Edexcel GCSE Maths Paper 3: Calculator Higher June 2024 question paper 1MA1/3H

Find the highest common factor (HCF) of 63 and 105

Write 5.3×10⁴as an ordinary number.

Write 7.4×10^–5as an ordinary number.

Calculate the value of 9.7×10⁶ + 2.45×10⁷ Give your answer in standard form.

The diagram shows a solid triangular prism.

Rana is trying to draw the side elevation of the solid prism from the direction of the arrow. Here is her answer on a centimetre grid.

Explain why Rana’s side elevation is not correct.

On the centimetre grid below, draw a plan of the solid prism.

A company has 25 000 workers. The number of workers increases at a rate of 6% per year for 3 years. Calculate the total number of workers at the end of the 3 years.

Habib has two identical tins. He puts 600 grams of flour into one of the tins. The flour fills the tin completely. The density of the flour is 0.6 g/cm³ Habib puts 600 grams of salt into the other tin. The salt does not fill the tin completely. The volume of the space in the tin that is not filled with salt is 700 cm³ Work out the density of the salt. You must show all your working.

Tim has two biased coins, coin A and coin B. He is going to throw both coins. The probability that coin A will land on heads is 0.6 The probability that coin B will land on heads is 0.55

Complete the probability tree diagram.

Tim throws coin A once and he throws coin B once.

Work out the probability that both coins land on heads.

A paddling pool is in the shape of a cylinder.

The pool has radius 100 cm. The pool has depth 30 cm. The pool is empty. It is then filled with water at a rate of 250 cm³ per second. Work out the number of minutes it takes to fill the pool completely. Give your answer correct to the nearest minute. You must show all your working.

On the grid below, draw and label the vector 2a + b

The diagram shows a cube and a square-based pyramid.

The volume of the cube is equal to the volume of the pyramid. Work out the perpendicular height, hcm, of the pyramid.

There are only red counters and yellow counters in bag A. number of red counters: number of yellow counters = 3: 5 There are only green counters and blue counters in bag B. The number of counters in bag B is half the number of counters in bag A. Given that there are x red counters in bag A, use algebra to show that the total number of counters in bag A and bag B is 4x

Mina records the speeds, in mph, of some cars on a road on Friday. She uses her results to work out the information in this table.

On the grid, draw a box plot to show the information in the table.

Mina also records the speeds of some cars on the same road on Sunday. She uses her results to draw this box plot.

Compare the distribution of the speeds on Friday with the distribution of the speeds on Sunday.

The diagram shows triangle T drawn on a grid.

Enlarge triangle T by scale factor –2 with centre of enlargement (0, 0)

There are 30 students in a class. A teacher is going to choose at random 2 of the students. Work out the number of different pairs of students that the teacher can choose.

At the start of 2022 Kim invested some money in a savings account. The account paid 3.5% compound interest each year. At the end of 2022 interest was added to the account then Kim took £750 from the account. At the end of 2023 interest was added to the account then Kim took £1000 from the account. There was then £2937.14 in the account. Work out how much money Kim invested at the start of 2022 You must show all your working.

Factorise 3k² + 11k – 4

The functions f and g are given by

Find f(–3)

Find fg(1)

Find g^–1(4)

A ball is thrown upwards and reaches a maximum height. The ball then falls and bounces repeatedly. After the nth bounce, the ball reaches a height of h_n After the next bounce, the ball reaches a height given by h_{n+ 1} = 0.55h_n After the 1st bounce, the ball reaches a height of 8 metres. What height does the ball reach after the 4th bounce?

ABCD is a quadrilateral.

The area of triangle ABC is 54 cm² Calculate the area of triangle ACD. Give your answer correct to 3 significant figures.

P = 5.8810⁸correct to 3 significant figures. Q = 3.610⁵correct to 2 significant figures. Work out the lower bound for R. Give your answer as an ordinary number correct to the nearest integer. You must show all your working.

x – 4, x + 2 and 3x + 1 are three consecutive terms of an arithmetic sequence.

Find the value of x.

y – 4, y + 2 and 3y + 1 are three consecutive terms of a geometric sequence.

Find the possible values of y.

The diagram shows a circle, radius r cm and two regular hexagons.

Each side of the larger hexagon ABCDEF is a tangent to the circle. Each side of the smaller hexagon PQRSTU is a chord of the circle. By considering perimeters, show that