WJEC GCSE Mathematics Unit 1: Non-calculator Higher November 2017 question paper 3300U50-1

Look at the following descriptions of special quadrilateral shapes.

Circle the correct name for each one.

Its diagonals intersect at 90°.

Only one diagonal is a line of symmetry.

Kite Rhombus Square Trapezium Rectangle

Only one pair of sides are parallel.

Kite Rhombus Square Trapezium Rectangle

All four sides are equal.

Its diagonals are not equal in length.

Kite Rhombus Square Trapezium Rectangle

The sketch above can represent only one of the equations given below.

Circle this equation.

Rotate triangle A through 90° anticlockwise, about the point (–2, 3).

Enlarge triangle B by a scale factor of , using (0, 0) as the centre of enlargement.

Express 0·000 42 in standard form.

Give your answer in standard form.

Factorise x² – 7x – 18, and hence solve x² – 7x – 18 = 0.

A cylinder just fits inside a hollow cube with sides of length m cm.

The radius of the cylinder is cm. The height of the cylinder is mcm.

The ratio of the volume of the cube to the volume of the cylinder is given by

volume of cube: volume of cylinder

= k: ,

where k is a number.

Find the value of k.

You must show all your working.

Complete the following table to give the set of inequalities that describes the shaded region

shown above.

Two different squares are constructed. The side length of the smaller square is xcm. The side length of the larger square is 3 cm longer than the side length of the smaller square. The combined area of the two squares is 22∙5 cm².

Show that 4x² + 12x − 27 = 0.

Given that y is inversely proportional to x³ and that y = 120 when x = 2,

find an expression for y in terms of x,

use the expression you found in part (a) to complete the following table.

p is equal to

pq is equal to

Two of the cards shown above are selected at random, without being replaced.

Find the probability that

the product of the two numbers selected is 12,

the sum of the two numbers selected is even.