Eduqas GCSE Maths Component 1H Higher June 2024 question paper

Solve 11 c + 3 = 4 (c + 2).

Write 2475 as a product of its prime factors in index form.

Write down the square root of 64×5⁴ ×7⁴.

Give your answer as a product of prime factors in index form.

Sara works for the winter-clothing company Zipski.

The table below shows the monthly sales figures for 2023.

Sara used the information in the table to draw the graph below.

Give two reasons why Sara’s graph may be misleading.

Pippa and Joe are working on a school project.

The project is based on the use of the local leisure facilities.

Explain why the mean is not the best average to use for this data.

Give one other reason why Joe’s results may not be reliable.

An empty water tank is filled using a hose with a steady rate of flow.

The tank takes: • 30 minutes to fill if water is added at x litres/min • 40 minutes to fill if the water is added at (x − 2) litres/min. Form an equation in terms of x.

Solve the equation and hence find the capacity of the tank in litres.

Three friends, Louis, Krystal and Jamal win some money in a competition.

They share the money in the ratio 3: 7: 11.

What fraction of the total money won is given to Jamal?

Jamal spends £45 of the money he won. He now has exactly twice as much as Louis won.

How much money did Krystal win?

p and n are two non-zero numbers. p is a positive number and n is a negative number.

Look at the statements in the table below. For each statement, choose one of the following: ‘Always true’, ‘Never true’ or ‘Sometimes true’.

Tick (√) one box for each statement.

Write down the value of 0∙2⁰.

6 printers take 36 minutes to print a number of identical booklets. How long will it take 9 printers to print half as many of these booklets?

You may assume that all printers print at the same rate.

The price of an item in a sale has been reduced by 25%.

If the sale price is £54, what was the original price of the item?

Percentage change can be calculated using multipliers.

A number is decreased by 33% of its value.

Circle the multiplier that would find the value after this decrease.

0∙67 –1∙33 –0∙67 0∙33 0∙77

A number is increased by 6% of its value. This is done 3 times, each time increasing the previous value by 6%.

Circle the multiplier that would find the value after the 3 increases.

Use an algebraic method to calculate how much Nina pays for 4 apples and 2 bananas.

Give your answer in standard form.

Give your answer in standard form.

Write 32×(2³)⁷ in the form 2ⁿ.

The nth term of a sequence is given by the expression n² + 3n + 2. Prove that every term of the sequence is an even number.

Show all your working.

The diagram shows four patterns made using rectangular tiles.

Pattern 1 Pattern 2
Pattern 3
Pattern 4

Find an expression for the number of rectangular tiles needed for the nth pattern.

Pupils in a GCSE class have to perform two experiments.

Jenny performs the first experiment. She sketches a graph of her results. She thinks the graph shows that the variable h is proportional to the cube root of the variable g.

Explain why Jenny cannot be correct.

Results of a second experiment show that there is a relationship between two positive variables p and q. It has been found that p is inversely proportional to the square root of q.

When p = 36, q = 25.

Write a formula for p in terms of q.

Use the formula to complete the table below.

2. The number of large tables must be less than double the number of small tables. 3. The total number of seats must be less than 120.

Let s represent the number of small tables and l represent the number of large tables.

Complete the table below by writing the inequalities for conditions 2 and 3.

On the graph paper opposite, draw the region that satisfies all three inequalities.

Indicate clearly the region that is your answer.

The restaurant owner makes a 4th condition. There cannot be exactly 13 large tables.

From your graph, write down the number of small and the number of large tables

that can be bought where all four conditions are satisfied.

Large tables (l)

On the opening night of the restaurant, the time that each customer had to wait for their meal was recorded.

It is known that: • 110 customers ate a meal at the restaurant • 9 customers had to wait between 0 and 15 minutes • every customer waited less than 1 hour.

Complete the histogram below.

Calculate the percentage of the 110 customers who had to wait longer than

30 minutes for their meal.

Factorise and hence solve the following equation.

A cheese factory makes two different types of cheese.

Both types of cheese are in the shape of a cylinder.

The first cheese has radius 12 cm and height 7 cm. Work out the total surface area of this cheese.

Give your answer as a multiple of π.

The second cheese has radius r cm and height 25 cm. A cheese taster working at the factory cuts a wedge-shaped piece out of this cheese. It is cut to the centre of the cheese with an angle of 30° and a depth of 8 cm.

Work out the volume of the wedge-shaped piece as a fraction of the whole cheese.

Give your answer in its simplest form.

Anya and Elis sit examinations at a college.

Anya sits two examinations, one for Spanish and the other for French. The probability that Anya passes Spanish is 0∙6. The probability that Anya passes French is 0∙7. The probability of Anya passing Spanish is independent of her passing French. Anya tries to calculate the probability of her passing exactly one examination. She writes 0∙6 × 0∙3 = 0∙18

Without giving any calculations, explain why this answer is not fully correct.

Calculate the probability of Anya passing exactly one examination.

Elis sits one examination. The examination has 75 multiple choice questions. For each question: • there are five possible answers to choose from • only one of the five possible answers is correct. Elis knows the answer to 60% of the questions and will get these correct. Of the remaining questions, he randomly selects one of the five possible answers. A question is selected at random.

What is the probability that Elis answers this question correctly?

Complete the table below. Write both missing values in surd form.

The sketch of the equilateral triangle may help you.

Calculate the value of x.

Use the method of completing the square to find the coordinates of the turning point of the

curve y = x² +14x + 70.

Coordinates of the turning point (_........ ,_........ )

The vectors OP, OQ and OR are shown in the diagram.

RQ = kOP. Find the value of k.

You must show all your working.

O is the midpoint of the line PX.

Find PX in the form mf + ng where m and n are integers.