Eduqas GCSE Maths Component 1H Higher November 2023 question paper

Ivy mixes lemon juice, pineapple juice and orange juice in the ratio 1: 2: 7 to make a fruit drink.

Ivy has 330 ml of her fruit drink in a glass.

How much pineapple juice is in Ivy’s glass?

The shape below consists of a square surrounded by four semi-circles.

The diameter of each semi-circle is 12 cm.

Work out the area of the shape.

Give your answer in the form a + bπ.

Oliver and Kian bake cakes.

The mass of Oliver’s cake is between 400 g and 500 g inclusive. The mass of Kian’s cake is between 200 g and 300 g inclusive.

Complete the inequality to show the least and greatest possible differences between the mass

of their cakes.

Jen is mixing some paints to make brown paint.

She made orange paint by mixing red paint and yellow paint. 40% of the orange paint was red paint.

She then mixes the orange paint with some blue paint in the ratio 20: 21 to make brown paint.

What fraction of the brown paint is red paint?

The diagram below shows an equilateral triangle and a square.

Use an algebraic method to find the value of x and the value of y.

You must show all your working.

Complete the calculation below.

Factorise 3xy² + 6x²y

Hans thinks of a number.

When his number is multiplied by 2·4 × 10⁵, the answer is 9·6 × 10⁸.

What number did Hans think of?

Write your answer in standard form.

Kate is visiting London.

The probability that she will go on a train is 0·4. The probability of Kate going to the theatre is independent of her going on a train.

The probability that she goes on a train and goes to the theatre is 0·28.

Complete the following tree diagram.

It takes 2 hours to empty 8 identical tanks of water using 9 identical pumps.

How long would it take to empty 2 of these tanks using 3 of these pumps?

₇y

Triangle B is reflected in the line x = 0 to give triangle C.

Triangle C is rotated 90° clockwise about (0, 0) to give triangle D.

Draw triangle C and triangle D.

Describe the single transformation that maps triangle B to triangle D.

Show that the lines

3 y − 12 x = 9 and 2 y = 8 x − 13

are parallel to each other.

The diagram shows the curve y = 5 − 4x − x².

Calculate the coordinates of the turning point of the curve.

Find the next term in this sequence.

Find the next term in this Fibonacci-style sequence.

Calculate the 4th term of this sequence.

You must simplify your answer.

Find the nth term of the sequence below.

Factorise 5x² + 13x + 6.

Adrian is trying to solve 3 − 4x > 11. He writes the following:

Adrian’s method is incorrect. Explain why.

7 − 2 16. (a) The vector t = and the vector w =. − 2 4

On the grid below, draw the vector t + w.

WYZ is a straight line.

The vectors WX and YX are shown in the diagram.

Given that WY: YZ = 2: 3, write the vector WZ in the form ma + nb.

Write your answer in standard form.

Lena sold 200 drinks on Saturday.

This table shows some information about these drinks.

On that Saturday: • 15% of the drinks sold were large teas. • The ratio of the number of medium teas to the number of medium milkshakes sold was 3:1. • The number of large milkshakes sold was double the number of small milkshakes sold.

Complete the table above using this information.

One of the drinks is selected at random.

Find the probability that this drink was either a medium tea or a medium coffee.

1134 can be written as 2 × 3⁴ × 7.

Find the highest common factor of 504 and 1134.

Give your answer as an integer.

What is the smallest whole number 1134 can be divided by to give a square number?

X, Y and Z are points on the circumference of a circle with centre O.

Maia thinks that XYZ is 58°. Prove that Maia is incorrect.

You must show all your working and give a reason for each step of your proof.

Alice is investigating how much time, in minutes, pupils at her school spend on their mobile phones.

She asks 100 students in Year 11 and 100 students in Year 7 to record how much time they each spend on their mobile phones on a Monday.

The results for Year 11 are shown in the table below.

Time t (minutes)	0t 50	50t 100	100t 200	200t 300	300t 400	400t 500
Number of students	3	5	20	28	30	14

Alice displays her results in the histogram shown below.

Give one criticism of Alice’s histogram.

Alice’s histogram showing the results for the 100 Year 7 students is shown below. The group with time 200t 300 is missing.

Complete the histogram.

You must show all your working.

Make one comparison between the amount of time spent on their mobile phones by all

the students in Year 11 and all the students in Year 7.

The following iterative formula can be used to find the number of cells of bacteria after n days.

Show that the number of cells of bacteria after 1 day is 1200.

Use this formula to find the number of cells of bacteria after 3 days.

Adina has 5 wooden blocks. Each block is a different colour.

Adina selects 3 of these wooden blocks at random. Each time she does this, she places them on top of each other. Two ways of arranging the blocks are shown below.

Calculate the number of different ways of arranging the blocks.

How many arrangements are there where the middle block is either blue or red?

The velocity-time graph below shows the velocity of a car for the first 20 seconds from rest.

Calculate an estimate of the acceleration of the car at time 8 seconds.

Use 5 vertical strips of equal width to calculate an estimate of the distance travelled by

the car during the first 20 seconds of motion.

h(x) = x² + 3.

Show that h^–1(x) has no solutions for x 3.

f(x) = x² + 5. g(x) = x − 4.

Show that f g(x) − gf(x) = 20 − 8x.

You must show all your working.

Make e the subject of the following formula.

Express 0·345^{● ●} as a fraction.

Sofia’s dog is running through a field. Its speed at t seconds is w metres per second. The diagram below shows the speed of the dog for part of its run.

When t = 5, w = 12. The average deceleration of the dog between 5 and 10 seconds is 1·5 m/s². Calculate the speed of Sofia’s dog when t = 10.

You must show all your working.

Speed when t = 10 is_........ m/s