Question
The price of a game increases from \(\$48\) to \(\$56.40\) .
Calculate the percentage increase in the price.
▶️Answer/Explanation
$17.5$
$
\text{Percentage increase} = \frac{\text{New price} – \text{Original price}}{\text{Original price}} \times 100
$
$
= \frac{56.40 – 48}{48} \times 100
$
$
= \frac{8.40}{48} \times 100
$
$
= 0.175 \times 100
$
$
= 17.5\%
$
Question
(a) Shade $\frac{2}{9}$ of this shape.
(b) Write $\frac{2}{9}$ as a percentage.
▶️Answer/Explanation
(a) 8 squares shaded
(b) 22.2 or 22.22…
Detailed Solution:
(a)
The grid is $6 × 6,$ so there are 36 squares in total.
$
\frac{2}{9} \times 36 = 8 \text{ squares}.
$
any 8 squares on the grid to represent \(\frac{2}{9}\).
(b)
$
2 \div 9 \approx 0.2222
$
$
0.2222 \times 100 \approx 22.22\%
$
Question
Use your calculator to work out
\(\frac{8.2^2-52.48}{7.38-6.18}\)
▶️Answer/Explanation
Using a calculator, the expression \(\frac{8.2^2-52.48}{7.38-6.18}\) can be calculated as follows:
\(\frac{8.2^2-52.48}{7.38-6.18} = \frac{67.24-52.48}{1.2} = \frac{14.76}{1.2} = 12.3\)
Therefore, the result is 12.3.
Question
(a) Calculate \(\sqrt{2.3+6.4^{2}}\), writing down your full calculator display.
……………………………………….
(b) Write your answer to part (a) correct to 4 decimal places.
……………………………………….
▶️Answer/Explanation
(a) The calculator display would show:
\(\sqrt{2.3+6.4^{2}} = \sqrt{2.3+40.96} = \sqrt{43.26}\)
\(\sqrt{43.26} \approx 6.583314\)
(b) Rounding the result to 4 decimal places, we have:
\(\sqrt{2.3+6.4^{2}} \approx 6.5833\)
Therefore, the correct answer to part (b) is 6.5833, correct to 4 decimal places.
Question
(a) Calculate \(\sqrt[3]{-4.3\times 6.7^{2}}\) and write down all the figures shown on your calculator.
(b) Write your answer to part (a) correct to 4 decimal places.
▶️Answer/Explanation
(a) To calculate \(\sqrt[3]{-4.3\times 6.7^{2}}\):
Calculate \(6.7^{2}\):
\(6.7 \times 6.7 = 44.89\)
\(-4.3 \times 44.89 = -193.927\)
\(\sqrt[3]{-193.927} \approx -5.779266\)
(b) To write the answer correct to 4 decimal places, we round the result from part (a) to four decimal places:
\(-5.7793\) (rounded to four decimal places)
Question
This is Edha’s method to work out\( 99\times 27 \) without using a calculator.
Show how to use Edha’s method to work out \(99\times 68\) without using a calculator.
▶️Answer/Explanation
100× 68 -68
= − 6800 -68
= 6732