MCQ test, Set 10

Set 10 of 10
25 questions
25 marks
30 minutes

Download the PDF (with key sheet and solutions, 71.4 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.

$9 \times 9 \times 9 = 9^{\square}$ . The number in the box is
A $3$ B $27$ C $9$ D $2$

Answer and solution

Answer: (A) $3$

9 is multiplied by itself 3 times, so the power is 3.

$9 \times 9 \times 9 = 9^3$
$x \times x \times x \times y \times y \times y$ in power form is
A $x^3 \times y^3$ B $3x \times 3y$ C $(x \times y)^6$ D $x^2 \times y^2$

Answer and solution

Answer: (A) $x^3 \times y^3$

$x \times x \times x = x^3$ and $y \times y \times y = y^3$

So it is $x^3 \times y^3$ .
$c^3$ means
A $3 \times c$ B $c \times c \times c$ C $3 \times c \times c$ D $c \times c$

Answer and solution

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

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

$c^3 = c \times c \times c$
How many cubes of whole numbers lie between 200 and 800?
A $5$ B $6$ C $4$ D $3$

Answer and solution

Answer: (C) $4$

From the table of cubes, the cubes between 200 and 800 are $216$ , $343$ , $512$ , $729$ .

That is 4 cubes.
Which of these can be written as $k^3$ for a whole number $k$ ?
A $81$ B $900$ C $729$ D $300$

Answer and solution

Answer: (C) $729$

$729 = 9 \times 9 \times 9 = 9^3$

The other numbers are not in the table of cubes.
The next number in $64, 125, 216, 343, \ldots$ is
A $64$ B $470$ C $729$ D $512$

Answer and solution

Answer: (D) $512$

These are $4^3$ , $5^3$ , $6^3$ , $7^3$ .

Next is $8^3 = 512$
How many small cubes make a big cube that has 7 small cubes along each edge?
A $343$ B $294$ C $49$ D $21$

Answer and solution

Answer: (A) $343$

Each layer has $7 \times 7$ cubes and there are 7 layers.

Number = $7^3 = 343$
$21^3 =$
A $63$ B $9261$ C $441$ D $8000$

Answer and solution

Answer: (B) $9261$

$21 \times 21 = 441$

$441 \times 21 = 9261$
To find $12^3$ , Rani first works out $12 \times 12 = 144$ . What should she do next?
A $144 \times 3$ B $12 \times 3$ C $144 \times 12$ D $144 \times 144$

Answer and solution

Answer: (C) $144 \times 12$

$12^3 = 12 \times 12 \times 12$ , so the product $144$ must be multiplied by 12 once more.

$144 \times 12 = 1728$
$16^3 = 256 \times \square$ . The number in the box is
A $256$ B $16$ C $2$ D $3$

Answer and solution

Answer: (B) $16$

$16^3 = 16 \times 16 \times 16$ and $16 \times 16 = 256$

$\therefore 16^3 = 256 \times 16$
$(-16) \times (-16) \times (-16) =$
A $256$ B $-48$ C $-768$ D $-4096$

Answer and solution

Answer: (D) $-4096$

$(-16) \times (-16) = 256$

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

Answer and solution

Answer: (B) $-t^3$

$(-t)^3 = (-t) \times (-t) \times (-t) = -t^3$
$(-4)^3 = -\square$ . The number in the box is
A $125$ B $12$ C $16$ D $64$

Answer and solution

Answer: (D) $64$

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

So the box is 64.
$10^3 + 1^3 =$
A $101$ B $1001$ C $33$ D $1331$

Answer and solution

Answer: (B) $1001$

$10^3 + 1^3 = 1000 + 1$

$= 1001$
$1^3 + 2^3 + 5^3 =$
A $24$ B $30$ C $134$ D $512$

Answer and solution

Answer: (C) $134$

$1^3 + 2^3 + 5^3 = 1 + 8 + 125$

$= 134$
The sum of the cubes of 3 and 9 is
A $36$ B $90$ C $1728$ D $756$

Answer and solution

Answer: (D) $756$

$3^3 + 9^3 = 27 + 729$

$= 756$
$(-3)^3 + 8^3 =$
A $55$ B $539$ C $485$ D $125$

Answer and solution

Answer: (C) $485$

$(-3)^3 + 8^3 = -27 + 512$

$= 485$
$(-2)^3 + (-7)^3 =$
A $-53$ B $-729$ C $335$ D $-351$

Answer and solution

Answer: (D) $-351$

$(-2)^3 + (-7)^3 = -8 + (-343)$

$= -8 - 343$

$= -351$
$4^3 + (-2)^3 =$
A $12$ B $8$ C $72$ D $56$

Answer and solution

Answer: (D) $56$

$4^3 + (-2)^3 = 64 + (-8)$

$= 64 - 8$

$= 56$
What must be added to $6^3$ to get $7^3$ ?
A $127$ B $559$ C $13$ D $1$

Answer and solution

Answer: (A) $127$

Required number = $7^3 - 6^3$

$7^3 - 6^3 = 343 - 216$

$= 127$
By how much is $10^3$ greater than $5^3$ ?
A $1125$ B $125$ C $875$ D $75$

Answer and solution

Answer: (C) $875$

Difference = $10^3 - 5^3$

$10^3 - 5^3 = 1000 - 125$

$= 875$
Ravi says $5^3 - 9^3 = 604$ . The correct value is
A $-604$ B $-854$ C $-56$ D $-64$

Answer and solution

Answer: (A) $-604$

$5^3 - 9^3 = 125 - 729$

$= -604$

Ravi took the smaller cube from the bigger one.
$-2^3 - 6^3 =$
A $-40$ B $-224$ C $208$ D $-512$

Answer and solution

Answer: (B) $-224$

$-2^3 - 6^3 = -8 - 216$

$= -224$
$2^3 \times (-3)^3 =$
A $36$ B $-216$ C $-18$ D $-19$

Answer and solution

Answer: (B) $-216$

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

$8 \times (-27) = -216$
$15^3 \div 5^3 =$
A $27$ B $3250$ C $3$ D $1000$

Answer and solution

Answer: (A) $27$

$15^3 = 3375$ , $5^3 = 125$

$3375 \div 125 = 27$

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MCQ test, Set 10