Year 10 Paper 2: Graphs and Sequences

Question 1 [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 2 [2 marks]

Angles and Geometrical Reasoning

Shape P has vertices at (1, 1), (1, 3) and (3, 1). Shape Q has vertices at (1, -1), (1, -3) and (3, -1).

Question 3 [2 marks]

Number and Calculation

Round 15.976 to 3 significant figures.

Question 4 [3 marks]

Linear Algebra

Each part below shows a different function machine with input n. Select the expression that represents the output.

input n --> [ x 2 ] --> [ +5 ] --> output. Which expression represents the output?

input n --> [ +3 ] --> [ x 4 ] --> output. Which expression represents the output?

input n --> [ x 5 ] --> [ -2 ] --> output. Which expression represents the output?

Question 5 [3 marks]

Ratio and Proportion

A football squad has 24 players. The ratio of forwards to midfielders to defenders is 3:5:4. Work out the percentage of the squad who are defenders.

Question 6 [3 marks]

Linear Algebra

x = -2 and y = 1/4. Work out the value of 1/x + 1/y.

Question 7 [4 marks]

Graphs and Coordinates

A sequence of points is generated on a grid. The first point is (1, -2). Each new point is formed by adding 3 to the x-coordinate and adding 2 to the y-coordinate of the previous point.

Write down the coordinates of the second point in the sequence.

Write down the coordinates of the third point in the sequence.

One of the points in the sequence has coordinates (16, y). Work out the value of y.

Question 8 [1 marks]

Number and Calculation

Work out 9^2 - 12.

Question 9 [2 marks]

Ratio and Proportion

Share £63 in the ratio 1:2. Work out how much the smaller share is.

Question 10 [2 marks]

Angles and Geometrical Reasoning

The exterior angle of a regular polygon is 15 degrees. Work out the number of sides of the polygon.

Question 11 [2 marks]

Sequences

The sequence is 5, 9, 13, 17, ... Find the value of n for the term 29.

Question 12 [2 marks]

Number and Calculation

Show that 41472 is divisible by 8.

Question 13 [2 marks]

Angles and Geometrical Reasoning

v is the column vector (9, 12). Calculate the magnitude of v, |v|.

Question 14 [3 marks]

Number and Calculation

A jacket normally costs £45. In a sale, the price is reduced by 1/5. Work out the sale price of the jacket.

Question 15 [3 marks]

Linear Algebra

The formula for the cost C (in pounds) of m apples and n bananas is C = 0.30m + 0.20n. Work out C when m = 4 and n = 6. Give your answer to the nearest penny.

Question 16 [3 marks]

Number and Calculation

Use long division to work out 9876 ÷ 12.

Question 17 [4 marks]

Ratio and Proportion

Sara walks 3.6 km in 45 minutes, at a constant speed. Calculate her average speed in m/s. Give your answer to 3 significant figures.

Question 18 [4 marks]

Linear Algebra

Form and solve an equation. "Sarah has £2.50. She buys a drink costing d pounds and has £1.10 left. How much did the drink cost?"

Form an equation in d to represent the situation.

Solve the equation and give the cost of the drink.

Question 19 [6 marks]

Number and Calculation

The integers a, b and c are given by a = -4, b = 7 and c = -3. This question has four parts.

Work out a + b - c.

Work out a x c.

Hence or otherwise, work out (a x c) / b, giving your answer as a decimal rounded to 1 decimal place.

Given that d is an integer such that b + d = a, work out the value of d.

Question 20 [5 marks]

Sequences

Here are the first four terms of a geometric sequence. 5, 15, 45, 135

Find the common ratio of the sequence.

Find the 6th term of the sequence.

Explain whether 3000 is a term of the sequence.

Question 21 [2 marks]

Number and Calculation

Work out (-8) + 15 - 6.