Summer workbook — GCSE Foundation

1.Two bags of mixed nuts are combined. Bag A has peanuts and cashews in the ratio 2 : 3. Bag B has peanuts and cashews in the ratio 1 : 4. Both bags contain the same total number of nuts. Work out the fraction of the combined mixture that is peanuts.

2.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

3.Work out √144 − 2 × 3 + √25

4.Work out 15% of £40, using 10% and 5%.

5.Work out 2/3 × 3/4 exactly, giving your answer in its simplest form.

6.Write 0.00072 in standard form.

7.Write 0.36 as a fraction in its simplest form.

8.Write these numbers in order, starting with the smallest: 3, −1, 0, −5

9.The length of a pencil is 8.4 cm, correct to 1 decimal place. Using L for the length of the pencil in centimetres, write down the error interval for L.

10.Work out 3 1/5 + 1 2/3. Give your answer as a mixed number in its simplest form.

1.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

2.The graph of P = 480 ÷ V shows how the pressure, P pascals, of a gas depends on its volume, V cm³, at constant temperature. Use the relationship to work out the volume when the pressure is 32 pascals, and then work out by how much the volume increases when the pressure drops to 24 pascals.

3.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

4.Solve 5x² − 15x = 0.

5.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.

6.Solve 4x² − 9 = 0.

7.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.

8.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

9.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.

10.A number machine multiplies its input by 3. The output is 15. Work out the input.

1.To make a shade of green paint, the amount of yellow paint used is always 0.75 times the amount of blue paint used. Write the amount of blue paint as a fraction of the amount of yellow paint, in its simplest form.

2.A force of 126 N acts on an area of 3.5 m². Work out the pressure on the area, in N/m².

3.A train travels at a constant speed of 90 km/h. Work out the speed in m/s.

4.A metal cylinder has a mass of 356.5 g and a volume of 47 cm³. Work out the density of the cylinder, in g/cm³, to 1 decimal place.

5.A recipe for 4 people needs 300 g of rice. Work out how much rice is needed for 6 people, assuming the amount is in direct proportion to the number of people.

6.Two taxi firms show their charges on straight-line graphs, with the cost in pounds on the vertical axis and the distance in miles on the horizontal axis. Firm A's line passes through (0, 4) and (5, 14). Firm B's line passes through (0, 6) and (5, 21). Work out which firm charges more per mile.

7.A coach travels the 54 miles from London to Brighton in 1 hour 30 minutes. Work out the average speed of the coach, in mph.

8.A tray holds 8 muffins and 20 cupcakes. Write the ratio of the number of muffins to the number of cupcakes in its simplest form.

9.Sam has £24. Tom has £16. Write the amount of money Sam has as a fraction of the amount of money Tom has, giving your answer in its simplest form.

10.Zara is paid £9 per hour. Her wage is directly proportional to the number of hours she works. Work out her wage for working 6 hours.