MCQ test, Set 2

Set 2 of 10
25 questions
25 marks
30 minutes

Download the PDF (with key sheet and solutions, 75.7 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.

$5 \times 5 \times 5 = 5^{\square}$ . The number in the box is
A $5$ B $2$ C $15$ D $3$

Answer and solution

Answer: (D) $3$

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

$5 \times 5 \times 5 = 5^3$
In $t^3$ , the small 3 tells us that
A $t$ is multiplied by itself 3 times B $t$ is multiplied by 3 C 3 is added to $t$ D $t$ is added to itself 3 times

Answer and solution

Answer: (A) $t$ is multiplied by itself 3 times

$t^3 = t \times t \times t$ : three $t$ 's are multiplied.
$m \times m \times m \times n \times n \times n$ in power form is
A $m^3 \times n^3$ B $m^2 \times n^2$ C $3m \times 3n$ D $(m \times n)^6$

Answer and solution

Answer: (A) $m^3 \times n^3$

$m \times m \times m = m^3$ and $n \times n \times n = n^3$

So it is $m^3 \times n^3$ .
300 lies between
A $8^3$ and $9^3$ B $5^3$ and $6^3$ C $7^3$ and $8^3$ D $6^3$ and $7^3$

Answer and solution

Answer: (D) $6^3$ and $7^3$

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

$216 < 300 < 343$
Which of these is NOT a cube?
A $343$ B $27$ C $60$ D $125$

Answer and solution

Answer: (C) $60$

$27 = 3^3$ , $125 = 5^3$ , $343 = 7^3$ .

60 is not in the table of cubes.
A carton has 9 layers. Each layer has 9 rows of 9 packets. How many packets are in the carton?
A $27$ B $729$ C $90$ D $81$

Answer and solution

Answer: (B) $729$

Number = $9 \times 9 \times 9$

$= 9^3 = 729$
The largest cube less than 500 is
A $512$ B $343$ C $400$ D $216$

Answer and solution

Answer: (B) $343$

From the table: $7^3 = 343$ and $8^3 = 512$

$343 < 500 < 512$ , so the largest cube below 500 is 343.
A big cube is built from small cubes, with 11 small cubes along each edge. How many small cubes does it have?
A $121$ B $132$ C $1331$ D $726$

Answer and solution

Answer: (C) $1331$

Number = $11^3$

$11 \times 11 = 121$ , $121 \times 11 = 1331$
$13^3 = 169 \times \square$ . The number in the box is
A $3$ B $13$ C $2$ D $169$

Answer and solution

Answer: (B) $13$

$13^3 = 13 \times 13 \times 13$ and $13 \times 13 = 169$

$\therefore 13^3 = 169 \times 13$
To find $17^3$ , Rani first works out $17 \times 17 = 289$ . What should she do next?
A $289 \times 289$ B $17 \times 3$ C $289 \times 3$ D $289 \times 17$

Answer and solution

Answer: (D) $289 \times 17$

$17^3 = 17 \times 17 \times 17$ , so the product $289$ must be multiplied by 17 once more.

$289 \times 17 = 4913$
$(-10)^3 = -\square$ . The number in the box is
A $1331$ B $30$ C $1000$ D $100$

Answer and solution

Answer: (C) $1000$

$(-10)^3 = -10^3 = -1000$

So the box is 1000.
$(-12) \times (-12) \times (-12) =$
A $-432$ B $-1728$ C $144$ D $-36$

Answer and solution

Answer: (B) $-1728$

$(-12) \times (-12) = 144$

$144 \times (-12) = -1728$
$(-30)^3 =$
A $-2700$ B $900$ C $-27000$ D $-90$

Answer and solution

Answer: (C) $-27000$

$(-30) \times (-30) = 900$

$900 \times (-30) = -27000$
Two big cubes are made of small cubes, with 3 and 4 small cubes along each edge. How many small cubes are there in the two cubes together?
A $25$ B $343$ C $150$ D $91$

Answer and solution

Answer: (D) $91$

Total = $3^3 + 4^3$

$3^3 + 4^3 = 27 + 64$

$= 91$
$1^3 + 2^3 + 4^3 =$
A $21$ B $343$ C $9$ D $73$

Answer and solution

Answer: (D) $73$

$1^3 + 2^3 + 4^3 = 1 + 8 + 64$

$= 73$
The sum of the cubes of 1 and 8 is
A $729$ B $513$ C $27$ D $65$

Answer and solution

Answer: (B) $513$

$1^3 + 8^3 = 1 + 512$

$= 513$
$(-1)^3 + 2^3 + (-3)^3 =$
A $-20$ B $34$ C $-8$ D $36$

Answer and solution

Answer: (A) $-20$

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

$= -1 + 8 - 27$

$= -20$
$6^3 + (-4)^3 =$
A $152$ B $8$ C $20$ D $280$

Answer and solution

Answer: (A) $152$

$6^3 + (-4)^3 = 216 + (-64)$

$= 216 - 64$

$= 152$
$(-2)^3 + (-4)^3 =$
A $-216$ B $56$ C $-20$ D $-72$

Answer and solution

Answer: (D) $-72$

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

$= -8 - 64$

$= -72$
By how much is $8^3$ greater than $6^3$ ?
A $728$ B $8$ C $28$ D $296$

Answer and solution

Answer: (D) $296$

Difference = $8^3 - 6^3$

$8^3 - 6^3 = 512 - 216$

$= 296$
One big cube has 6 small cubes along each edge and another has 5. How many more small cubes does the first one have?
A $91$ B $341$ C $1$ D $11$

Answer and solution

Answer: (A) $91$

More = $6^3 - 5^3$

$6^3 - 5^3 = 216 - 125$

$= 91$
Ravi says $2^3 - 7^3 = 335$ . The correct value is
A $-335$ B $-45$ C $-351$ D $-125$

Answer and solution

Answer: (A) $-335$

$2^3 - 7^3 = 8 - 343$

$= -335$

Ravi took the smaller cube from the bigger one.
$10^3 \div 2^3 =$
A $512$ B $992$ C $125$ D $5$

Answer and solution

Answer: (C) $125$

$10^3 = 1000$ , $2^3 = 8$

$1000 \div 8 = 125$
If $x = -3$ and $y = 2$ , then $x^3 + y^3 =$
A $-1$ B $13$ C $-19$ D $35$

Answer and solution

Answer: (C) $-19$

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

$= -19$
$(-3)^3 - (-5)^3 =$
A $8$ B $98$ C $16$ D $-152$

Answer and solution

Answer: (B) $98$

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

$= -27 + 125$

$= 98$

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MCQ test, Set 2