WJEC GCSE Mathematics Unit 2: Calculator-allowed Higher June 2017 question paper 3300U60-1

Calculate the reciprocal of −0.07, correct to 1 decimal place.

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

Diagram not drawn to scale

A solution to the equation

lies between 3 and 4.

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

You must show all your working.

A right-angled triangle LMN is shown below.

LN = 16.9 cm and LM = 6.5 cm.

Calculate the length MN.

Calculate the length of the side QR in the triangle PQR shown below.

100 boxes each contain 10 balls.

45 of the boxes are labelled A. They each contain 7 black balls and 3 white balls.

25 of the boxes are labelled B. They each contain 4 black balls and 6 white balls.

The rest of the boxes are labelled C. They each contain 8 black balls and 2 white balls.

In a game, a player chooses a box at random, and then chooses a ball at random from that box.

Complete the tree diagram shown below.

What is the probability that a player will select a black ball?

If a large number of people played the game, approximately what fraction of them would you expect to choose a white ball?

Circle your answer.

Factorise x³ − 5x.

Expand and simplify (2x – 3)(x + 4).

Factorise x² − 3x – 28.

Circle the equation of a straight line that is perpendicular to the line y = 5x − 3.

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

The area of triangle ABD, shown in the diagram below, is 35 cm². AD = 5 cm and BC = 32 cm. D is on the line AC, and BD is perpendicular to AC.

Calculate the size of angle x.

You must show all your working.

Make c the subject of the following formula.

Give your answer in its simplest form.

By first calculating the size of BAC, calculate the area of triangle ABC.

You must show all your working.

Describe fully a single transformation that transforms shape A onto shape B.

The table below shows the three-day rain forecast for Monday, Tuesday and Wednesday in Eglwyswrw.

For these three days,

calculate the probability that it will rain on all three days.

calculate the probability that it will rain on exactly 2 consecutive days.

Give one example to show that the square of an irrational number is not always rational.

Find two different irrational numbers to make the answer to the calculation below rational.

Complete the calculation by filling in the three boxes.

A sketch of the graph y = f (x) is shown below.

Two specific points are shown on the graph. They are called a maximum point and a minimum point. The maximum point shown is (–2, 2) and the minimum point shown is (2, –2).

The graphs on the opposite page are transformations of y = f(x). Draw a line connecting each graph to the equation describing the transformation.

One has been done for you.

The cube below has an internal diagonal of length 20 cm. Each edge of the cube is of length xcm.

Calculate the value of x.

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