AQA-Style Year 10 Higher Paper 2

Question 1 [1 marks]

Angles and Geometrical Reasoning

Triangle A has a vertex at (-4, 3). After a translation, the corresponding vertex on triangle B is at (1, -2). Which vector describes this translation?

Question 2 [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 3 [3 marks]

Indices and Standard Form

Write each of the following as a single power.

4 x 4 x 4 x 4 x 4

7 x 7 x 7

2 x 2 x 2 x 2 x 2 x 2 x 2

Question 4 [4 marks]

Graphs and Coordinates

A straight line has equation y = 4x - 7

Write down the gradient of the line.

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

Show that the point (3, 5) lies on the line.

Question 5 [1 marks]

Fractions, Decimals and Percentages

Work out 5/12 of 84 cm.

Question 6 [2 marks]

Ratio and Proportion

A traveller has 500 Australian dollars. How many pounds can they get if the rate is 1 GBP = 1.85 AUD? Give your answer to 2 decimal places.

Question 7 [2 marks]

Angles and Geometrical Reasoning

OA = <1, 0>, OB = <4, 3>, OC = <7, 6>. Show that A, B and C are collinear.

Question 8 [2 marks]

Area, Volume and Measures

Write 0.45 litres as a number of cubic centimetres (cm^3).

Question 9 [2 marks]

Linear Algebra

Factorise x^2 - 4x - 21

Question 10 [2 marks]

Area, Volume and Measures

Two similar triangles have corresponding sides in the ratio 5:8. A side of the smaller triangle is 15 cm. Work out the length of the corresponding side in the larger triangle.

Question 11 [3 marks]

Number and Calculation

Five different novels are placed in a row on a bookshelf. Work out the number of different ways the five novels can be arranged.

Question 12 [3 marks]

Fractions, Decimals and Percentages

A tin contains 40 litres of paint. Aisha uses 3/8 of the paint to paint a fence. Of the paint she uses on the fence, 2/5 is white paint and the rest is blue paint. Work out how many litres of blue paint Aisha uses on the fence.

Question 13 [3 marks]

Area, Volume and Measures

Two water containers are both cuboids. Container A measures 12 cm by 8 cm by 5 cm. Container B measures 10 cm by 9 cm by 6 cm. By calculating the volume of each container, determine which container has the greater capacity. You must show your working.

Question 14 [3 marks]

Graphs and Coordinates

Given that sin 25 degrees = 0.423 (3 s.f.),

use the symmetry of the sine graph to write down the value of sin 155 degrees.

Hence write down the two solutions of sin x = 0.423 in the range 0 <= x <= 360.

Question 15 [3 marks]

Ratio and Proportion

In a choir, the ratio of sopranos to altos is 4 : 5. The ratio of altos to tenors is 3 : 2. Find the ratio of sopranos : altos : tenors in its simplest form.

Question 16 [3 marks]

Linear Algebra

The temperature T in degrees C is given by T = 20 - 5k, where k is a constant. If k = (2p - 1)/4 and p = 5, find T.

Question 17 [3 marks]

Fractions, Decimals and Percentages

The number of pupils at a school increased by 6% this year to 477. Work out the number of pupils at the school last year.

Question 18 [4 marks]

Linear Algebra

Solve the simultaneous equations: (x + y) / 2 = 5 2x - y = 2

Question 19 [4 marks]

Fractions, Decimals and Percentages

The recurring decimal 0.a7a7a7... (where the two-digit block a7 recurs, and a is a single digit) is equal to 29/33. Find the value of a.

Question 20 [5 marks]

Sequences

The nth term of a sequence is 7n - 3.

Is 74 a term of the sequence? You must show working to justify your answer.

Is 101 a term of the sequence? You must show working to justify your answer.

Question 21 [5 marks]

Area, Volume and Measures

A sector of a circle has area 154 cm^2 and angle 100 degrees. Calculate the radius of the circle, giving your answer correct to 3 significant figures.

Question 22 [2 marks]

Number and Calculation

The height of a tree is 35 m, measured to the nearest 5 m.

Write down the lower bound of the height.

Write down the upper bound of the height.

Question 23 [3 marks]

Linear Algebra

Simplify fully (x^2 - x - 12)/(x^2 - 16)

Question 24 [3 marks]

Angles and Geometrical Reasoning

OA = a and OB = b. D is a point on AB such that AD = 2 DB. Show that OD = (1/3) a + (2/3) b.

Question 25 [4 marks]

Fractions, Decimals and Percentages

A car's value decreased by 22% over one year. At the end of the year it was worth £10530. Work out the value of the car at the start of the year.

Question 26 [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 27 [4 marks]

Indices and Standard Form

Solve the equation 9^x - 3^(x+1) = 0