4MA1 Mathematics A: January 2023 Paper 1FFoundation Tier Paper 1

The table gives information about six plays written by William Shakespeare.

(a)Which of these six plays has the greatest number of words?

[1]

Two of these six plays were written in the same year.

(b)Write down the name of each of these plays.

_and [1]

The play Othello has 9329 more words in it than the play Macbeth.

(c)Work out the number of words in the play Othello.

[1]

(d)Write the number 21 055 in words.

[1]

Luca has 5 kg of chopped tomatoes. He also has some empty tins.

When full, each tin holds 350 g of chopped tomatoes.

Luca fills as many tins as possible with the chopped tomatoes.

Work out the weight of the chopped tomatoes remaining after Luca has filled as many tins as possible. Give the units of your answer.

[4]

A sequence of patterns is made from squares.

(a)In the space below, draw Pattern number 4

[1]

(b)Complete the table.

[1]

(c)Work out the number of squares in Pattern number 8

[1]

Angus says

Angus is incorrect.

(d)Explain why.

[1]

(a)Write 0.8 as a percentage.

_%[1]

(b)Write down the value of the 3 in the number 4.7634

[1]

(c)Write these decimals in order of size. Start with the smallest decimal.

[1]

(d)Write 25.786 21 correct to 2 decimal places.

[1]

(e)Find the square root of 1296

[1]

Adam has 8 packets of noodles. Here is the flavour of noodles in each packet.

Adam takes at random a packet of noodles.

(a)(i)On the probability scale, mark with a cross (×) the probability that Adam takes a packet of Hot and Spicy noodles.

[1]

(ii)Circle the word that best describes the likelihood that Adam takes a packet of Vegetarian noodles.

[1]

Belinda asks 20 people to name the type of rice that they each like the best.

Here are her results.

(b)Complete the frequency table for Belinda’s results.

[2]

Sandeep sells 600 tickets for an event. He receives a total of $7200 from selling the tickets.

14 of the tickets sold are child tickets.

The rest of the tickets sold are adult tickets.

The cost of an adult ticket is $13.60

Work out the cost of a child ticket.

$ [4]

(a)Simplify 5p × 9k

[1]

(b)Simplify 3e + 2f + 8e – 7f

[2]

(c)Solve 2d + 7 = 16

d = [2]

Here is a scale drawing showing the positions of Paris and Bordeaux.

Alain drives from Paris to Bordeaux. The distance that he drives is 590 km.

This distance is greater than the actual straight line distance between Paris and Bordeaux.

How much greater? Show your working clearly.

_km[4]

Avner has two fair spinners.

Spinner A can land on 1, 2 or 3 Spinner B can land on 1, 2, 3 or 4

Avner multiplies the number on which spinner A lands by the number on which spinner B lands to find his score.

(a)Complete the table to show all possible scores. Seven of the scores have been completed for you.

Spinner A

[2]

Avner spins spinner A once and spinner B once.

(b)Find the probability that his score is an odd number.

[1]

Orange squash is made from orange juice and water.

Sean has two different cartons of orange squash, carton P and carton Q. The table gives information about the two cartons.

Total volume of orange squash is Total volume of orange squash is

30% of the total volume is orange juice 160 millilitres of the total volume is water

Work out the difference in the volume of orange juice in carton P and the volume of orange juice in carton Q.

_millilitres[3]

On the grid below, draw the graph of y = 1 – 2x for values of x from –2 to 3

[3]

(a)Show that 78 – 512 = 1124[2]

(b)Find the highest common factor (HCF) of 130 and 208 Show your working clearly.

[2]

p = t – ac

t = 18 a = –3 c = 5

(a)Work out the value of p

p = [2]

(b)Make x the subject of the formula d = 3x + 10

[2]

(a)On the grid, rotate triangle A 90° anticlockwise about centre O[2]

(b)Describe fully the single transformation that maps triangle B onto triangle C

[2]

Here is a floor plan of a stage. The plan is formed from a triangle and a rectangle.

The stage manager is going to paint the floor.

One tin of paint covers an area of 1.8 m² One tin of paint costs $16.40

Paint can only be bought in full tins.

The stage manager has $190 to spend.

Does the stage manager have enough money to buy enough tins to paint all of the floor? Show your working clearly.[5]

80 students entered a dancing competition.

The table gives information about the length of time, in minutes, for which each student spent dancing.

12 < m  24 25

24 < m  36 23

36 < m  48 15

48 < m  60 6

Work out an estimate for the mean length of time the students spent dancing.

_minutes[4]

Solve 3(2 – 4x) = 5 – 8x Show clear algebraic working.

x = [3]

Use ruler and compasses only to construct the perpendicular bisector of line AB You must show all your construction lines.

[2]

The diagram shows a pentagon.

Work out the value of x

x = [3]

In a box, there are only green sweets, orange sweets and yellow sweets.

There are 280 sweets in the box so that

the number of green sweets : the number of orange sweets = 2 : 3 and the number of orange sweets : the number of yellow sweets = 1 : 5

Work out how many green sweets there are in the box.

[3]

Shane bought a car.

The amount Shane paid for the car was $32 000

Theresa also bought a car. To pay for this car, Theresa paid a deposit of $18 000 together with 14 monthly payments of $1160

Theresa paid more for her car than Shane paid for his car.

(a)Work out how much more Theresa paid as a percentage of the amount Shane paid.

%[4]

Kylie bought a van.

After 1 year, the value of the van was $39 865 During this year, the value of the van decreased by 15%

(b)Work out the value of the van when Kylie bought it.

$ [3]

Some members of a library were asked to name the type of book that they each liked to read the best.

One of the members is chosen at random. The table shows information about the probability of the type of book that this member answered.

48 members answered comedy books.

Work out how many of the members answered mystery books.

[4]

The diagram shows a triangle ABC inside a semicircle.

A, B and C are points on the semicircle.

AB is the diameter of the semicircle.

Angle ACB = 90° Angle BAC = 50° AC = 18 cm

Work out the perimeter of the semicircle. Give your answer correct to 2 significant figures.

cm[5]

(a)Write 6.25 × 10⁻⁴ as an ordinary number.

[1]

(b)Work out (2.4 × 10¹²) ÷ (9.6 × 10⁴) Give your answer in standard form.

[2]

(a)Factorise y²– 2y – 48

[2]

(b)Write down the inequality shown on the number line

[1]

(c)Solve the inequality 7w + 6 > 12w + 14

[3]