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Basic Maths: Test 31

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Question 1
Simplify: $\frac{{{\left( 4.5 \right)}^{3}}+{{\left( 1.7 \right)}^{3}}+{{\left( 2.8 \right)}^{3}}-3\times 4.5\times 1.7\times 2.8}{{{\left( 4.5 \right)}^{2}}+{{\left( 1.7 \right)}^{2}}+{{\left( 2.8 \right)}^{2}}-4.5\times 1.7-1.7\times 2.8-2.8\times 4.5}$
A
9
B
11
C
12
D
3
Question 1 Explanation:
$\frac{{{\left( 4.5 \right)}^{3}}+{{\left( 1.7 \right)}^{3}}+{{\left( 2.8 \right)}^{3}}-3\times 4.5\times 1.7\times 2.8}{{{\left( 4.5 \right)}^{2}}+{{\left( 1.7 \right)}^{2}}+{{\left( 2.8 \right)}^{2}}-4.5\times 1.7-1.7\times 2.8-2.8\times 4.5}$ $\begin{align} & =\frac{\left( 4.5+1.7+2.8 \right)\,\left( {{4.5}^{2}}+{{1.7}^{2}}+{{2.8}^{2}}-4.5\times 1.7-1.7\times 2.8-2.8\times 4.5 \right)}{{{\left( 4.5 \right)}^{2}}+{{\left( 1.7 \right)}^{2}}+{{\left( 2.8 \right)}^{2}}-4.5\times 1.7-1.7\times 2.8-2.8\times 4.5} \\ & =4.5+1.7+2.8=9 \\ \end{align}$
Question 2
The value of $0.006\times 0.07\times 0.026\div \left( 0.13\times 0.0003 \right)$is:
A
2.8
B
0.28
C
0.028
D
2.08
Question 2 Explanation:
$\begin{align} & 0.006\times 0.07\times 0.026\div \left( 0.13\times 0.0003 \right) \\ & =0.006\times 0.07\times 0.026\div \left( 0.000039 \right) \\ & =0.006\times 0.07\times \frac{0.026}{0.000039} \\ & =\frac{0.00001092}{0.000039}=0.28 \\ \end{align}$. 
Question 3
Find the sum of the following: \[\left[ \frac{1}{28}+\frac{1}{70}+\frac{1}{130}+\frac{1}{208} \right]\div {{\left( \frac{3}{4} \right)}^{2}}\]
A
$\frac{1}{2}$
B
1
C
$\frac{1}{9}$
D
$\frac{1}{2520}$
Question 3 Explanation:
$\begin{align} & \left[ \frac{1}{28}+\frac{1}{70}+\frac{1}{130}+\frac{1}{208} \right]\div {{\left( \frac{3}{4} \right)}^{2}} \\ & =\left[ \frac{1}{4\times 7}+\frac{1}{7\times 10}+\frac{1}{10\times 13}+\frac{1}{13\times 16} \right]\times {{\left( \frac{4}{3} \right)}^{2}} \\ & =\frac{1}{3}\left[ \frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16} \right]\times \frac{16}{9} \\ & =\frac{1}{3}\left[ \frac{1}{4}-\frac{1}{16} \right]\times \frac{16}{9} \\ & =\frac{1}{3}\times \frac{12}{64}\times \frac{16}{9}=\frac{1}{9} \\ \end{align}$
Question 4
Simplify: $\frac{2.68\times 36+2.68\times 24}{{{\left( 6.34 \right)}^{2}}-{{\left( 3.66 \right)}^{2}}}$
A
7.2
B
8
C
6
D
10
Question 4 Explanation:
$\begin{align} & =\frac{2.68\left( 60 \right)}{\left( 6.34+3.66 \right)\,\left( 6.34-3.66 \right)} \\ & =\frac{2.68(60)}{10\times 2.68}=6 \\ \end{align}$
Question 5
The value of $\frac{{{\left( 0.05 \right)}^{2}}-{{\left( 0.02 \right)}^{2}}}{0.05-0.02}$is :
A
0.4
B
0.007
C
0.07
D
0.04
Question 5 Explanation:
$\begin{align} & \frac{{{\left( 0.05 \right)}^{2}}-{{\left( 0.02 \right)}^{2}}}{0.05-0.02} \\ & \left[ U\sin g\,\,\,{{a}^{2}}-{{b}^{2}}=\left( a+b \right)\left( a-b \right) \right] \\ & =\frac{\left( 0.05+0.02 \right)\,\left( 0.05-0.02 \right)}{0.05-0.02} \\ & =0.05+0.02=0.07 \\ \end{align}$
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