OCR-Style Year 10 Foundation Paper 1

Question 1 [1 marks]

Area, Volume and Measures

Convert 2 days to hours.

Question 2 [1 marks]

Angles and Geometrical Reasoning

A scale drawing is to be made of a school hall that is 30 m long in real life. Explain why a scale of 1 : 1 would not be sensible to use for this drawing.

Question 3 [1 marks]

Number and Calculation

Work out the missing number. 12 + ___ = 20

Question 4 [2 marks]

Linear Algebra

Solve 6x = -0.9

Question 5 [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 6 [2 marks]

Graphs and Coordinates

A student, Erin, says: 'If you translate a point 5 units up and then 5 units down, you always end up back at the point you started with, whatever point you start at.' Decide whether Erin is correct. Justify your answer with an example.

Question 7 [2 marks]

Ratio and Proportion

Given that 5:x = 15:24, work out the value of x.

Question 8 [2 marks]

Indices and Standard Form

Work out each cube root.

cbrt(-27)

cbrt(-1000)

Question 9 [3 marks]

Angles and Geometrical Reasoning

Quadrilateral WXYZ has angle W = 80 degrees, angle X = 95 degrees, angle Y = 110 degrees and angle Z = k. Work out the size of angle k.

Question 10 [6 marks]

Number and Calculation

m = -4, n = 3, k = -5

Work out m + nk

Work out (m - k)^2

Sam says: 'mk is definitely greater than m + k.' Determine, with working, whether Sam is correct.

Question 11 [4 marks]

Fractions, Decimals and Percentages

Simplify each fraction fully.

36/48

28/70

32/40

63/81

Question 12 [6 marks]

Number and Calculation

Priya and Tomasz are comparing scores in a quiz. A wrong answer scores negative points. Priya's scores in four rounds: -3, 5, -2, 6 Tomasz's scores in four rounds: 2, -1, 4, -3

Work out Priya's total score.

Work out Tomasz's total score.

Priya says: 'I scored more than double Tomasz's total.' Is Priya correct? Show working to justify your answer.

Question 13 [1 marks]

Area, Volume and Measures

Convert 74 millimetres to centimetres.

Question 14 [1 marks]

Number and Calculation

Work out 7 + 3 x 5.

Question 15 [1 marks]

Fractions, Decimals and Percentages

State an equivalent fraction to 7/8 that has numerator 21.

Question 16 [1 marks]

Angles and Geometrical Reasoning

On a scale drawing, 1 cm represents 40 m in real life. Write this scale as a ratio in the form 1:n.

Question 17 [1 marks]

Graphs and Coordinates

Write down the equation of the graph obtained by translating y = f(x) 2 units to the right.

Question 18 [1 marks]

Angles and Geometrical Reasoning

Reflect the point A(-1, 4) in the y-axis. Give the coordinates of the reflected point.

Question 19 [1 marks]

Sequences

Work out the 6th term of the sequence defined by nth term = 4n - 1.

Question 20 [1 marks]

Fractions, Decimals and Percentages

Write 125% as a decimal.

Question 21 [1 marks]

Angles and Geometrical Reasoning

Look at this description of a solid and its three elevations. - Plan (view from above): a 6 cm by 4 cm rectangle with a 2 cm by 2 cm square removed from one corner. - Front elevation: a rectangle 6 cm by 3 cm with a 2 cm square notch at the top right. - Side elevation: a rectangle 4 cm by 3 cm. Which of these statements must be true? Tick the correct answer. A. The solid has overall height 3 cm. B. The solid has a full 2 cm cube removed from its corner. C. The plan shows a hole all the way through the solid. D. The front elevation shows a triangular shape.

Question 22 [1 marks]

Area, Volume and Measures

A ferry leaves at 23:40. The next ferry leaves at 01:20. How long does a passenger wait for the next ferry?

Question 23 [1 marks]

Indices and Standard Form

Work out the value of 10^0.

