Eduqas GCSE Maths Component 1H Higher November 2024 question paper

18 questions

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(a)

Expand and simplify 3 (5 a − 2) − 7 (a − 4).

[2]

Answer

(b)

Show that the triangle below is not isosceles.

You must use an algebraic method and not trial and improvement.

[5]

Answer

(a)

[3]

Answer

(b)

[1]

Answer

(a)

Calculate an estimate of the mean time for these 50 deliveries.

[4]

Answer

(b)

Calculate an estimate of the percentage of these deliveries that took 25 minutes or

more.

[2]

Answer

(a)

Write 882 as a product of its prime factors in index form.

[3]

Answer

(b)

Two numbers, S and T, have been written as a product of prime factors in index form:

(b)(i)

Circle the correct expression for the highest common factor of S and T.

[1]

Answer

(b)(ii)

Circle the correct expression for the lowest common multiple of S and T.

[1]

Answer

(c)

Find the values of p, q and r so that the following is correct.

[2]

Answer

(a)

Write down the next term in the following sequence.

[2]

Answer

(b)

Write down an expression for the nth term of the following sequence.

–3, 3, 9, 15, 21, …

[2]

Answer

(c)

(c)(i)

The first seven terms of a Fibonacci sequence are given by

1, 1, 2, 3, 5, 8, 13, …

Find the 11th term of this sequence.

[1]

Answer

(c)(ii)

The first four terms of a different Fibonacci-type sequence have been expressed algebraically.

c, d, c + d, c + 2 d, …

Write the expression for the 7th term of this sequence.

Give your answer in its simplest form.

[2]

Answer

(a)

Simplify the following ratio,

$Question 6, shown as an image$

[2]

Answer

(b)

Sura is making a cake. The main ingredients are flour, sugar and dried fruit. She uses these ingredients with their masses in the ratio 5: 3: 7.

(b)(i)

What fraction of the main ingredients is the mass of the dried fruit?

[1]

Answer

(b)(ii)

The combined mass of the flour and sugar is 560 g.

What is the mass of the dried fruit?

[3]

Answer

Hannah and Imran often play badminton and tennis matches against each other.

The probability that Hannah wins a badminton match is $fraction$ The probability that Hannah wins both a badminton match and a tennis match is $fraction$ One Saturday, Hannah and Imran play one badminton match and one tennis match. The outcomes of the matches are independent.

(a)

Complete the tree diagram below.

[4]

Answer

(b)

Calculate the probability that Hannah wins exactly one match.

[3]

Answer

(a)

[2]

Answer

(b)

[2]

Answer

(c)

Two triangles are shown in the diagram below.

Show that the two triangles are mathematically similar.

[2]

Answer

The solid cylinder shown below has radius 4 cm and height h cm.

The total surface area of the cylinder is 104π cm².

Calculate the value of h.

[5]

Answer

280 students took tests in each of the three subjects, Biology, Chemistry and Physics. Each test consisted of questions worth a total of 40 marks.

(a)

The following table shows a summary of the Biology test data.

Lowest mark	Highest mark	Lower quartile	Median	Interquartile range
12	40	22	29	13

On the grid below, draw a box plot to represent this data.

[3]

Answer

(b)

Two box plots have been drawn representing the test data for Chemistry and Physics.

(b)(i)

Calculate the number of students that were awarded 10 or more marks in Physics.

[2]

Answer

(b)(ii)

Two teachers disagree over the spread of the marks.

One teacher states that the spread of marks is the same for all three tests. The other teacher states that the spread of the marks is the same in only two of the tests.

Explain why both teachers are correct.

You must give values to justify your answer.

[3]

Answer

(c)

A different set of students sat a mathematics test. The test was out of 60 marks. The results obtained were recorded in a table and a cumulative frequency graph was

Cumulative

Criticise the above graph.

[1]

Answer

Alison lives in a town with a population of 45 000.

It is predicted that the population of the town will: • increase by 2% every six months for the next 4 years • decrease by 5% per year for the following 3 years.

(a)

Alison wants to calculate what the population of the town will be after 7 years. She completes the boxes in the calculation below:

$Question 11, shown as an image$

Both boxes have been completed incorrectly.

Complete each box below with the correct calculation.

[2]

Answer

(b)

Circle the sketch that best shows the town’s changing population over the 7-year

period.

$Question 11, shown as an image$

[1]

Answer

(a)

$Question 12, shown as an image$

[2]

Answer

(b)

Two solid shapes are similar. The ratio of their surface areas is 1: k.

Write, in terms of k, an expression for the ratio of their volumes.

[1]

Answer

(c)

Rearrange the following formula to make g the subject.

[4]

Answer

(a)

Show that 2x² + 3x − 27 = 0.

[4]

Answer

(b)

Calculate the perimeter of the shape.

You must use an algebraic method and show all your working.

[6]

Answer

The graph shows the depth of water in a container over a period of 7 minutes.

Depth of water (cm)

(a)

Calculate an estimate of the rate at which the water level is changing at t = 6.

Simplify your answer as far as possible.

[3]

Answer

(b)

Calculate the average rate at which the water level is changing between t = 1 and t = 3.

[2]

Answer

(c)

From time t = 7 minutes, the rest of the water flows out of the container until it is empty. During this time the depth of water decreases at a constant rate of $fraction$ cm per second.

Complete the graph.

[2]

Answer