Year 10 Paper 4: Ratio and Geometry

Question 1 [1 marks]

Indices and Standard Form

Write the number 45000 in standard form.

Question 2 [2 marks]

Angles and Geometrical Reasoning

The diagram shows a solid made from four identical 1 cm cubes joined edge-to-edge in a single straight row. Draw the front elevation of the solid, as viewed from arrow F, and state its dimensions.

Question 3 [2 marks]

Graphs and Coordinates

A line has equation y = -2x + 7.

Write down the gradient of the line.

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

Question 4 [3 marks]

Ratio and Proportion

Declan is deciding how to pay for his bus travel for one day. A day ticket costs £4.50 and allows unlimited journeys. A single ticket costs £1.20 and Declan plans to make 4 journeys that day.

Question 5 [1 marks]

Linear Algebra

A box contains 8 chocolates. Write down an expression for the number of chocolates in k boxes.

Question 6 [1 marks]

Indices and Standard Form

Work out the cube root of -8.

Question 7 [1 marks]

Graphs and Coordinates

Write down the gradient of the line with equation y = 7x + 2.

Question 8 [1 marks]

Linear Algebra

Given that y = 2x + 3, which of the following correctly makes x the subject of the formula?

Question 9 [2 marks]

Graphs and Coordinates

Plot the three points from the table on graph paper and draw the straight line joining them. x: 0, 2, 4 y: -1, 0, 1

Question 10 [3 marks]

Angles and Geometrical Reasoning

Enlarge triangle T with vertices (2, 1), (4, 1) and (2, 3) by a scale factor of -2 centre (1, 1). Find the coordinates of the image vertices.

Question 11 [2 marks]

Linear Algebra

Anjali has p pounds. She has more than £15 but no more than £40. Write down an inequality, in terms of p, to show this information.

Question 12 [3 marks]

Angles and Geometrical Reasoning

A regular hexagon has an interior angle of 120 degrees. A regular nonagon (a 9-sided polygon) has an interior angle of 140 degrees. Using calculations, explain why regular hexagons tessellate but regular nonagons do not.

Question 13 [2 marks]

Linear Algebra

Let f(x) = 2x - 7 and g(x) = x + 3. Work out g(f(2)).

Question 14 [4 marks]

Area, Volume and Measures

A sector has arc length 15 cm and area 90 cm^2. Find the radius of the circle. Give your answer correct to 3 significant figures.

Question 15 [4 marks]

Linear Algebra

The area of a trapezium with parallel sides a and b and height h is given by A = (1/2)(a + b)h

Make h the subject of the formula.

Make a the subject of the formula.

Question 16 [4 marks]

Graphs and Coordinates

A cubic graph has the equation y = (x - 1)(x + 3)(x - 2).

Find the three x-coordinates of the points where the graph crosses the x-axis.

Find the coordinates of the point where the graph crosses the y-axis.

Question 17 [5 marks]

Linear Algebra

Rearrange the formula for the frequency f of a wave: v = f * lambda, to make lambda the subject. Then a wave has speed v = 330 m/s and frequency f = 440 Hz. Calculate the wavelength lambda to 3 significant figures.

Make lambda the subject of v = f * lambda.

Calculate lambda for v = 330 m/s and f = 440 Hz and give the answer to 3 significant figures.

Question 18 [5 marks]

Area, Volume and Measures

An isosceles triangular prism has a cross-section with base 6 cm and two equal sides of 5 cm. The prism has length 12 cm.

Show that the perpendicular height of the triangular cross-section is 4 cm.

Work out the total surface area of the prism.

Question 19 [6 marks]

Angles and Geometrical Reasoning

Lines AB and CD are crossed by a straight transversal EF at G (on AB) and H (on CD). Angle EGB = (5x - 12) degrees and angle GHD = (3x + 8) degrees; these two angles are co-interior.

Find the value of x for which AB would be parallel to CD.

Priya says that, in fact, x = 11, and that AB is parallel to CD. Determine, with full reasons, whether Priya is correct.

Question 20 [8 marks]

Angles and Geometrical Reasoning

Show that the vectors (2, -1), (5, 2) and (7, 1) are coplanar in R^2 and then determine whether they are linearly dependent by finding constants x, y, z, not all zero, such that x(2, -1) + y(5, 2) + z(7, 1) = (0, 0). Give one nontrivial solution.