Algebra foundations · Compendia

Notation, powers and roots

Question 1

Simplify $\sqrt{50}-\sqrt{18}$ .

A.

8\sqrt{2}

B.

\sqrt{32}

C.

2\sqrt{2}

D.

2

Question 2

What is $(-2)^{-4}$ ?

A.

\dfrac{1}{16}

B.

16

C.

-\dfrac{1}{16}

D.

-16

Question 3

The statement $|x - 7| \le 4$ describes which set of numbers?

A.

[7, 11]

B.

[3, 11]

C.

[-11, -3]

D.

[-4, 4]

Question 4

Which interval is $\{\, x \mid -3 < x \le 5 \,\}$ ?

A.

[-3, 5]

B.

(-3, 5)

C.

(-3, 5]

D.

[-3, 5)

Question 5

What is $\sqrt[3]{-64}$ ?

A.

-8

B.It is not a real numberC.

-4

D.

4

Manipulation

Question 6

Factor $x^{3}-4x$ completely.

A.

x(x-2)^{2}

B.

(x-2)(x+2)

C.

x(x^{2}-4)

D.

x(x-2)(x+2)

Question 7

Write $\dfrac{3}{x}-\dfrac{2}{x+1}$ as a single fraction.

A.

\dfrac{1}{x(x+1)}

B.

\dfrac{5x+3}{x(x+1)}

C.

\dfrac{x+3}{x(x+1)}

D.

\dfrac{x-3}{x(x+1)}

Question 8

Rationalise the numerator of $\dfrac{\sqrt{x+2}-\sqrt{2}}{x}$ .

A.

\dfrac{1}{\sqrt{x+2}+\sqrt{2}}

B.

\dfrac{\sqrt{x+2}+\sqrt{2}}{x}

C.

\dfrac{x}{\sqrt{x+2}+\sqrt{2}}

D.

\dfrac{1}{\sqrt{x+2}-\sqrt{2}}

Question 9

Write $x^{2}-6x+11$ in completed square form.

A.

(x-3)^{2}+11

B.

(x-6)^{2}-25

C.

(x-3)^{2}+20

D.

(x-3)^{2}+2

9 questions left to answer.