Edexcel-Style Year 10 Foundation Paper 1

Question 1 [1 marks]

Indices and Standard Form

Write 9.1 x 10^4 as an ordinary number.

Question 2 [2 marks]

Area, Volume and Measures

Rectangle A measures 5 cm by 8 cm.

Which of these rectangles is mathematically similar to rectangle A?

Write down the scale factor of enlargement from rectangle A to the rectangle you chose in part (a).

Question 3 [2 marks]

Angles and Geometrical Reasoning

Lines l and m are parallel and are crossed by a straight transversal. Angle y is in the corresponding position to the 118 degree angle marked above line l.

Question 4 [2 marks]

Sequences

Here are the first four terms of a sequence. 2, 6, 10, 14

Write down the next two terms of the sequence.

Describe, in words, the term-to-term rule for the sequence.

Question 5 [3 marks]

Graphs and Coordinates

Complete the table of values for y = x^3 - 1. x : -2 , -1 , 0 , 1 , 2 y : -9 , _ , _ , _ , 7

Question 6 [1 marks]

Ratio and Proportion

Write the ratio of red pens to green pens. There are 6 red pens and 10 green pens.

Question 7 [1 marks]

Graphs and Coordinates

Find the gradient of the line passing through the points (1, 2) and (4, 8).

Question 8 [1 marks]

Angles and Geometrical Reasoning

A cuboid has length 6 cm, width 3 cm and height 2 cm. Write down the shape of the top elevation (the view from above).

Question 9 [1 marks]

Graphs and Coordinates

Find the gradient of the straight line joining the points (5, -2) and (5, 6).

Question 10 [1 marks]

Linear Algebra

a = 6 and c = 2. Work out the value of ac.

Question 11 [1 marks]

Ratio and Proportion

Express the ratio 12:20 in its simplest form.

Question 12 [1 marks]

Number and Calculation

Calculate 175 x 4.

Question 13 [1 marks]

Indices and Standard Form

Work out the value of 2^-4.

Question 14 [1 marks]

Ratio and Proportion

Given that y = 8/3 x, write down the ratio x:y using whole numbers.

Question 15 [1 marks]

Number and Calculation

Work out 432 ÷ 8.

Question 16 [1 marks]

Ratio and Proportion

Simplify the ratio 45:60.

Question 17 [1 marks]

Fractions, Decimals and Percentages

Work out 1/4 + 1/2.

Question 18 [1 marks]

Number and Calculation

Decide whether 51 is prime or composite. Give a short reason.

Question 19 [2 marks]

Linear Algebra

Solve 12 - 3x = 4x - 9 Show your working.

Question 20 [2 marks]

Fractions, Decimals and Percentages

Work out 2 2/5 + 1 4/5. Give your answer as a mixed number.

Question 21 [2 marks]

Number and Calculation

Write 2^3 x 3^2 x 5 as an ordinary number.

Question 22 [2 marks]

Graphs and Coordinates

Find the gradient of the straight line joining the points (-1, 6) and (3, -2).

Question 23 [2 marks]

Linear Algebra

Solve 7x - 4 = 3x + 20

Question 24 [2 marks]

Number and Calculation

Sam and Aisha practise the same music piece in cycles. Sam repeats it every 8 days, Aisha every 12 days. If they both practise today, after how many days will they next practise together?

Question 25 [2 marks]

Linear Algebra

Expand and simplify (x - 3)(x - 8)

Question 26 [2 marks]

Graphs and Coordinates

Find the gradient of the straight line joining the points (2, 5) and (8, 1).

Question 27 [2 marks]

Number and Calculation

A student calculates 384 x 6 and writes: 384 x 6 = 2504 Identify the mistake in the calculation and write down the correct answer.

Question 28 [2 marks]

Linear Algebra

Factorise fully 16x^2 - 81

Question 29 [2 marks]

Number and Calculation

Show that 108 = 2^2 x 3^3.

Question 30 [3 marks]

Fractions, Decimals and Percentages

Sam paints 3/5 of a fence in the morning. In the afternoon he paints 1/4 of the remaining part. What fraction of the whole fence has Sam painted by the end of the day?

Question 31 [3 marks]

Number and Calculation

Three warning lights on a factory control panel all flash together at the start of a shift. The red light then flashes every 8 seconds, the amber light every 12 seconds and the green light every 20 seconds. Find how many seconds it takes until all three lights next flash together.

Question 32 [3 marks]

Fractions, Decimals and Percentages

A class completed 5/8 of a test. Later, 3/10 of the pupils who had not completed it finished the test. What fraction of the class have now completed the test?

Question 33 [3 marks]

Angles and Geometrical Reasoning

OABC is a parallelogram, with vertices in order. OA = a and OC = c.

Find OB in terms of a and c.

Find CA in terms of a and c.

Question 34 [4 marks]

Linear Algebra

Ben is x years old. His sister Priya is 4 years older than Ben. Their mother's age is 8 years less than three times the sum of Ben's and Priya's ages. Their mother is 52 years old. Form an equation in x and solve it to find Ben's age.

Question 35 [4 marks]

Ratio and Proportion

The table shows some values of x and y, where y is directly proportional to x^2. x: 2, 4, 6 y: 12, 48, ?

Find the value of k in y = kx^2.

Complete the table by finding the missing value of y when x = 6.

Question 36 [4 marks]

Angles and Geometrical Reasoning

A cyclist rides from a cafe C to a viewpoint V. This part of the journey is modelled by the column vector (5, 2) km. She then rides from V to a picnic site P, modelled by the column vector (4, 10) km.

Find the column vector representing the direct journey from C to P.

Calculate the direct distance, in km, from C to P.

Find the column vector representing the return journey directly from P to C.

Question 37 [4 marks]

Graphs and Coordinates

Use your table of values from Question 5 for y = 4/x.

Draw the graph of y = 4/x for -4 <= x <= 4, x not equal to 0, on the grid provided.

Explain why there is no point on the graph when x = 0.

Question 38 [7 marks]

Sequences

Arjun is training for a marathon. In week 1, he runs 8 km. Each week after that, he runs 3 km more than the week before.

Work out how far Arjun runs in week 6.

Find an expression, in terms of n, for the distance, in km, Arjun runs in week n.

Arjun wants to know the first week in which he will run at least 50 km. Find this week number.