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Basic Maths: Test 44

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