Basic Maths: Test 44

This is an assessment test.
These tests focus on the basics of Maths and are meant to indicate your preparation level for the subject.
Kindly take the tests in this series with a pre-defined schedule.

Basic Maths: Test 44

Please wait while the activity loads.
If this activity does not load, try refreshing your browser. Also, this page requires javascript. Please visit using a browser with javascript enabled.

If loading fails, click here to try again

Question 1

$\frac{{{\left( 3.2 \right)}^{3}}+0.008}{\left( {{3.2}^{2}}-0.0256+0.04 \right)}$ is equal to:

A	3.60
B	3.00
C	3.33
D	3.40

Question 1 Explanation:

$\begin{align} & \frac{{{\left( 3.2 \right)}^{3}}+{{\left( 0.2 \right)}^{3}}}{{{\left( 3.2 \right)}^{2}}-3.2\times 0.2+0.2\times 0.2} \\ & Let\,\,\,3.2=a\,\,\,\,and\,\,0.2=b \\ & Therefore\,\,\,\exp ression \\ & =\frac{{{a}^{3}}+{{b}^{3}}}{{{a}^{2}}-ab+{{b}^{2}}} \\ & =a+b \\ & =3.2+0.2 \\ & =3.4 \\ \end{align}$

Question 2

The value of

$\frac{0.4\times 0.4\times 0.4+0.06\times 0.06\times 0.06}{0.8\times 0.8\times 0.8+0.12\times 0.12\times 0.12}$ is:

A	0.0125
B	0.125
C	0.25
D	0.5

Question 2 Explanation:

Let 0.4= a Therefore 0.8= 2a
And 0.06= b therefore 0.12= 2b
Therefore expression

$\begin{align} & =\frac{{{a}^{3}}+{{b}^{3}}}{8{{a}^{3}}+8{{b}^{3}}} \\ & =\frac{{{a}^{3}}+{{b}^{3}}}{8\left( {{a}^{3}}+{{b}^{3}} \right)} \\ & =\frac{1}{8}=0.125 \\ \end{align}$

Question 3

The value of

$\frac{7.15\times 7.15\times 7.15-3.97\times 3.97\times 3.97}{7.15\times 7.15+7.15\times 3.97+3.97\times 3.97}$ in simplified form is:

A	3.15
B	3.18
C	7.15
D	2.18

Question 3 Explanation:

Let 7.15= a and 3.97= b
Therefore expression

$\begin{align} & =\frac{{{a}^{3}}-{{b}^{3}}}{{{a}^{2}}+ab+{{b}^{2}}} \\ & =\frac{\left( a-b \right)\left( {{a}^{2}}+ab+{{b}^{2}} \right)}{{{a}^{2}}+ab+{{b}^{2}}} \\ & =a-b=7.15-3.97=3.18 \\ \end{align}$

Question 4

The value of

$\frac{{{\left( 4.5 \right)}^{3}}+{{\left( 3.7 \right)}^{3}}+{{\left( 1.8 \right)}^{3}}-3\times 4.5\times 3.7\times 1.8}{{{\left( 4.5 \right)}^{2}}+{{\left( 3.7 \right)}^{2}}+{{\left( 1.8 \right)}^{2}}-4.5\times 3.7-3.7\times 1.8-1.8\times 4.5}$ is:

A	0
B	1
C	10
D	30

Question 4 Explanation:

Let 4.5= a, 3.7= b, 1.8= c
Therefore expression

$\begin{align} & =\frac{{{a}^{3}}+{{b}^{3}}{{+}^{3}}-3abc}{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-bc-ca} \\ & =a+b+c \\ & =4.5+3.7+1.8 \\ & =10 \\ \end{align}$

Question 5

The value of

$\overline{0.5}+\overline{0.7}+0.\overline{57}$ is:

A	$1.\overline{87}$
B	$1.\overline{90}$
C	$1.\overline{82}$
D	$0.\overline{98}$

Question 5 Explanation:

$\begin{align} & \overline{0.5}+\overline{0.7}+0.\overline{57} \\ & =\frac{5}{9}+\frac{7}{9}+\frac{57}{99} \\ & =\frac{55+77+57}{99} \\ & =\frac{189}{99}=1\frac{90}{99} \\ & =1.\overline{90} \\ \end{align}$

Once you are finished, click the button below. Any items you have not completed will be marked incorrect. Get Results

There are 5 questions to complete.

List

→

Return

Shaded items are complete.