Basic Maths: Test 14

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Basic Maths: Test 14

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Question 1

On Simplification of $ \displaystyle \frac{{{\left( 2.644 \right)}^{2}}-{{\left( 2.356 \right)}^{2}}}{0.144}$

A	1
B	4
C	5
D	10

Question 1 Explanation:

$ \displaystyle \begin{array}{l}p=\frac{{{\left( 2.644 \right)}^{2}}-{{\left( 2.356 \right)}^{2}}}{0.144}\\=\frac{\left( 2.644-2.356 \right)\left( 2.644+2.356 \right)}{0.144}\\=\frac{0.288\times 5}{0.144}=10\end{array}$

Question 2

Evaluate $ \displaystyle \frac{9\left| 3-5 \right|-5\left| 4 \right|\div 10}{-3\left( 5 \right)-2\times 4\div 4}$

A	$ \displaystyle \frac{9}{10}$
B	$ \displaystyle -\frac{8}{17}$
C	$ \displaystyle -\frac{16}{17}$
D	$ \displaystyle \frac{4}{7}$

Question 2 Explanation:

$ \displaystyle \begin{array}{l}?=\frac{9\left| 3-5 \right|-5\left| 4 \right|\div 10}{-3\left( 5 \right)-2\times 4\div 4}\\=\frac{9\times 2-5\times 4\div 10}{-15-8\div 4}\\=\frac{18-2}{-17}=-\frac{16}{17}\end{array}$

Question 3

Simplification of $ \displaystyle \frac{{{\left( 3.4567 \right)}^{2}}-{{\left( 3.4533 \right)}^{2}}}{0.0017}$ yields the results:

A	13.82
B	7
C	6.81
D	7.1

Question 3 Explanation:

$ \displaystyle \begin{array}{l}?=\frac{\left( 3.4567+3.4533 \right)\left( 3.4567-3.4533 \right)}{0.0017}\\=\frac{6.9100\times 0.0034}{0.0017}=\text{13}\text{.82}\end{array}$

Question 4

$ \displaystyle \left( \frac{\sqrt{625}}{12}\times \frac{14}{\sqrt{25}}\times \frac{12}{\sqrt{196}} \right)$

A	6
B	5
C	8
D	11

Question 4 Explanation:

$ \displaystyle \begin{array}{l}p=\left( \frac{\sqrt{625}}{12}\times \frac{14}{\sqrt{25}}\times \frac{12}{\sqrt{196}} \right)\\=\frac{25}{12}\times \frac{14}{5}\times \frac{12}{14}=5\end{array}$

Question 5

Simplify $ \displaystyle \frac{1}{2}-\left[ 3\frac{1}{4}\div \left\{ 1\frac{1}{4}-\frac{1}{2}\left( 1\frac{1}{2}-\frac{1}{3}-\frac{1}{6} \right) \right\} \right]$

A	$ \displaystyle \frac{23}{6}$
B	$ \displaystyle \frac{-23}{6}$
C	$ \displaystyle 9\frac{1}{2}$
D	$ \displaystyle \frac{2}{9}$

Question 5 Explanation:

$ \displaystyle \begin{array}{l}\frac{1}{2}-\left[ 3\frac{1}{4}\div \left\{ 1\frac{1}{4}-\frac{1}{2}\left( 1\frac{1}{2}-\frac{1}{3}-\frac{1}{6} \right) \right\} \right]\\=\frac{1}{2}-\left[ \frac{13}{4}\div \left\{ \frac{5}{4}-\frac{1}{2}\left( \frac{9-2-1}{6} \right) \right\} \right]\\=\frac{1}{2}-\left[ \frac{13}{4}\div \left\{ \frac{5}{4}-\frac{1}{2}\times \frac{6}{6} \right\} \right]\\=\frac{1}{2}-\left[ \frac{13}{4}\div \left\{ \frac{5}{4}-\frac{1}{2} \right\} \right]\\=\frac{1}{2}-\left[ \frac{13}{4}\div \left\{ \frac{5-2}{4} \right\} \right]\\=\frac{1}{2}-\left[ \frac{13}{4}\div \frac{3}{4} \right]\\=\frac{1}{2}-\left[ \frac{13}{4}\times \frac{4}{3} \right]\\=\frac{1}{2}-\frac{13}{3}\\=\frac{3-26}{6}\\=\frac{-23}{6}\end{array}$

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