Brilliant work, mate! You smashed it with 80%!
Question Breakdown
Write \( 0.0045 \) in standard form.
Standard form is \( A \times 10^n \) where \( 1 \leq A < 10 \). Move the decimal point 3 places to the right to get \( 4.5 \): \( 0.0045 = 4.5 \times 10^{-3} \).
The graph shows a straight line. Find the equation of the line in the form \( y = mx + c \).
Gradient \( m = \frac{\text{rise}}{\text{run}} = \frac{5 - 1}{2 - 0} = \frac{4}{2} = 2 \).
The line crosses the \( y \)-axis at \( 1 \), so \( c = 1 \). The equation is \( y = 2x + 1 \).
The diagram shows a triangle. The diagram is not drawn accurately. Work out the size of angle \( x \).
The angles inside a triangle add up to \( 180° \).
\( x = 180° - 55° - 80° = 45° \).
The diagram shows a right-angled triangle. The diagram is not drawn accurately. Work out the length of the hypotenuse.
By Pythagoras' theorem, \( c^2 = a^2 + b^2 = 6^2 + 8^2 = 36 + 64 = 100 \).
\( c = \sqrt{100} = 10 \) cm.
The bar chart shows the number of goals a team scored on each day of a week. Work out the range of the number of goals scored.
The range is the highest value minus the lowest value.
Highest = 7 (Tuesday), lowest = 2 (Wednesday), so range \( = 7 - 2 = 5 \).
180 students were asked their favourite sport. The pie chart shows the results, and the angle for Football is \( 120° \). Work out the number of students whose favourite sport is Football.
The whole pie represents 180 students across \( 360° \).
Football \( = \frac{120}{360} \times 180 = \frac{1}{3} \times 180 = 60 \) students.
A biased coin has \( P(\text{Heads}) = 0.6 \). The tree diagram shows the coin being flipped twice. Work out the probability of getting two heads.
Multiply along the branches for Heads then Heads:
\( P(\text{H, H}) = 0.6 \times 0.6 = 0.36 \).
The distance–time graph shows part of a car journey. Work out the speed of the car during the first 2 hours. Give the units of your answer.
Speed \( = \frac{\text{distance}}{\text{time}} = \frac{120}{2} = 60 \) km/h.
Share £120 in the ratio \( 3 : 2 \). Work out the larger share.
Total parts \( = 3 + 2 = 5 \).
Larger share \( = \frac{3}{5} \times 120 = £72 \).
In a sale, the price of a coat is reduced by 20%. The sale price is £64. Work out the original price of the coat.
The sale price is \( 100\% - 20\% = 80\% \) of the original price.
So \( 80\% = £64 \), which means original price \( = \frac{64}{0.8} = £80 \).
