Edexcel GCSE Maths Paper 3: Calculator Higher November 2023 question paper 1MA1/3H

Write 468 000 in standard form.

Write 5.03710^–4 as an ordinary number.

Here is a biased spinner.

The table shows the probabilities that when the spinner is spun it will land on A, on B, on C and on D.

Luka will spin the spinner 200 times. Work out an estimate for the number of times the spinner will land on A.

Seija works at a weather station. The table gives information about the temperature, T °C, at midday for each of 50 cities in the UK on Tuesday.

Temperature (T °C)	Frequency
10 T 15	2
15 T 20	8
20 T 25	13
25 T 30	21
30 T 35	6

Calculate an estimate for the mean temperature.

Seija says, “The median temperature is 22.5 °C because 22.5 is the middle number in the middle group.”

Is Seija correct? Give a reason for your answer.

Jenna is asked to show the inequality –3 < x ≤ 4 on a number line. Here is her answer.

Write down two mistakes Jenna has made.

Work out the greatest integer that satisfies the inequality

Ali buys packs of balloons and boxes of pencils. There are 30 balloons in each pack. There are 24 pencils in each box. Ali buys exactly the same number of balloons and pencils. Work out how many packs of balloons and how many boxes of pencils she could have bought. You must show all your working.

_........ packs of balloons

A company orders a large number of plates from a factory. It would take 30 hours to make all the plates using 4 machines. How many machines are needed to make all the plates in 6 hours?

Riley travelled by car and by aeroplane. He travelled 143 miles by car at an average speed of 55 miles per hour. Riley then travelled for 5 hours and 20 minutes by aeroplane. Work out, in hours and minutes, Riley’s total travelling time.

The diagram shows a solid cube placed on a horizontal table.

The pressure on the table due to the cube is 3.5 newtons/cm² The force exerted by the cube on the table is 504 newtons. Show that the total surface area of the cube is less than 900 cm²

The line L is shown on the grid.

Find an equation for L.

The floor plan of a house is drawn using a scale of 1: 50 On the plan, a room in the house has a floor area of 48 cm² Work out the real area of the floor of this room. Give your answer in m²

The diagram shows a shaded sector POQ of a circle with centre O and radius 6.2 cm.

The area of the shaded sector is 82.6 cm² Calculate the size of angle x. Give your answer correct to 3 significant figures.

Alan grew 80 plants of the same type outside. The cumulative frequency graph shows information about the heights, in cm, of these plants.

One of the plants is chosen at random.

Find an estimate for the probability that this plant will have a height greater than 90 cm.

Use the graph to find an estimate for the median height.

Use the graph to find an estimate for the interquartile range of the heights.

Alan also grew plants of the same type inside. The interquartile range of the heights of these plants is 30 cm.

Give one comparison between the distribution of the heights of the plants grown inside with the distribution of the heights of the plants grown outside.

Here are the first six terms of a quadratic sequence. 5 11 21 35 53 75 Find an expression, in terms of n, for the nth term of this sequence.

The diagram shows triangle ABC and triangle AED.

Show that triangle ABC and triangle AED are similar.

Zia has to set a 4‑digit security passcode on her phone. Each digit of the passcode is a number from 1 to 9 She can use each number more than once. Zia tells her friend Amber that the first digit is a cube number the second digit is a prime number the third digit is greater than 6 the fourth digit is an odd number. The diagram shows one possible 4‑digit passcode.

Amber is going to have one attempt at guessing Zia’s passcode. Work out the probability that Amber guesses Zia’s passcode on the first attempt.

Write x² – 8x + 3 in the form (x – a)² – bwhere a and b are integers.

Hence, write down the coordinates of the turning point on the graph

Solve 7x² + 8x – 5 = 0 Give your solutions correct to 3 significant figures.

Alex has to find the solutions of the quadratic equation 3k² + 10k – 8 = 0 Here is his working and answer. (3 k – 2)(k + 4) = 0 k = 2 or k = –4

What mistake has Alex made?

Enlarge triangle P by scale factor –1 with centre of enlargement (–2, –1) Label your image Q. Triangle P is transformed by a combined transformation of a rotation of 90° anticlockwise about the origin followed by a translation to give triangle R. Exactly one vertex of triangle P is invariant under the combined transformation.

Find one possible column vector for the translation.

The diagram above shows a frustum F of a cone. The frustum is made by removing a cone with height 10 cm from a solid cone with height 15 cm and base diameter 24 cm. The solid S is made by removing F from a solid hemisphere as shown in the diagram below.

The hemisphere has diameter 24 cm. Calculate the volume of solid S. Give your answer correct to 3 significant figures.

The turning point on the graph of y = g(x) has coordinates (–3, 6)

Write down the coordinates of the turning point on the graph of y = g(x – 7)

The graph of y = f(x) is shown on the grid.

On the grid, sketch the graph of y = f(–x) + 3

A, B, C and D are points on the circumference of a circle, centre O. AC is a diameter of the circle. ADE and BCE are straight lines. Work out the size of angle BDC. Write down any circle theorems that you use.

Ebony makes some bracelets to sell. The materials to make all the bracelets cost £190, correct to the nearest £5 Ebony sells all the bracelets for a total of £875, correct to the nearest £5 The total time taken to make and sell all these bracelets was 72 hours, correct to the nearest hour. Ebony uses this method to calculate her hourly rate of pay total selling price total cost of materials Hourly rate of pay total time taken

The minimum hourly rate of pay for someone of Ebony’s age is £8.20 By considering bounds, determine if Ebony’s hourly rate of pay was definitely more than £8.20 You must show all your working.

find, in its simplest form, the ratio x:y

The diagram shows a triangular prism with a horizontal rectangular base ABCD.

M is the midpoint of AD. The vertex T of the prism is vertically above M. AB = 14.7 cm BC = 3.8 cm MT = 2.3 cm P is the point on AB such that AP: PB = 5: 2 Calculate the size of the angle between TP and the base ABCD of the prism. Give your answer correct to 1 decimal place.