OCR-Style Year 10 Higher Paper 3

Question 1 [1 marks]

Indices and Standard Form

Write the number 0.0032 in standard form.

Question 2 [1 marks]

Graphs and Coordinates

Find the gradient of the straight line joining the points (0, 7) and (4, -1).

Question 3 [2 marks]

Ratio and Proportion

A car travels 150 km in 3 hours, travelling at a constant average speed. Calculate the average speed of the car in km/h.

Question 4 [2 marks]

Fractions, Decimals and Percentages

Write 0.3333... (3 recurring) as a fraction in its simplest form.

Question 5 [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 6 [4 marks]

Area, Volume and Measures

Priya's living room is L-shaped. It is made from a rectangle 5 m by 4 m with an alcove that adds a rectangle 2 m by 1.5 m.

Work out the total floor area of the living room.

Carpet for the room costs £18.50 per m^2. Work out the total cost of the carpet.

Question 7 [1 marks]

Fractions, Decimals and Percentages

Write 7/20 as a decimal.

Question 8 [1 marks]

Angles and Geometrical Reasoning

State a simple compass-and-straightedge construction to find the midpoint of segment AB.

Question 9 [1 marks]

Linear Algebra

A function machine multiplies the input by 7 then subtracts 2. Write an expression in terms of x for the output.

Question 10 [1 marks]

Angles and Geometrical Reasoning

Two straight roads cross at a roundabout. One of the four angles formed between the roads is 63 degrees. Work out the size of the angle that is vertically opposite this 63 degree angle.

Question 11 [2 marks]

Linear Algebra

Solve 5x + 2 = 2x + 14 Show your working.

Question 12 [2 marks]

Number and Calculation

Write 84 as a product of its prime factors, giving your answer in index form.

Question 13 [2 marks]

Linear Algebra

Expand and simplify (x - 5)(x + 9)

Question 14 [2 marks]

Indices and Standard Form

Simplify sqrt(8) + sqrt(2) fully.

Question 15 [2 marks]

Linear Algebra

The formula v = u + at connects speeds u and v, acceleration a and time t. Make t the subject of the formula.

Question 16 [2 marks]

Angles and Geometrical Reasoning

A shape is enlarged by scale factor -1. Sunita says, 'The image will have the same area as the original shape.' Is Sunita correct? Justify your answer.

Question 17 [2 marks]

Number and Calculation

Work out sqrt(225) + cube root(64).

Question 18 [2 marks]

Area, Volume and Measures

A trapezium-shaped tabletop has parallel sides of length 12 cm and 18 cm and a height of 9 cm. Calculate the area of the tabletop.

Question 19 [2 marks]

Angles and Geometrical Reasoning

Point W has coordinates (5, 3). Find the coordinates of the image of W after a rotation of 180 degrees about the point (2, 2).

Question 20 [2 marks]

Fractions, Decimals and Percentages

Simplify 45/60 to lowest terms.

Question 21 [2 marks]

Area, Volume and Measures

The linear scale factor between two mathematically similar shapes is 0.4. Work out the area scale factor.

Question 22 [3 marks]

Fractions, Decimals and Percentages

Show that 0.363636... (36 recurring) = 4/11.

Question 23 [3 marks]

Angles and Geometrical Reasoning

A model car is similar to the real car. The scale factor of similarity (model : real) for linear dimensions is 1:18. (a) Work out the area scale factor (model : real). (b) The model has a painted roof area of 12 cm^2. Work out the area of the real car roof in square metres. Give your answer in standard form to 2 significant figures.

The model roof area is 12 cm^2. Work out the real roof area in m^2, give answer in standard form to 2 s.f.

Question 24 [3 marks]

Fractions, Decimals and Percentages

Chloe buys a sofa on a deferred payment plan. She pays a deposit equal to 15% of the cash price of the sofa. The remaining amount is then increased by 8%, to cover a credit charge, before being split into equal monthly instalments. The remaining amount, after the 8% credit charge has been added, is £642.60. Work out the cash price of the sofa.

Question 25 [3 marks]

Graphs and Coordinates

A school marks out a square flower bed on a coordinate grid, where 1 unit represents 1 metre. Three of its corners are at A(-3, -3), B(2, -3) and C(2, 2). Find the coordinates of the fourth corner D, and work out the perimeter of the flower bed.

Question 26 [3 marks]

Indices and Standard Form

Show that x^(2/3) / x^(1/6) = x^(1/2). State any restriction on x.

Question 27 [4 marks]

Linear Algebra

An old recipe book gives a formula for converting a temperature C degrees Celsius into F degrees Fahrenheit: F = 9C/5 + 32

Make C the subject of the formula.

Use your formula to work out the value of C when F = 68. Give your answer in degrees Celsius.

Question 28 [4 marks]

Area, Volume and Measures

A rectangular garden measures 15 m by 8 m. A uniform path of width x m is laid around the inside so that the lawn that remains has area 66 m^2 less than the original garden. Work out x, giving your answer correct to 2 decimal places.

Question 29 [4 marks]

Linear Algebra

Given g(x) = 5x^2 - 2x + 3,

Simplify g(x) - (2x^2 - 3x + 1).

The table below shows two values of x. Use your answer to part (a) to complete the table, giving each value of 3x^2 + x + 2. x | -2 | 3 3x^2 + x + 2 | ___ | ___

Question 30 [4 marks]

Ratio and Proportion

Aaliyah needs at least 2 kg of sugar for a school bake sale. A shop sells sugar in bags of 750 g for 90p each, and bags of 1 kg for £1.10 each. She can only buy whole bags.

Question 31 [5 marks]

Graphs and Coordinates

Work out the intersection point of the lines y = 2x + 1 and y = -x + 7. Give full working and the final coordinates.

Question 32 [3 marks]

Indices and Standard Form

A rectangular garden bed has length (6 + sqrt(11)) m and width (6 - sqrt(11)) m. Find the area of the garden bed, giving your answer as an integer.

Question 33 [3 marks]

Number and Calculation

A rectangular photo has length 15 cm and width 10 cm, each measured correct to the nearest cm. A framer claims the area of the photo could be as large as 160 cm^2. Using bounds, show whether the framer's claim is correct. You must show your working.

Question 34 [3 marks]

Graphs and Coordinates

The graph of y = 3^x is an exponential curve.

Write down the coordinates of the point where the graph crosses the y-axis.

Write down the equation of the horizontal asymptote of the graph.

State whether y = 3^x is increasing or decreasing as x increases.

Question 35 [3 marks]

Area, Volume and Measures

Two spheres are mathematically similar. Their radii are in the ratio 2:3. The volume of the smaller sphere is 96 cm^3. Work out the volume of the larger sphere.

Question 36 [4 marks]

Graphs and Coordinates

The graph of y = 2cos x - 1 is a transformation of y = cos x.

Write down the maximum and minimum values of y = 2cos x - 1.

Write down the coordinates of the y-intercept of the graph.

State the period of the graph.

Question 37 [5 marks]

Fractions, Decimals and Percentages

Priya has 10 1/2 metres of ribbon. She cuts off 1/4 of it. From the remaining ribbon she uses 3/5 for making bows. How much ribbon remains unused? Give your answer as a mixed number in simplest form.

Question 38 [5 marks]

Area, Volume and Measures

Triangle ABC has AB = 15 cm, AC = 10 cm and area 36 cm^2. Work out angle A and then calculate the length BC. Give the final length BC to the nearest whole number.