Foundation Stretch A

Question 1 [1 marks]

Number and Calculation

Round 3,652 to the nearest 100.

Question 2 [2 marks]

Pythagoras and Trigonometry

A right-angled triangle has two shorter sides of length 6 cm and 8 cm. Diagram: right-angled triangle with the two shorter sides marked 6 cm and 8 cm meeting at the right angle, hypotenuse unmarked labelled x cm. Calculate the length of the hypotenuse.

Question 3 [2 marks]

Indices and Standard Form

Simplify each expression, leaving your answer as a single power.

a^4 x a^3

y^5 x y

Question 4 [2 marks]

Sequences

Here are the first five terms of a sequence. 2, 5, 7, 12, 19

Explain how each term of the sequence, after the first two, is found from the previous two terms.

Work out the next term in the sequence.

Question 5 [3 marks]

Fractions, Decimals and Percentages

A car park has 84 spaces. On Saturday, 35 spaces are used by staff, 21 spaces are used by visitors and the rest are empty.

Work out the number of empty spaces.

Write the fraction of spaces that were empty, in its simplest form.

Question 6 [3 marks]

Graphs and Coordinates

On a treasure map, positions are given as coordinates (across, up) on a grid. The chest is at (2, 3). The key is 5 units to the right and 4 units up from the chest.

Work out the coordinates of the key.

The cave entrance lies on the y-axis, 6 units above the origin. Write down the coordinates of the cave entrance.

Question 7 [4 marks]

Angles and Geometrical Reasoning

A rectangular kitchen measures 4.8 m by 3.6 m in real life. A scale drawing is made using a scale of 1 : 60.

Work out the dimensions of the kitchen on the scale drawing, in centimetres.

Work out the area of the kitchen on the scale drawing, in cm^2.

Question 8 [4 marks]

Ratio and Proportion

At the start of the year, the exchange rate was £1 = 1.20 euros. By the summer, the rate had increased by 5%.

Work out the new exchange rate.

Kwame changes £300 into euros using the new rate. Work out how many euros he receives, ft from (a).

Question 9 [5 marks]

Statistics and Probability

Mrs Devine, an assistant head teacher, checked whether 90 pupils across three tutor groups had completed their homework. The completed two-way table is shown below.

Write down the number of pupils in 7B who had not completed their homework.

Find the probability that a randomly chosen pupil (from all 90) had completed their homework.

One pupil is chosen at random from 7C. Find the probability that this pupil had completed their homework.

Question 10 [1 marks]

Area, Volume and Measures

Convert 3500 metres to kilometres.

Question 11 [1 marks]

Number and Calculation

A shop price is £24.95. Give a quick estimate of the price to 2 significant figures for a mental comparison.

Question 12 [1 marks]

Indices and Standard Form

Work out the cube root of 27.

Question 13 [1 marks]

Statistics and Probability

A cycling club recorded the distances, in km, ridden by members last weekend. Distance (km): 0-10, 10-25, 25-40, 40-60 Frequency: 5, 12, 9, 4 Find the midpoint of the class 10-25.

Question 14 [1 marks]

Number and Calculation

Round 3.846 to 2 decimal places.

Question 15 [2 marks]

Linear Algebra

Solve x / 3 + 4 = 9 Show your working.

Question 16 [2 marks]

Angles and Geometrical Reasoning

Three parallel lines, l, m and n, are all crossed by the same straight transversal. The angle between the transversal and l is 58 degrees. Angle y is in the corresponding position where the transversal crosses n. Work out y, giving a reason.

Question 17 [2 marks]

Number and Calculation

Work out the highest common factor (HCF) of 42 and 56.

Question 18 [2 marks]

Graphs and Coordinates

The graphs of y = 2x - 6 and y = -x + 6 are drawn on the grid. Write down the solution of the simultaneous equations y = 2x - 6 and y = -x + 6.

Question 19 [2 marks]

Linear Algebra

a = 6 and b = -3. Work out the value of 2a - b.

Question 20 [2 marks]

Fractions, Decimals and Percentages

Tom says, 'A laptop's price was reduced by 15% in a sale. To find the original price from the sale price, you should increase the sale price by 15%.' Tom is wrong. Explain why Tom is wrong. You should include an example with numbers to support your answer.

Question 21 [2 marks]

Linear Algebra

A square has side length (3x - 2) cm. Show that the perimeter of the square can be written as 12x - 8.

Question 22 [2 marks]

Number and Calculation

Work out the least common multiple of 14, 21 and 35.

Question 23 [9 marks]

Graphs and Coordinates

y = x^3 - 9x x : -3 , -2 , -1 , 0 , 1 , 2 , 3 y : 0 , _ , 8 , _ , -8 , _ , 0

Complete the table of values for y = x^3 - 9x.

Draw the graph of y = x^3 - 9x for -3 <= x <= 3 on the grid provided.

By drawing the line y = 5 on the same grid, use your graph to find estimates for the three solutions of x^3 - 9x = 5.

Write down the three values of x for which x^3 - 9x = 0.

Question 24 [2 marks]

Number and Calculation

The number line shows the midday temperature recorded at two weather stations in Scotland. Station A, near the summit of Ben Nevis, is at -12 degrees C. Station B, in the valley below, is at 9 degrees C. Work out the difference between the temperature at Station B and the temperature at Station A.

Question 25 [2 marks]

Graphs and Coordinates

The line has equation y = -x + 4. Part (a) Work out y when x = 2. Part (b) Work out y when x = -1.

Question 26 [2 marks]

Linear Algebra

Solve 0.25m = 1.5. Show your method.

Question 27 [3 marks]

Area, Volume and Measures

Triangle ABC is similar to triangle XYZ, with AB corresponding to XY and BC corresponding to YZ. AB = 8 cm, XY = 12 cm and BC = 10 cm.

Question 28 [3 marks]

Statistics and Probability

In a pictogram for a car park each car symbol represents 8 cars. There are 9 car symbols and 2 quarter symbols (each quarter symbol represents a quarter of one car symbol). How many cars are represented?

Question 29 [3 marks]

Graphs and Coordinates

A straight line has gradient -2 and passes through the point (3, 1). Find the equation of the line, giving your answer in the form y = mx + c.

Question 30 [4 marks]

Area, Volume and Measures

A pipe is a hollow cylinder with outer radius 8 cm and inner radius 6 cm. The pipe is 50 cm long. Diagram: hollow cylindrical pipe, outer radius 8 cm, inner radius 6 cm, length 50 cm. Work out the volume of material used to make the pipe. Give your answer correct to 3 significant figures.

Question 31 [2 marks]

Ratio and Proportion

A 1.2 kg bag of sugar costs £3.60. Work out the cost of 300 g of sugar.

Question 32 [3 marks]

Graphs and Coordinates

A quadrilateral has vertices at A(0, 0), B(4, 2), C(6, -2) and D(2, -4). Show that AB is parallel to DC.