4MA1 Mathematics A: Oct/Nov 2020 Paper 2FRFoundation Tier Paper 2

The table shows the depth of six ocean trenches.

(a)Which of these trenches has the greatest depth?

[1]

(b)Write down the value of the 5 in the number 8594

[1]

(c)Write the number 4437 in words.

[1]

When written correct to the nearest hundred, one of the numbers in the table is 8500

(d)What is this number?

[1]

The Mariana Trench is 2864 metres deeper than the Diamantina Trench.

(e)Work out the depth of the Mariana Trench.

_metres[2]

The diagram shows some 3‑D shapes.

(a)What is the mathematical name of shape A?

[1]

(b)How many edges has shape B?

[1]

(c)How many faces has shape C?

[1]

Here are the first five terms of a number sequence.

(a)Find the next term of this sequence.

[1]

(b)Explain how you found this term.

[1]

The 9th term of this number sequence is 6561

(c)Find the 10th term of this sequence.

[1]

The bar chart shows information about the number of visitors to China from each of four countries in 2015

(a)Write down the number of visitors from Japan.

_million[1]

(b)From which country were there 1.1 million visitors?

[1]

The number of visitors from Taiwan was 5.4 million.

(c)Draw a bar on the bar chart to show this information.[1]

The number of visitors from one country was twice the number of visitors from Malaysia.

(d)Write down the name of this country.

[1]

The diagram shows a quadrilateral ABCD drawn on a square grid.

(a)Measure the length of BC.

_cm[1]

(b)Write down the mathematical name of quadrilateral ABCD.

[1]

(c)Write down the order of rotational symmetry of quadrilateral ABCD.

[1]

(d)On the diagram, mark an obtuse angle with the letter x.[1]

Here is a diagram of a trapezium.

(e)Work out the area of the trapezium.

_cm²[2]

There are 32 children in a nursery.

Sandeep buys 5 boxes of balloons. There are 25 balloons in each box.

Sandeep shares the balloons equally between the 32 children so that each child gets as many balloons as possible.

Work out the number of balloons that are not shared between the 32 children.

[4]

The diagram shows a trapezium ABCD in which AB and DC are parallel.

Work out the value of x. Give a reason for each stage of your working.

x = [4]

The following rule is used to work out the total cost, in euros, of hiring a room.

Paolo hires the room for 5 hours.

(a)Work out the total cost.

_euros[2]

Agathe also hires the room. The total cost is 164 euros.

(b)For how many hours does Agathe hire the room?

_hours[3]

The total cost of hiring the room for n hours is T euros.

(c)Write down a formula for T in terms of n.

[2]

(a)Work out 16 ÷ 4 + 3 × 8

[1]

(b)Find the cube root of 5832

[1]

(c)Write 85% as a decimal.

[1]

(d)Write these fractions in order of size. Start with the smallest fraction.

[2]

(e)Write 36 as a fraction of 96 Give your fraction in its simplest form.

[2]

Freda is playing a car racing game on her computer.

She sets up her computer so that her car completes each lap in the same number of seconds. Her car completes 3 laps in 72 seconds.

To win the game, Freda has to complete 68 laps in less than half an hour.

Does Freda win the game? Give a reason for your answer.[4]

Show that 512 + 38 = 1924[2]

(a)Expand 4(m + 2)

[1]

(b)Solve 2x + 5 = –19

x = [2]

On the grid above, triangle A is the reflection of triangle B in the mirror line M.

(a)On the grid, draw the mirror line M. Label the line M.[1]

(b)On the grid above, rotate the shaded shape C 90° anticlockwise about the point with coordinates (0, 0)[2]

Here are two fair spinners.

Chanthira spins each spinner once.

She adds together the number that spinner A lands on and the number that spinner B lands on to find the score.

(a)Complete the table to show all possible scores. Three scores have been done for you.

[2]

(b)Find the probability that the score will be 4 or less.

[2]

Chanthira now spins both spinners together 84 times.

(c)Find an estimate for the number of times that spinner A and spinner B land on the same number.

[2]

Write 880 as a product of powers of its prime factors. Show your working clearly.

[3]

(a)Write 2.46 × 10⁶ as an ordinary number.

[1]

(b)Write 0.000 74 in standard form.

[1]

(c)Work out (5.6 × 10⁶) + (2.3 × 10⁵)

[2]

Alexa has five cards. Each card has a number on it.

The table gives information about the numbers on the five cards.

Using the information in the table, complete each card by writing its number on it.[3]

The length of a book is 33.8 cm, correct to one decimal place.

(a)Write down the lower bound of the length of the book.

_cm[1]

(b)Write down the upper bound of the length of the book.

_cm[1]

Nav has worked out 68 .3 × 42 .80. 021 on his calculator.

His answer is 139 201.9048

Without using a calculator and using suitable approximations, check that his answer is sensible. Show your working clearly.[2]

Markus makes a steel framework. The framework is in the shape of the right‑angled triangle ABC shown in the diagram.

The steel that Markus uses costs $22 per metre. The steel can only be bought in a length that is a whole number of metres.

Work out the total cost of the steel that Markus buys in order to make the framework.

$ [4]

Alison buys 2 boxes of strawberries, box A and box B.

Box A contains 15 strawberries. The strawberries in box A have a mean weight of 24 grams.

Box B contains 25 strawberries. The strawberries in box B have a mean weight of 18 grams.

Alison puts all 40 strawberries into a bowl. Work out the mean weight of the 40 strawberries.

_grams[3]

(a)Factorise x²– x – 42

[2]

(b)Solve the inequality 3x + 15 < 8x + 3

Show clear algebraic working.

[3]

Given that 150^x = 1

(a)write down the value of x.

x = [1]

Given that 3^–8÷ 3^–6= 3ⁿ

(b)find the value of n.

n = [1]

Show, by shading on the grid, the region that satisfies all three of the inequalities

Label the region R.

[3]

Find the gradient of the straight line with equation 5x + 2y = 7

[2]

The diagram shows four congruent right‑angled triangles ABJ, BCI, CDH and DEG. The diagram also shows the straight line ABCDEF.

AJ = 15 cm Angle BAJ = 35°

AF = 80 cm

Work out the length of EF. Give your answer correct to 3 significant figures.

_cm[5]