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

Simplify (m²)³

Simplify x⁵x⁸

Expand 4p(p² + 3p)

Jonny wants to know how much coffee he will need for 800 people at a meeting. Each person who drinks coffee will drink 2 cups of coffee. 10.6 g of coffee is needed for each cup of coffee. Jonny assumes 68% of the people will drink coffee.

Using this assumption, work out the amount of coffee Jonny needs. Give your answer correct to the nearest gram.

Jonny’s assumption is wrong. 72% of the people will drink coffee.

How does this affect your answer to part (a)?

ACF and ADG are straight lines. BCD and EFG are parallel lines.

Show that triangle ACD is isosceles. Give a reason for each stage of your working.

It takes 14 hours for 5 identical pumps to fill a water tank. How many hours would it take 4 of these pumps to fill another water tank of the same size?

A and B are numbers such that A = 2²×3⁴×7

Find the highest common factor (HCF) of A and B.

Find the lowest common multiple (LCM) of A and B.

Lava flows from a volcano at a constant rate of 11.9 m³/s How many days does it take for 67 205 600 m³ of lava to flow from the volcano? Give your answer correct to the nearest day.

Here is the graph of y = x² – 2x – 2

Write down the coordinates of the turning point on the graph of y = x² – 2x – 2

Write down an estimate for one of the roots of x² – 2x – 2 = 0

A solid cuboid is made of metal. The metal has a density of 9 g/cm³ The volume of the cuboid is 72 cm³ Work out the mass of the cuboid.

Some people were asked if they wanted a new television. 70% of the people said yes. 80% of the people who said yes wanted a television with a large screen. What percentage of the people asked said they wanted a television with a large screen?

ABD is a triangle. C is a point on BD.

Work out the length of DC. Give your answer correct to 1 decimal place.

The table shows some information about the heights of a group of adults.

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

The box plot below shows the distribution of the heights of a group of teenagers.

Compare the distribution of the heights of the adults with the distribution of the heights of the teenagers.

12Show that (x – 1)(x + 3)(x – 5) can be written in the form ax³ + bx² + cx + d where a, b, c and d are integers.

13An expression for the nth term of the sequence of triangular numbers is Prove that the sum of any two consecutive triangular numbers is a square number.

OAB is a triangle. OBC is a sector of a circle, centre O.

Calculate the area of OBC. Give your answer correct to 3 significant figures.

Factorise a² – b²

Show that 2⁴⁰ – 1 is the product of two consecutive odd numbers.

On the grid, enlarge triangle T by scale factor –2 with centre of enlargement (–2, –2)

Here is a distance-time graph.

Find an estimate of the gradient of the graph at time 2.5 seconds. You must show how you get your answer.

What does the gradient of the graph represent?

A solid frustum is made by removing a small cone from a large cone as shown in the diagram.

The slant height of the small cone is 6 cm. The slant height of the large cone is 10 cm. The radius of the base of the large cone is 3 cm. Calculate the total surface area of the frustum. Give your answer correct to 3 significant figures.

19Sana needs to draw the graph of y = 3^x for 0 ≤ x ≤ 4 She draws the graph shown on the grid.

Write down one thing Sana has done wrong.

2 8 13 22Given that the vector a b is parallel to the vector

find an expression for b in terms of a.

23A circle has equation x² + y² = 25 The point P with coordinates (–3, 4) lies on the circle. Alex says that the tangent to the circle at P crosses the x-axis at the point (–8, 0) Is Alex correct? You must show how you get your answer.

There is a total of y counters in a box. There are x pink counters and 5 blue counters in the box. The rest of the counters are green. x:y = 1: 3 Freda takes at random two counters from the box. Find, in terms of x, an expression for the probability that Freda takes two counters of the same colour.