WJEC GCSE Mathematics Unit 2: Calculator-allowed Higher November 2021 question paper 3300U60-1

A rectangle has sides of length 2(3 a – 7) cm and (5 a + 4) cm.

Form an expression, in terms of a, for the perimeter of this rectangle.

You must simplify your expression.

A company has two sites.

One is in North Wales and the other is in South Wales.

The pie charts below show the distribution of its 96 part-time staff and its 150 full-time staff.

A person is chosen at random from the company’s 246 staff members.

What is the probability that this person works at the site in North Wales?

A solution of the equation

lies between 2 and 3.

Use the method of trial and improvement to find this solution correct to 1 decimal place.

You must show all your working.

Show that the triangle below is not a right-angled triangle.

Diagram not drawn to scale

Calculate the length of the side AB in the triangle shown below.

Expand x(x² + 7).

Expand and simplify (x – 5)(3x − 4).

Sarah buys and sells antique clocks. On Monday, Sarah had n clocks. At the end of the day on Tuesday, she had 5 times as many clocks as she had on Monday. On Wednesday, she sold 27 clocks.

At the end of the day on Wednesday, Sarah had fewer clocks than she had on Monday.

Write an inequality, in terms of n, that shows this information.

Solve your inequality to find the greatest number of clocks that Sarah could have

had on the Monday.

The number shown on each diagram below is 20% greater than the number shown on the previous diagram.

Diagram 1 Diagram 2 Diagram 3

Diagram not drawn to scale

Find the number that should be shown on Diagram 6.

Factorise x² − 4x − 12, and hence solve x² − 4x − 12 = 0.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

A circle with centre O is shown below. The radius of the circle is 7·3 cm.

Calculate the perimeter of the shaded region.

You must show all your working.

Use the expression you found in part (i) to complete the following table.

The table below shows the value of d and the value of e.

It also shows the degree of accuracy of each value.

Use the formula

to calculate the least possible value of c.

You must show all your working.

Simplify the following expression.

Show that

Solve the equation

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

Give your answers correct to 2 decimal places.

Evaluate the length of AC.

You must justify any decision that you make.

The following diagram shows a sketch of the curve y = f (x).

In each of the following questions, the graph of y = f(x) has been transformed.

Circle the only possible equation of the transformed curve.