MCQ test, Set 3

Set 3 of 10
25 questions
25 marks
30 minutes

Download the PDF (with key sheet and solutions, 72.3 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.

$5^3$ is the same as
A $3 \times 3 \times 3 \times 3 \times 3$ B $5 \times 3$ C $5 \times 5 \times 5$ D $5 \times 5$

Answer and solution

Answer: (C) $5 \times 5 \times 5$

$5^3$ means 5 multiplied by itself 3 times.

$5^3 = 5 \times 5 \times 5 = 125$
$4 \times 4 \times 4 \times 5 \times 5 \times 5$ can be written as
A $9^3$ B $12 \times 15$ C $4^2 \times 5^2$ D $4^3 \times 5^3$

Answer and solution

Answer: (D) $4^3 \times 5^3$

Three 4's multiplied give $4^3$ ; three 5's multiplied give $5^3$ .
$p^3$ is read as
A $p$ squared B 3 times $p$ C $p$ plus 3 D $p$ cubed

Answer and solution

Answer: (D) $p$ cubed

$p^3 = p \times p \times p$ is read as ' $p$ power 3' (or) ' $p$ cubed'.
$\square^3 = 216$ . The number in the box is
A $72$ B $36$ C $6$ D $7$

Answer and solution

Answer: (C) $6$

$6 \times 6 \times 6 = 216$

So the box is 6.
The smallest cube greater than 150 is
A $343$ B $216$ C $125$ D $200$

Answer and solution

Answer: (B) $216$

From the table: $5^3 = 125$ and $6^3 = 216$

$125 < 150 < 216$ , so the smallest cube above 150 is 216.
How many cubes of whole numbers lie between 100 and 600?
A $5$ B $6$ C $4$ D $3$

Answer and solution

Answer: (C) $4$

From the table of cubes, the cubes between 100 and 600 are $125$ , $216$ , $343$ , $512$ .

That is 4 cubes.
$8^3 =$
A $24$ B $512$ C $729$ D $64$

Answer and solution

Answer: (B) $512$

$8^3 = 8 \times 8 \times 8 = 512$
$40^3 =$
A $1600$ B $64000$ C $6400$ D $120$

Answer and solution

Answer: (B) $64000$

$40 \times 40 = 1600$

$1600 \times 40 = 64000$
A cube-shaped stack has 12 small cubes along each edge. The number of small cubes in it is
A $1728$ B $144$ C $864$ D $36$

Answer and solution

Answer: (A) $1728$

Number = $12^3$

$12 \times 12 = 144$ , $144 \times 12 = 1728$
$15^3 = 225 \times \square$ . The number in the box is
A $225$ B $15$ C $2$ D $3$

Answer and solution

Answer: (B) $15$

$15^3 = 15 \times 15 \times 15$ and $15 \times 15 = 225$

$\therefore 15^3 = 225 \times 15$
$(-7)^3 =$
A $-343$ B $49$ C $-21$ D $-147$

Answer and solution

Answer: (A) $-343$

$(-7)^3 = (-7) \times (-7) \times (-7)$

$= 49 \times (-7) = -343$
If $k$ is a positive number, then $(-k)^3$ is
A negative B equal to $k^3$ C positive D zero

Answer and solution

Answer: (A) negative

$(-k)^3 = -k^3$ : a negative number multiplied 3 times gives a negative number.
$(-9)^3 = -\square$ . The number in the box is
A $27$ B $1000$ C $81$ D $729$

Answer and solution

Answer: (D) $729$

$(-9)^3 = -9^3 = -729$

So the box is 729.
$3^3 + 3^3 =$
A $54$ B $27$ C $216$ D $729$

Answer and solution

Answer: (A) $54$

$3^3 + 3^3 = 27 + 27$

$= 54$
$2^3 + 3^3 + 4^3 + 5^3 =$
A $2744$ B $224$ C $54$ D $99$

Answer and solution

Answer: (B) $224$

$2^3 + 3^3 + 4^3 + 5^3 = 8 + 27 + 64 + 125$

$= 224$
Two big cubes are made of small cubes, with 1 and 7 small cubes along each edge. How many small cubes are there in the two cubes together?
A $300$ B $512$ C $344$ D $50$

Answer and solution

Answer: (C) $344$

Total = $1^3 + 7^3$

$1^3 + 7^3 = 1 + 343$

$= 344$
$14^3 + (-14)^3 =$
A $2 \times 14^3$ B $0$ C $14^6$ D $14^3$

Answer and solution

Answer: (B) $0$

$(-14)^3 = -14^3$

$14^3 - 14^3 = 0$
$(-1)^3 + 5^3 =$
A $24$ B $126$ C $64$ D $124$

Answer and solution

Answer: (D) $124$

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

$= 124$
$(-2)^3 + 3^3 + (-1)^3 =$
A $20$ B $0$ C $18$ D $36$

Answer and solution

Answer: (C) $18$

$(-2)^3 + 3^3 + (-1)^3 = -8 + 27 + (-1)$

$= -8 + 27 - 1$

$= 18$
$10^3 - 11^3 =$
A $-2331$ B $-1$ C $-21$ D $-331$

Answer and solution

Answer: (D) $-331$

$11^3 = 121 \times 11 = 1331$

$10^3 - 11^3 = 1000 - 1331$

$= -331$
What must be added to $4^3$ to get $8^3$ ?
A $64$ B $448$ C $48$ D $576$

Answer and solution

Answer: (B) $448$

Required number = $8^3 - 4^3$

$8^3 - 4^3 = 512 - 64$

$= 448$
By how much is $4^3$ greater than $1^3$ ?
A $63$ B $15$ C $65$ D $27$

Answer and solution

Answer: (A) $63$

Difference = $4^3 - 1^3$

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

$= 63$
$p^3 - (-p)^3 =$
A $2p$ B $0$ C $p^6$ D $2p^3$

Answer and solution

Answer: (D) $2p^3$

$(-p)^3 = -p^3$

$p^3 - (-p^3) = p^3 + p^3 = 2p^3$
$2^3 \times (-5)^3 =$
A $100$ B $-117$ C $-1000$ D $-30$

Answer and solution

Answer: (C) $-1000$

$2^3 = 8$ , $(-5)^3 = -125$

$8 \times (-125) = -1000$
$8^3 \div 2^3 =$
A $64$ B $216$ C $4$ D $504$

Answer and solution

Answer: (A) $64$

$8^3 = 512$ , $2^3 = 8$

$512 \div 8 = 64$

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MCQ test, Set 3