Year 11 Paper 2: Graphs and Shape

Question 1 [1 marks]

Area, Volume and Measures

Convert 2 kg to g

Question 2 [1 marks]

Angles and Geometrical Reasoning

An angle measures 265 degrees. Write down the mathematical name for this type of angle.

Question 3 [1 marks]

Area, Volume and Measures

The volume of a sphere of radius r is given by one of the formulae below.

Question 4 [2 marks]

Ratio and Proportion

Given that 5:x = 15:24, work out the value of x.

Question 5 [2 marks]

Graphs and Coordinates

On the grid provided, draw the following straight lines.

Draw the graph of x = -3.

Draw the graph of y = 2.

Question 6 [2 marks]

Indices and Standard Form

Show that 4^2 + 3^2 = 5^2

Question 7 [2 marks]

Angles and Geometrical Reasoning

Lines l and m are parallel and are crossed by a straight transversal. Angle y is in the corresponding position to the 118 degree angle marked above line l.

Question 8 [3 marks]

Sequences

Three sequences are shown below. Sequence A: 7, 11, 15, 19 Sequence B: 4, 12, 36, 108 Sequence C: 3, 6, 11, 18

State whether Sequence A is arithmetic, geometric, or neither of these. Give a reason for your answer.

State whether Sequence B is arithmetic, geometric, or neither of these. Give a reason for your answer.

State whether Sequence C is arithmetic, geometric, or neither of these. Give a reason for your answer.

Question 9 [3 marks]

Angles and Geometrical Reasoning

A ship sails from port A on a bearing of 065 degrees.

Write down why the bearing is given as 065 and not 65.

Work out the bearing needed to sail back to port A (the back bearing).

Question 10 [1 marks]

Area, Volume and Measures

Two squares are drawn, of any size.

Question 11 [1 marks]

Ratio and Proportion

Convert the ratio 2:7 into a fraction.

Question 12 [1 marks]

Indices and Standard Form

Work out the value of 5^-1. Give your answer as a fraction.

Question 13 [3 marks]

Angles and Geometrical Reasoning

Lines l and m are parallel. A transversal crosses l at P and m at Q, and the angle between the transversal and l is 118 degrees. At Q, three further angles going all the way around the point are marked 90 degrees, 150 degrees and w, in addition to the angle co-interior to the 118 degree angle.

Question 14 [1 marks]

Indices and Standard Form

Work out (-3)^3.

Question 15 [2 marks]

Angles and Geometrical Reasoning

Triangle PQR has vertex P at (-3, 2). Triangle PQR is translated by the vector (4, -5) to give triangle P'Q'R'.

Write down the coordinates of P'.

Write down the column vector that translates P' back to P.

Question 16 [2 marks]

Graphs and Coordinates

Complete the table for y = x^3. Give values for the missing entries.

x = -2, y = ____

x = 1, y = ____

Question 17 [1 marks]

Area, Volume and Measures

A parallelogram-shaped ceramic tile has a base of 13 cm and a perpendicular height of 7 cm. Calculate the area of the tile.

Question 18 [3 marks]

Angles and Geometrical Reasoning

Triangle ABC has a straight line DAE through vertex A, parallel to side BC (D on the same side as B, E on the same side as C). The angle between DAE and AB is 52 degrees; the angle between DAE and AC is 65 degrees. Work out the size of angle BAC. Show your reasoning.

Question 19 [3 marks]

Ratio and Proportion

Ravi has £3.60 and his sister has 90p. Write the ratio of Ravi's money to his sister's money in its simplest form.

Question 20 [4 marks]

Graphs and Coordinates

Use your table of values from Question 5 for y = 4/x.

Draw the graph of y = 4/x for -4 <= x <= 4, x not equal to 0, on the grid provided.

Explain why there is no point on the graph when x = 0.

Question 21 [4 marks]

Angles and Geometrical Reasoning

On a map with scale 1 : 50,000, the distance between town A and town B is 8.4 cm. The bearing of town B from town A is 072. Diagram: Point A is shown with a North arrow and a ray to B at a bearing of 072 degrees, with a parallel North arrow at B.

Calculate the real-life distance AB, giving your answer in km.

State the bearing of town A from town B.

Question 22 [5 marks]

Area, Volume and Measures

A circular garden has radius 14 m. A path is made that follows an arc of 120 degrees around the garden. The path is 2 m wide and runs along the outside edge of the garden (so the outer radius is 16 m). Work out the area of the path only. Give your answer to 1 decimal place. Use pi = 3.14159.

Question 23 [6 marks]

Graphs and Coordinates

The pressure, P pascals, of a fixed mass of gas is inversely proportional to its volume, V m^3, so that P = k/V for a constant k. When V = 2, P = 150.

Find the value of k.

Find the value of P when V = 5.

Describe the shape of the graph of P against V for V > 0.

State what happens to the pressure P if the volume V is doubled.

Question 24 [6 marks]

Area, Volume and Measures

A cone and a cylinder have the same radius 3 cm. The cone has height 8 cm and the cylinder has height 8 cm. Work out the total volume of the two solids. Give your answer in terms of pi.