a)

x>2

b)

x<2

c)

x<-22

d)

x>-22

23.

a)

A)

b)

B)

c)

C)

d)

D)

24.

Expand and simplify 4(m + 3) + 3 (2m -5)

a)

4m + 12 + 6m + 15

b)

10m + 27

c)

4m + 12 + 6m - 15

d)

10m - 3

25.

Expand and simplify

(x + 4)²

a)

x²+ 16

b)

x² + 4x + 4x + 16

c)

x² + 8x + 16

d)

x² + 4x

26.

Work out the value of p for the following:

(x - 3)² = x² + px + 9

a)

6

b)

-6

c)

0

d)

1

27.

Factorise fully 12y² - 8y

a)

2 (6y² - 8)

b)

2y (6y - 2)

c)

4y (3y² - 2)

d)

4y (3y - 2)

28.

y = 2(x - 8)

Expand and rearrange to obtain an equation for x

a)

x = y/2 - 8

b)

x = y/2 + 8

c)

x = 2y - 8

d)

x = 2y + 8

29.

Identify the following polynomial.
$36x^2-y^2$

a)

Difference of Squares

b)

Perfect Square Trinomial

c)

Sum of Cubes

d)

Difference of Cubes

30.

Identify the following polynomial.
$1-a^3$

a)

Difference of Squares

b)

Perfect Square Trinomial

c)

Sum of Cubes

d)

Difference of Cubes

31.

$\left(a+b\right)^2\equiv$

a)

$a^2+b^2$

b)

$a^2-2ab+b^2$

c)

$a^2-b^2$

d)

$a^2+2ab+b^2$

32.

$\left(a-b\right)^2\equiv$

a)

$a^2+b^2$

b)

$a^2-2ab+b^2$

c)

$a^2-b^2$

d)

$a^2+2ab+b^2$

33.

$\left(a+b\right)\left(a-b\right)\equiv$

a)

$a^2-b^2$

b)

$a^2+b^2$

c)

$a^2-2ab+b^2$

d)

$a^2+2ab+b^2$

34.

$\left(4a+2b\right)^2=$

a)

$16a^2+8ab-4b^2$

b)

$16a^2-8ab-4b^2$

c)

$16a^2-8ab+4b^2$

d)

$16a^2+8ab+4b^2$

35.

What is the solution?

a)

(6, 3)

b)

(3, 6)

c)

(-6, 3)

d)

No solution

36.

Solve the system.

a)

(3, -2, 4)

b)

(2, -3, 1)

c)

(-3, 2, -1)

d)

Infinitely many solutions

37.

Determine the number of solutions to the given linear-quadratic system.

a)

0 solutions

b)

1 solution

c)

2 solutions

d)

3 solutions

38.

Determine if the point (2,0) is a solution to the following system:

y=2x - 4

y=x²- 4

a)

Yes, because it works in one equation.

b)

Yes, because it works in the both equations.

c)

No, because it works in neither equation.

d)

No, because it works in only one equation.

39.

Which of the following graphs correctly represents:

y=x²

y=-2x+1

a)

b)

c)

d)

40.

$y-3=\left(x-1\right)^2$
$2x+y=5$
Solve the system.

a)

(-1,7) and (1,3)

b)

(7,-1) and (3,1)

c)

(1,-7) and (-1,3)

d)

(-1,7) and (1,-3)

Surds

Total questions: 40

Worksheet time: 3hrs 20mins

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