3 Marks Question

Question 13 Marks

In a stack there are $5$ books each of thickness $20 mm$ and $5$ paper sheets each of thickness $0.016 mm$. What is the total thickness of the stack?

Answer

Total thickness of books $= 5 \times 20 mm = 100 mm$
Total thickness of paper sheets $= 5 \times 0.016 mm = 0.080 mm$
$\therefore$ Total thickness of the stack
$=$ Total thickness of books $+$ Total thickness of paper sheets
$= 100 mm + 0.080 mm$
$= (100 + 0.080) mm$
$= 100.080 mm$
$= 1.0008 \times 10^2$ mm.

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Question 23 Marks

Evaluate :${\left( {\frac{5}{8}} \right)^{ - 7}} \times {\left( {\frac{8}{5}} \right)^{ - 4}}$

Answer

${\left( {\frac{5}{8}} \right)^{ - 7}} \times {\left( {\frac{8}{5}} \right)^{ - 4}}$
$ = \frac{{{5^{ - 7}}}}{{{8^{ - 7}}}} \times \frac{{{8^{ - 4}}}}{{{5^{ - 4}}}}$
$ = \frac{{{5^{ - 7}}}}{{{5^{ - 4}}}} \times \frac{{{8^{ - 4}}}}{{{8^{ - 7}}}}$
$ =5^{(-7)-(-4)} \times 8^{(-4)-(-7)} $
$ =5^{-7+4} \times 8^{-4+7} $
$ =5^{-3} \times 8^3 $
$\frac{1}{{{5^3}}} \times {8^3}$
$ = \frac{{{8^3}}}{{{5^3}}}$
$ = \frac{{512}}{{125}}$$ = 4\frac{{12}}{{125}}$

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Question 33 Marks

Find the value of :${\left\{ {{{\left( {\frac{{ - 2}}{3}} \right)}^{ - 2}}} \right\}^2}$

Answer

${\left\{ {{{\left( {\frac{{ - 2}}{3}} \right)}^{ - 2}}} \right\}^2}$
$ = {\left( {\frac{{ - 2}}{3}} \right)^{( - 2) \times 2}}$
$ = {\left( {\frac{{ - 2}}{3}} \right)^{ - 4}}$
$ = \frac{{{{( - 2)}^{ - 4}}}}{{{{(3)}^{ - 4}}}}$
$ = \frac{{{3^4}}}{{{{( - 2)}^4}}}$
$ = \frac{{3 \times 3 \times 3 \times 3}}{{( - 2) \times ( - 2) \times ( - 2) \times ( - 2)}}$
$ = \frac{{81}}{{16}}$

= $5{1\over16}$

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Question 43 Marks

Find the value of :${\left( {\frac{1}{2}} \right)^{ - 2}} + {\left( {\frac{1}{3}} \right)^{ - 2}} + {\left( {\frac{1}{4}} \right)^{ - 2}}$

Answer

${\left( {\frac{1}{2}} \right)^{ - 2}} + {\left( {\frac{1}{3}} \right)^{ - 2}} + {\left( {\frac{1}{4}} \right)^2}$
$ = \frac{{{1^{ - 2}}}}{{{2^{ - 2}}}} + \frac{{{1^{ - 2}}}}{{{3^2}}} + \frac{{{1^2}}}{4}$
$ = \frac{{{2^2}}}{{{1^2}}} + \frac{{{3^2}}}{{{1^2}}} + \frac{{{4^2}}}{{{1^2}}}$
$\frac{4}{1} + \frac{9}{1} + \frac{{16}}{1}$
= 4 + 9 + 16
= 29

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Question 53 Marks

Find the value of :$(2^{-1}$ $\times$ $4^{-1})$ $\div$ $2^{-2}$

Answer

$ \left(2^{-1} \times 4^{-1}\right) \div 2^{-2} $
$= \left\{2^{-1} \times\left(2^2\right)^{-1}\right\} \div 2^{-2} $
$= \left\{2^{-1} \times 2^2 \times(-1)\right\} \div 2^{-2} $
$= \left(2^{-1} \times 2^{-2}\right) \div 2^{-2} $
$ =2^{(-1)} \times 2^{(-2)} \div 2^{-2} $
$= 2^{-3} \div 2^{-2} $
$ = \frac{{{2^{ - 3}}}}{{{2^{ - 2}}}}$
$ = \frac{1}{{{2^{( - 2) - ( - 3)}}}}$
$ = \frac{1}{{{2^{ - 2 + 3}}}}$
$ = \frac{1}{{{2^1}}}$
$ = \frac{1}{2}$

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Maths 3 Marks Question

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