12 questions · 100 marks · ≈ 2 hours
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Write 2.51×10⁴ as an ordinary number.
Write 0.000 006 37 in standard form.
Calculate 5 10100 7 1099 Give your answer in standard form.
Calculate 5 10100 7 1099 Give your answer in standard form.
5 cm Diagram NOT accurately drawn 8 cm Figure 1 Figure 1 shows a right circular solid cylinder with radius 5 cm and height 8 cm
Calculate, in cm² to 3 significant figures, the total surface area of the cylinder. A and B are two mathematically similar solids. The surface area of A is 3051 cm² The surface area of B is 5424 cm² Given that volume of A + volume of B = 2548
…………… cm³
calculate the volume, in cm³, of B
Solve the inequality 3p − 2 > 4
Solve the inequality 5(2 q )
On the grid opposite, by drawing suitable straight lines and using shading, show the region R that satisfies the inequalities
y > 1 x + y < 5 y < 2x + 3
Label the region R
B C Diagram NOT accurately drawn 21.7 cm 56° A D 34.9 cm Figure 2 Figure 2 shows trapezium ABCD AB = 21.7 cm AD = 34.9 cm ∠ADC = 56° ∠ABC = ∠BAD = 90°
Calculate the perimeter, in cm to 3 significant figures, of trapezium ABCD P Diagram NOT accurately drawn r cm Q 72° r cm O Figure 3 Figure 3 shows sector POQ of a circle with centre O and radius r cm ∠POQ = 72° Given that the perimeter of trapezium ABCD is equal to the perimeter of sector POQ
calculate the area, in cm² to 3 significant figures, of sector POQ
Solve the simultaneous equations
x + 2y = 3
Show clear algebraic working.
The accurate pie chart below shows information about the ages, in years, of 120 runners. over 50 under 18 35 to 50 18 to 24 25 to 34
Calculate how many of these 120 runners are aged 25 to 34 Xavier is one of the runners. He runs 3000 metres to the nearest 100 metres in 18 minutes to the nearest minute
Calculate the lower bound, in metres/minute to 3 significant figures, for Xavier’s average speed. Show all your working.
The times, in minutes, for the 120 runners to complete 5 km is recorded. No runner takes less than 15 minutes or more than 70 minutes. The incomplete table and the incomplete histogram give information about the times.
| Minutes ( minutes) | Frequency |
|---|---|
| 10 | |
| 16 | |
| 28 | |
| 24 | |
Complete the table and the histogram.
Alex produces and sells cans of drink. The table shows the production costs for 80 000 cans of drink.
| Production cost (euros) | |
|---|---|
| Manufacturing | 31 000 |
| Other | 4 350 |
| Total production cost | 35 350 |
Calculate the manufacturing cost as a percentage of the total production cost. Give your answer to one decimal place. Alex sells each of the 80 000 cans of drink for £0.60 Using the exchange rate of £1 = 1.15 euros …………… , ……………
calculate the percentage profit that Alex makes. Give your answer to 3 significant figures. Alex borrows £20 000 on 1st January 2026 from a bank. On 31st December each year, starting on 31st December 2026, the bank charges interest of 8.4% on the amount of money that Alex owes the bank. This interest is added to the amount of money that he owes the bank. Given that Alex does not repay any of the money that he owes the bank …………… , ……………
calculate how much money Alex owes the bank on 1st January 2028 Give your answer to 2 decimal places. Alex also sells snacks. The selling price for each snack, after tax is added, is £0.90 Given that the rate of tax is 20%
calculate the selling price for each snack, in £, before tax is added.
Triangle A and triangle E are drawn on the grid opposite.
Describe fully the single transformation that maps triangle A onto triangle E Triangle A is transformed to triangle B under the translation
On the grid, draw and label triangle B Triangle A is transformed to triangle C under an enlargement with scale factor 3 and centre of enlargement (5, 7)
On the grid, draw and label triangle C Triangle A is transformed to triangle D under the transformation with matrix M where 1 0 M
On the grid, draw and label triangle D
Complete the table of values for
| x | −1 | 0 | 0.25 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|---|---|
| y | 7 | 7.22 | −11 |
On the grid opposite, plot the points from your completed table and join them to form a smooth curve.
By drawing a suitable straight line (at least 3 cm long) on the grid, find an estimate for the gradient of the curve at the point where x = 0.5
Use your graph, to estimate, to one decimal place, the solutions of the equation
By drawing a suitable straight line on the grid, find an estimate for the range of values of x, to one decimal place, in the interval 0 < x ≤ 4 for which
Show clear algebraic working.
Figure 4 shows solid ABCDE
The horizontal base CDE is a triangle.
The vertical face ABED is a trapezium.
The point F lies on BC such that BF : FC = 2 : 1
AC = 20 cm AD = 10 cm BE = 15 cm DE = 12 cm
∠BCE = 45° ∠ADC = ∠ADE = ∠BED = ∠BEC = 90°
Calculate the length, in cm to one decimal place, of AF
Show all your working.
[ Cosine rule: ]
Figure not shown in this reconstruction — the printed paper includes a 3-D diagram (not drawn accurately). Labels in the original figure: B, A, E, D, C, F · Figure values: 15 cm, 10 cm, 12 cm, 20 cm, 45°.
The function f has domain −8 ≤ x ≤ 8
Figure 5 shows the graph of y = f(x), which consists of a line segment from (–8, 3) to (–4, 0) and a line segment from (–4, 0) to (8, 9)
(a) Write down the range of the function f
The function g is defined as
Figure not shown in this reconstruction — the printed paper includes a graph (Figure 5); the segment description above is complete for this part.
State the value of x which must be excluded from any domain of the function g
Find gf(0)
Find the inverse function g–1 in the form g-1(x) = … Give your answer in its simplest form.
A bag contains n sweets. There are 9 orange sweets in the bag. The rest of the sweets are purple. Mina takes at random a sweet from the bag and eats it. Stuart then takes at random a sweet from the bag and eats it. The probability that Mina and Stuart both eat a sweet of the same colour is
Find the probability that all 9 orange sweets remain in the bag.
Show clear algebraic working.