4MA1 Mathematics A: Oct/Nov 2021 Paper 1FFoundation Tier Paper 1

Here are five fractions.

Two of the fractions in the table are equivalent to 15

(a)Put a tick () in the box underneath each of these two fractions.[2]

The diagram shows an 8-sided polygon and its diagonals.

(b)Write down the mathematical name of an 8-sided polygon.

[1]

(c)Shade 34 of the polygon shown in the diagram above.[1]

The area of a polygon is 56 cm²

(d)Find 34 of 56

[2]

The table shows the average number of spectators per match, for each of six Spanish football teams, in one season.

(a)Which team had the lowest average number of spectators per match?

[1]

(b)Write the number 65 731 correct to the nearest thousand.

[1]

(c)Write down the value of the 6 in the number 38 699

[1]

In one match, Sevilla played Valencia. In the match, Sevilla had 8 shots on target and Valencia had 12 shots on target.

(d)Write the ratio 8:12 in its simplest form.

[1]

In the same match, Valencia had 72% possession of the ball.

(e)Write 72% as a fraction in its simplest form.

[2]

The bar chart shows information about the numbers of text messages that Susan and Philip sent from their mobile phones on each of six days one week.

(a)On which day did Susan send twice as many text messages as Philip?

[1]

(b)How many text messages did Philip send on Sunday?

[1]

On Saturday, Susan sent 15 text messages and Philip sent 40 text messages.

(c)Show this information on the bar chart.[1]

In the following week, Philip sent a total of 180 text messages. Of these text messages, 25% were sent to Susan.

(d)Work out 25% of 180

[2]

The table shows the temperatures recorded at midnight and at midday for each of five North American cities on a Monday one week.

(a)Which city had the lowest midnight temperature?

[1]

(b)Find the difference between the midnight temperature and midday temperature for Boston.

°C[1]

From Monday to Thursday, the midday temperature in Detroit increased by 2°C each day.

(c)Work out the midday temperature in Detroit on Thursday.

°C[2]

James is on holiday in Canada. The exchange rate is £1 = 1.75 Canadian dollars.

(a)Change £800 into Canadian dollars.

Canadian_dollars[2]

James buys a watch in Canada.

The price of the watch is 98 Canadian dollars. In England the price of an identical watch is £60

(b)Work out the difference in the prices of the two watches. Give your answer in pounds (£)

£ [2]

The accurate scale diagram shows the map of an island drawn on a centimetre grid.

The position of Aaron’s house is A. The position of Bharat’s house is B.

(a)Write down the coordinates of A.

( , )[1]

(b)By measurement, find the bearing of A from B.

[2]

(c)Measure the length of the line AB. Give your answer in centimetres correct to one decimal place.

cm[1]

Aaron cycled along a straight path from his house to Bharat’s house. The scale of the map is 1 cm represents 5 km.

(d)Work out the distance, in kilometres, that Aaron cycled.

km[1]

Aaron left his house at 10 45 am and arrived at Bharat’s house at 1 05 pm.

(e)How long did Aaron’s cycle ride take him? Give your answer in hours and minutes.

_{hours minutes}[2]

(a)Solve 5x = 20

x = [1]

(b)Simplify 3a ´ 8b

[1]

(c)Simplify 8w – 4y + w – 3y

[2]

(d)Factorise fully 16 + 12t

[2]

The table shows information about the grades some Year 9 students gained in a biology test and in a physics test. The highest grade is A and the lowest grade is D.

(a)How many students gained a grade C in biology?

[2]

(b)How many students gained the same grade in biology as they gained in physics?

[2]

(c)How many students gained a higher grade in biology than they gained in physics?

[2]

The diagram shows two congruent triangles, ABC and DEF, drawn on a centimetre grid.

Find the area of the region R, shown shaded in the diagram.

_cm²[3]

(a)Show that 310 ÷ 14 = 65[2]

(b)Show that 56 - 34 = 112[2]

(a)Use your calculator to work out the value of 2. 141. 24

Write down all the figures on your calculator display.

[2]

(b)Write your answer to part (a) correct to 2 significant figures.

[1]

(a)Describe fully the single transformation that maps shape P onto shape Q.

[3]

(b)On the grid, reflect shape P in the line with equation x = 5 Label your shape R.[2]

(a)Simplify e⁸ ÷ e²

[1]

(b)Expand and simplify (x – 3)(x + 1)

[2]

Here is a right-angled triangle.

Calculate the value of h. Give your answer correct to 3 significant figures.

h = [3]

There are 54 fish in a tank. Some of the fish are white and the rest of the fish are red.

Jeevan takes at random a fish from the tank. The probability that he takes a white fish is 49

(a)Work out the number of white fish originally in the tank.

[2]

Jeevan puts the fish he took out, back into the tank. He puts some more white fish into the tank.

Jeevan takes at random a fish from the tank. The probability that he takes a white fish is now 12

(b)Work out the number of white fish Jeevan put into the tank.

[2]

The diagram shows the front of a wooden door with a semicircular glass window.

Julie wants to apply 2 coats of wood varnish to the front of the door, shown shaded in the diagram.

250 millilitres of wood varnish covers 4 m² of the wood.

Work out how many millilitres of wood varnish Julie will need. Give your answer correct to the nearest millilitre.

_millilitres[5]

Yasmin has some identical rectangular tiles. Each tile is L cm by W cm.

Diagram NOT

Using 9 of her tiles, Yasmin makes rectangle ABCD shown in the diagram below.

The area of ABCD is 1620 cm²

Work out the value of L and the value of W.

L = W = [5]

Alison buys 5 apples and 3 pears for a total cost of $1.96 Greg buys 3 apples and 2 pears for a total cost of $1.22

Michael buys 10 apples and 10 pears.

Work out how much Michael pays for his 10 apples and 10 pears. Show your working clearly.

$ [5]

Write 3.6 ´ 10³ as a product of powers of its prime factors. Show your working clearly.

[3]

In 2018, the population of Sydney was 5.48 million. This was 22% of the total population of Australia.

Work out the total population of Australia in 2018 Give your answer correct to 3 significant figures.

_million[3]

(i)Solve the inequalities –7  2x – 3 < 5

[3]

(ii)On the number line, represent the solution set to part (i)

[2]

A solid aluminium cylinder has radius 10 cm and height h cm.

The mass of the cylinder is 5.4 kg. The density of aluminium is 0.0027 kg/cm³

Calculate the value of h. Give your answer correct to one decimal place.

h = [5]