Question 24 [1 marks]

Angles and Geometrical Reasoning

Translate point P(2, 3) by the vector (4, -1). Write down the coordinates of the image.

Question 25 [2 marks]

Number and Calculation

Complete a prime factor tree for 45 and write the prime factorisation.

Question 26 [2 marks]

Graphs and Coordinates

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

Question 27 [2 marks]

Angles and Geometrical Reasoning

True or false? The locus of points equidistant from a fixed point F and a fixed line d is a parabola that can be constructed exactly using only compass and straightedge. Give a brief reason for your answer.

Question 28 [2 marks]

Fractions, Decimals and Percentages

Increase 160 by 35%.

Question 29 [2 marks]

Number and Calculation

Estimate 246 × 78 by rounding each number to 1 significant figure before multiplying.

Question 30 [2 marks]

Fractions, Decimals and Percentages

In a school raffle, 32 out of 72 tickets sold were bought by Year 11 students. Write the fraction of tickets bought by Year 11 students in its simplest form.

Question 31 [2 marks]

Indices and Standard Form

Simplify (4^2)^3 and give your answer as an ordinary number.

Question 32 [2 marks]

Angles and Geometrical Reasoning

A solid has a front elevation that is 8 cm wide and 6 cm high. The side elevation is 5 cm wide and 6 cm high. Work out the size of the plan (give length and width).

Question 33 [2 marks]

Indices and Standard Form

Simplify sqrt(180) giving your answer in simplest form.

Question 34 [3 marks]

Area, Volume and Measures

Small scented candles are cylinders with radius 2 cm and height 8 cm. A shop has a box with internal volume 5.0 litres. What is the maximum number of these candles that can fit in the box if only volume is considered? You may give an answer as a whole number.

Question 35 [3 marks]

Linear Algebra

A rectangle has length (x + 5) cm and width (x - 2) cm. The perimeter of the rectangle is 46 cm.

Question 36 [3 marks]

Number and Calculation

Aisha and Ben each go for a run. The table shows the distance each of them ran and the time each of them took. Runner | Distance (km) | Time (minutes) Aisha | 15 | 50 Ben | 21 | 60 Work out which runner had the greater average speed. You must show your working.

Question 37 [3 marks]

Fractions, Decimals and Percentages

A shop sets a selling price of £65 to make a 30% profit. Work out the cost price of the item to the shop.

Question 38 [3 marks]

Number and Calculation

Priya calculates (7 + 2) x 3^2 incorrectly as 7 + 2 x 3^2. Work out Priya's answer and the correct answer. Find the difference between the two answers.

Question 39 [3 marks]

Linear Algebra

Three angles lie on a straight line. The angles are x degrees, (2x + 8) degrees and (3x - 2) degrees.

Question 40 [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 41 [3 marks]

Angles and Geometrical Reasoning

O is the origin. The position vectors of points A and B, relative to O, are a and b. M is the midpoint of AB.

Find the vector AB in terms of a and b.

Find the position vector of M in terms of a and b, giving your answer in its simplest form.

Question 42 [3 marks]

Area, Volume and Measures

Work out the circumference of a circle with radius 2.5 cm. Use pi = 3.14 and give your answer to 2 decimal places.

Question 43 [4 marks]

Linear Algebra

Three consecutive integers have a sum of 96. Let n be the smallest integer.

Form an equation in n and solve it.

Hence write down the three consecutive integers.

Question 44 [4 marks]

Ratio and Proportion

A gardener mixes fertiliser and water in the ratio 1 : 24 to make feed for tomato plants. He has 6 litres of fertiliser.

Work out the maximum volume of feed he can make using all 6 litres of fertiliser.

He decides to use only 250 ml of fertiliser at a time, mixed with water in the same ratio. Work out how many litres of water are needed for one 250 ml application.

Question 45 [3 marks]

Area, Volume and Measures

A hollow tube has outer radius 5 cm, inner radius 3 cm and height 10 cm. Work out the total curved surface area (sum of the inner and outer curved surfaces) of the tube. Give your answer in terms of pi.