Algebra III - Ambitious

Question 1: Simplify:

4 x \div 2 \sqrt{x}

,

x > 0

A

\frac{1}{2} \sqrt{x}

B

x \sqrt{2}

C

\frac{1}{2} x \sqrt{2}

D

2 \sqrt{x}

Question 2: Solve:

\frac{x}{7} - 5 = 2

A

x = 7

B

x = 49

C

x = 21

D

x = 14

Question 3: Multiply out:

(t^{2} - 3 k + 3) (k + 9)

A

t^{2} k + 6 t^{2} - 3 k^{2} + 12 k + 27

B

t^{2} k - 9 t^{2} + k^{2} - 16 k + 27

C

t^{2} k + 9 t^{2} - 3 k^{2} - 24 k + 27

D

t^{2} k - 9 t^{2} + k^{2} - 24 k + 27

Question 4: Expand:

(4 x y - 6) (4 - 6 x y)

A

- 24 x^{2} y^{2} + 52 x y - 24

B

- 16 x^{2} y^{2} - 38 x y + 24

C

- 16 x^{2} y^{2} + 26 x y + 10

D

- 24 x^{2} y^{2} + 26 x y - 10

Question 5: Expand:

(3 x^{4} + y) (x^{4} - 2 y)

A

4 x^{8} - 7 x^{4} y - 2 y^{2}

B

3 x^{8} - 7 x^{4} y + 2 y^{2}

C

4 x^{8} - y

D

3 x^{8} - 5 x^{4} y - 2 y^{2}

Question 6: Expand:

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

A

- 2 x \sqrt{3} + 3 \sqrt{3}

B

6 x - x \sqrt{3} - 2 \sqrt{3}

C

9 x - x \sqrt{3} + 3 \sqrt{3} - 1

D

3 \sqrt{3}

Question 7: Expand:

(\sqrt{2} - \sqrt{3}) (\sqrt{3} + \sqrt{6})

A

2 \sqrt{6} - 2 \sqrt{3} - 3 \sqrt{2} - 3

B

\sqrt{6} - 3 \sqrt{2} + 3

C

\sqrt{6} + 2 \sqrt{3} - 3 \sqrt{2} - 3

D

\sqrt{6} - \sqrt{2} - 3

Question 8: Expand:

(a - 1) (a + 2) + (a - 3) (a + 2)

A

2 a^{2} - 5 a - 6

B

2 a^{2} - 8

C

2 a^{2} - 6 a + 4

D

a^{2} - 8 a - 6

Question 9: Expand:

{(x + y)}^{2} - (x^{2} + y^{2})

A

2 x^{2} + 2 x y

B

2 x^{2} + 2 y^{2} - 2 x y

C

2 x y

D

2 y^{2} + 2 x y

Question 10: Formula for the area of a trapezium is:

A = \frac{1}{2} (a + b) \cdot h

Rearrange the formula to make

h

the subject

A

h = \frac{1}{2} \cdot \frac{A}{a + b}

B

h = \frac{2 A}{a + b}

C

h = 2 A (a + b)

D

h = \frac{a + b}{2 A}

Test: Algebra III - Ambitious

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