OCR-Style Year 10 Higher Paper 1

Question 1 [1 marks]

Indices and Standard Form

Write the number 0.0032 in standard form.

Question 2 [1 marks]

Angles and Geometrical Reasoning

State, in degrees, the sum of the interior angles of a triangle.

Question 3 [1 marks]

Linear Algebra

Solve 8 + x = 15

Question 4 [2 marks]

Ratio and Proportion

A rectangular garden bed has length 24 m and width 18 m. Write the ratio of length to width in its simplest form.

Question 5 [2 marks]

Area, Volume and Measures

A cuboid has length 9 cm, width 6 cm and height 4 cm. Work out the volume of the cuboid.

Question 6 [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 7 [3 marks]

Fractions, Decimals and Percentages

(Non-calculator)

Write 45% as a decimal.

Write 3/4 as a percentage.

Write 0.2 as a percentage.

Question 8 [1 marks]

Number and Calculation

Write down the bounds for a number given as 5, correct to 1 significant figure, using inequality notation.

Question 9 [1 marks]

Fractions, Decimals and Percentages

Work out 1/6 of 42.

Question 10 [1 marks]

Graphs and Coordinates

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

Question 11 [1 marks]

Area, Volume and Measures

Work out the area of a square with side length 7 cm.

Question 12 [1 marks]

Indices and Standard Form

Work out 9^(1/2).

Question 13 [1 marks]

Fractions, Decimals and Percentages

A price is increased by 12%. State the single decimal multiplier used to find the new price directly from the original price.

Question 14 [1 marks]

Graphs and Coordinates

Plot the point with coordinates (3, -2) on a pair of axes.

Question 15 [1 marks]

Angles and Geometrical Reasoning

Work out the missing angle. On a straight line the two adjacent angles are 46 degrees and x. Find x.

Question 16 [2 marks]

Linear Algebra

Make x the subject of the formula: y = (x - 5)/3

Question 17 [2 marks]

Graphs and Coordinates

P has coordinates (-2, 3) and Q has coordinates (6, -9). Find the coordinates of the midpoint of PQ.

Question 18 [2 marks]

Linear Algebra

Simplify (6x^3) / (3x).

Question 19 [3 marks]

Number and Calculation

A cyclist travels 45 km, correct to the nearest km, in a time of 2 hours, correct to the nearest 0.5 hours. Work out the lower bound for the average speed of the cyclist. Give your answer correct to 3 significant figures.

Question 20 [2 marks]

Graphs and Coordinates

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

Question 21 [2 marks]

Linear Algebra

Solve 5 - 2x = 1 Show your working.

Question 22 [2 marks]

Fractions, Decimals and Percentages

A car is worth £12,000. It depreciates by 10% each year. Find its value after 2 years.

Question 23 [2 marks]

Graphs and Coordinates

The graph of y = x^3 - 7x passes through the point (2, -6).

Show that (2, -6) lies on the curve.

Use the symmetry of the graph to write down another point on the curve.

Question 24 [3 marks]

Number and Calculation

Calculate 46.8 x 3.25. Give your answer rounded to 2 decimal places. Then estimate the product by rounding each number to 1 significant figure and say whether your rounded answer is reasonable.

Question 25 [2 marks]

Graphs and Coordinates

Plot the three points from the table on graph paper and draw the straight line joining them. x: 0, 1, 2 y: 0, 3, 6

Question 26 [3 marks]

Fractions, Decimals and Percentages

A car service costs £96, including VAT at 20%. Work out the cost of the service before VAT was added.

Question 27 [3 marks]

Ratio and Proportion

An alloy is made from copper and tin in the ratio 7 : 3 by mass. A sample of the alloy has a mass of 450 g. Work out the mass of copper in the sample.

Question 28 [4 marks]

Linear Algebra

Make t the subject of s = vt + 0.5 a t^2. Give your answer in terms of s, v and a.

Question 29 [4 marks]

Ratio and Proportion

A map uses a scale of 1 cm to 7.5 km. A cyclist plans a route that is proportional to the straight-line distance. On the map the route would be 28 cm. Calculate the real distance and then the time taken if the cyclist rides at an average speed of 18 km/h. Give the time in hours and minutes, correct to the nearest minute.

Question 30 [4 marks]

Angles and Geometrical Reasoning

Triangle ABC has vertices A(3,4), B(5,4) and C(3,6). Triangle ABC is enlarged by scale factor -3, centre (1,2), to give triangle A'B'C'. Find the coordinates of A', B' and C'.

Question 31 [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 32 [5 marks]

Graphs and Coordinates

Find the equation of the perpendicular bisector of the line segment joining (1, 1) and (5, 3). Give your answer in the form y = mx + c.

Question 33 [5 marks]

Area, Volume and Measures

Freya drives a distance of 175 miles. You are given that 5 miles is approximately 8 km. The journey takes 2 hours 30 minutes.

Work out the distance in kilometres.

Work out Freya's average speed for the journey in km/h.

Question 34 [1 marks]

Graphs and Coordinates

The graph of y = f(x) is transformed to give the graph of y = f(x) + 4. Which of the following correctly describes this transformation?

Question 35 [2 marks]

Linear Algebra

Simplify fully (x^2 - 9)/(x + 3)

Question 36 [4 marks]

Area, Volume and Measures

Vase P and vase Q are mathematically similar. The volume of vase P is 250 cm^3 and the volume of vase Q is 500 cm^3. The height of vase P is 18 cm.

Question 37 [4 marks]

Linear Algebra

Prove algebraically that the sum of any four consecutive integers is always even, but is never a multiple of 4.

Question 38 [4 marks]

Graphs and Coordinates

Line L1 passes through the points A(2, 5) and B(8, k). Line L2 has equation 3x + y = 12 and is perpendicular to L1. Find the value of k.

Question 39 [5 marks]

Angles and Geometrical Reasoning

Let sum(n) = (n - 2) * 180 be the sum of the interior angles of a polygon with n sides.

Prove algebraically that sum(n + 1) - sum(n) = 180 for every whole number n, showing that increasing the number of sides of a polygon by 1 always increases the sum of its interior angles by exactly 180 degrees.

A polygon with 22 sides has an interior angle sum of 3600 degrees. Using the result from part (a), write down the sum of the interior angles of a polygon with 23 sides.

Question 40 [6 marks]

Graphs and Coordinates

Priya and Tom start cycling from the same point at the same time and travel along the same straight road for 20 seconds. Priya accelerates uniformly from rest to a velocity of 10 m/s in the first 5 seconds, then travels at this constant velocity for the remaining 15 seconds. Tom cycles at a constant velocity of 8 m/s for the whole 20 seconds.

Calculate the distance Priya has travelled after 20 seconds.

Calculate the distance Tom has travelled after 20 seconds.

Determine which cyclist is further along the road after 20 seconds, and by how much.