Free Printable Ch1-3

1.

A surd is...

a)

A root of a number that can be simplified to a rational number.

b)

A root of a number that cannot be simplified to a irrational number.

c)

A root of a number that cannot be simplified to a rational number.

d)

A square root that cannot be simplified to an irrational number.

2.

Which of the following is a surd?

a)

$\sqrt{289}$

b)

$2\sqrt{4}$

c)

$\sqrt{82}$

d)

$\sqrt{25}$

3.

$\sqrt{32xy^2}$

Simplify the surd.

a)

$2\sqrt{4}xy$

b)

$4\sqrt{2x}y$

c)

$4\sqrt{2xy}$

d)

$2\sqrt{2}xy$

4.

$\frac{1}{2+\sqrt{2}}$

How do you rationalise the denominator?

a)

$\times\sqrt{2}$ to numerator and denominator

b)

$\times\left(2-\sqrt{2}\right)\$ to denominator

c)

$\times\left(2-\sqrt{2}\right)\$ to numerator

d)

$\times\left(2-\sqrt{2}\right)\$ to both numerator and denominator

5.

(3+4i)(-8-i)

a)

-5+3i

b)

-24-4i

c)

-24-4i²

d)

-20

e)

-20-36i

6.

What is the conjugate of the following...

7-2i

a)

7 - 2i

b)

-7 - 2i

c)

-7 + 2i

d)

7 + 2i

7.

$8\left(\cos\ \frac{\pi}{6}+\ i\ \sin\ \frac{\pi}{6}\right)$
Write the complex number in rectangular form

a)

$4\sqrt{3}+4i$

b)

$4+4i\sqrt{3}$

c)

$4\sqrt{3}-4i$

d)

$-4\sqrt{3}+4i$

8.

To write the polar form of a complex number you have to: (check all those that apply)

a)

find the length of the modulus and the angle to the horizontal

b)

find the distance from the origin and the size of the angle from the positive sense of the x-axis

c)

calculate the modulus and argument

d)

measure the angle with a protractor

9.

Which of the following inequalities would require you to flip the sign when solving?

a)

2x < 3

b)

3x > - 9

c)

-4x ≥ 10

d)

5x ≤ 15

10.

0 < x + 7 < 9

a)

-7<x and x<2

b)

-7<x or x<2

c)

-7>x and x>2

d)

-7>x or x>2

11.

Today's temperature will be at least -4 degrees.

a)

t < -4

b)

t > -4

c)

t ≤ -4

d)

t ≥ -4

12.

| 2w - 1 | < 11

a)

No Solution

b)

All Real Numbers

c)

-5 < w < 6

d)

-6 < w < 5

13.

a)

(-2,2)

b)

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

c)

[-2,2]

d)

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

14.

a)

$\left[0,3\right)$

b)

$\left(0,3\right]$

c)

$\left(-\infty,3\right]$

d)

$\left(-\infty,0\right)$

15.

Find the fourth term of the expansion (5+3y)⁵.

a)

2025y⁴

b)

750y³

c)

75y⁴

d)

6750y³

16.

How many terms are the in the expansion of (1+b)⁵

a)

5

b)

6

c)

25

d)

50

e)

3

17.

Find the 2nd term in the expansion of
(2b + 1)³

a)

12b²

b)

6b

c)

8b³

d)

4b²

Ch1-3

Total questions: 17

Worksheet time: 23mins

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