MCQ test, Set 7

Set 7 of 10
25 questions
25 marks
30 minutes

Download the PDF (with key sheet and solutions, 70.2 KB)

Choose one answer for each question, then check your score at the end. Each correct answer carries 1 mark; there is no negative marking.

$2 \times 2 \times 2 \times 9 \times 9 \times 9$ can be written as
A $2^2 \times 9^2$ B $6 \times 27$ C $2^3 \times 9^3$ D $11^3$

Answer and solution

Answer: (C) $2^3 \times 9^3$

Three 2's multiplied give $2^3$ ; three 9's multiplied give $9^3$ .
$4 \times 4 \times 4$ in power form is
A $4^3$ B $4^2$ C $3^{4}$ D $12$

Answer and solution

Answer: (A) $4^3$

4 is multiplied by itself 3 times.

$\therefore 4 \times 4 \times 4 = 4^3$
$t^3$ means
A $t \times t$ B $t \times t \times t$ C $3 \times t \times t$ D $3 \times t$

Answer and solution

Answer: (B) $t \times t \times t$

The power 3 means $t$ is multiplied by itself 3 times.

$t^3 = t \times t \times t$
$\square^3 = 64$ . The number in the box is
A $3$ B $4$ C $16$ D $5$

Answer and solution

Answer: (B) $4$

$4 \times 4 \times 4 = 64$

So the box is 4.
A carton has 7 layers. Each layer has 7 rows of 7 packets. How many packets are in the carton?
A $56$ B $21$ C $49$ D $343$

Answer and solution

Answer: (D) $343$

Number = $7 \times 7 \times 7$

$= 7^3 = 343$
The largest cube less than 900 is
A $1000$ B $512$ C $729$ D $800$

Answer and solution

Answer: (C) $729$

From the table: $9^3 = 729$ and $10^3 = 1000$

$729 < 900 < 1000$ , so the largest cube below 900 is 729.
The smallest cube greater than 50 is
A $64$ B $125$ C $100$ D $27$

Answer and solution

Answer: (A) $64$

From the table: $3^3 = 27$ and $4^3 = 64$

$27 < 50 < 64$ , so the smallest cube above 50 is 64.
A cube-shaped stack has 15 small cubes along each edge. The number of small cubes in it is
A $1350$ B $3375$ C $225$ D $180$

Answer and solution

Answer: (B) $3375$

Number = $15^3$

$15 \times 15 = 225$ , $225 \times 15 = 3375$
$12^3 = 144 \times \square$ . The number in the box is
A $12$ B $2$ C $144$ D $3$

Answer and solution

Answer: (A) $12$

$12^3 = 12 \times 12 \times 12$ and $12 \times 12 = 144$

$\therefore 12^3 = 144 \times 12$
To find $16^3$ , Rani first works out $16 \times 16 = 256$ . What should she do next?
A $256 \times 3$ B $256 \times 16$ C $16 \times 3$ D $256 \times 256$

Answer and solution

Answer: (B) $256 \times 16$

$16^3 = 16 \times 16 \times 16$ , so the product $256$ must be multiplied by 16 once more.

$256 \times 16 = 4096$
$(-m)^3 =$
A $-3m$ B $m^2$ C $-3m^3$ D $-m^3$

Answer and solution

Answer: (D) $-m^3$

$(-m)^3 = (-m) \times (-m) \times (-m) = -m^3$
Which number, multiplied by itself 3 times, gives $-216$ ?
A $-72$ B $-7$ C $-36$ D $-6$

Answer and solution

Answer: (D) $-6$

$(-6)^3 = -6^3 = -216$
$(-8)^3 = -\square$ . The number in the box is
A $24$ B $64$ C $512$ D $729$

Answer and solution

Answer: (C) $512$

$(-8)^3 = -8^3 = -512$

So the box is 512.
$5^3 + 5^3 =$
A $15625$ B $250$ C $125$ D $1000$

Answer and solution

Answer: (B) $250$

$5^3 + 5^3 = 125 + 125$

$= 250$
$1^3 + 5^3 =$
A $216$ B $18$ C $26$ D $126$

Answer and solution

Answer: (D) $126$

$1^3 + 5^3 = 1 + 125$

$= 126$
The sum of the cubes of 4 and 6 is
A $280$ B $1000$ C $52$ D $30$

Answer and solution

Answer: (A) $280$

$4^3 + 6^3 = 64 + 216$

$= 280$
$6^3 + (-1)^3 =$
A $125$ B $35$ C $215$ D $217$

Answer and solution

Answer: (C) $215$

$6^3 + (-1)^3 = 216 + (-1)$

$= 216 - 1$

$= 215$
$(-2)^3 + (-6)^3 =$
A $-224$ B $-512$ C $208$ D $-40$

Answer and solution

Answer: (A) $-224$

$(-2)^3 + (-6)^3 = -8 + (-216)$

$= -8 - 216$

$= -224$
$(-1)^3 + 5^3 + (-3)^3 =$
A $97$ B $1$ C $153$ D $151$

Answer and solution

Answer: (A) $97$

$(-1)^3 + 5^3 + (-3)^3 = -1 + 125 + (-27)$

$= -1 + 125 - 27$

$= 97$
$10^3 - 6^3 =$
A $64$ B $1216$ C $784$ D $12$

Answer and solution

Answer: (C) $784$

$10^3 - 6^3 = 1000 - 216$

$= 784$
What must be added to $3^3$ to get $6^3$ ?
A $243$ B $189$ C $27$ D $3$

Answer and solution

Answer: (B) $189$

Required number = $6^3 - 3^3$

$6^3 - 3^3 = 216 - 27$

$= 189$
By how much is $5^3$ greater than $3^3$ ?
A $152$ B $16$ C $98$ D $8$

Answer and solution

Answer: (C) $98$

Difference = $5^3 - 3^3$

$5^3 - 3^3 = 125 - 27$

$= 98$
$(-1)^3 - (-4)^3 =$
A $15$ B $63$ C $27$ D $-65$

Answer and solution

Answer: (B) $63$

$(-1)^3 - (-4)^3 = -1 - (-64)$

$= -1 + 64$

$= 63$
$-1^3 - 8^3 =$
A $511$ B $-65$ C $-729$ D $-513$

Answer and solution

Answer: (D) $-513$

$-1^3 - 8^3 = -1 - 512$

$= -513$
$(-2)^3 \times 3^3 =$
A $19$ B $-18$ C $36$ D $-216$

Answer and solution

Answer: (D) $-216$

$(-2)^3 = -8$ , $3^3 = 27$

$(-8) \times 27 = -216$

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MCQ test, Set 7