Published on February 17th 2025 | 1 min , 76 words
Use Mathematical tables to find the reciprocal of 0.0247, hence evaluate \[\frac{\sqrt[3]{3.025}}{0.0247}\] Correct to 2 d.p (3 marks) \[\sqrt[3]{3.025} = 1.4462\] \[\frac{1}{0.0247} = (0.0247)^{-1}\] \[= (2.47 \times 10^{-2})^{-1}\] \[= 0.4049 \times 10^2\] \[= 40.49\]
Use reciprocal, square and square root tables to evaluate, to 4 significant figures, the expression
\[
\sqrt{\frac{1}{24.56} + 4.346^2}
\]
\[
24.56 = 2.456 \times 10
\]
\[
4.346^2 = 18.89
\]
\[
\sqrt{\frac{1}{2.456 \times 10} + 18.89}
\]
\[
= \sqrt{\frac{1}{2.456} \times \frac{1}{10} + 18.89}
\]
\[
= \sqrt{\left( 0.4072 \times \frac{1}{10} \right) + 18.89}
\]
\[
= \sqrt{0.04072 + 18.89}
\]
\[
= \sqrt{18.93072}
\]
\[
= \sqrt{18.93}
\]
\[
= 4.351 \quad \text{(Answer)}
\]
Use squares, square roots and reciprocal tables to evaluate (3mks)
\[
3.045^2 + \frac{1}{\sqrt{49.24}}
\]
\[
3.045^2 = 9.272
\]
\[
\sqrt{49.24} = 7.017
\]
\[
\frac{1}{7.017} = 0.1425
\]
\[
9.272 + \frac{1}{7.017}
\]
\[
= 9.272 + 0.1425
\]
\[
= 9.4175
\]