Week 48 · Maths Practice Paper

Work out:

Fill in the missing numbers in these sequences:

Find:

The shape below is made up of a 6cm square and a rectangle. The rectangle is 4cm wide and extends 4cm above the square's top edge, aligned to the right.

Fill in the blanks to make the calculation correct.

In the diagram, two straight lines cross to form a triangle with a base angle of 28°. The angle vertically opposite the triangle's apex angle, on the other side of the crossing point, is 95°. Find the third angle of the triangle (a), the exterior angle formed by extending the base line (b), and the exterior angle at the apex vertex (c).

Put these in order from smallest to largest:

0.68      78      1320

On a coordinate grid, points A(2,5), B(-1,3) and C(2,-2) are plotted.

You are given the following list of numbers: 5, 9, 7, 15, 9

What is the third smallest number which is a multiple of 1, 2, 3, 4 and 6?

A pattern is made of 4 regular hexagons and 7 equilateral triangles, all with the same side length (each hexagon's area equals 6 triangle areas). If one hexagon and three triangles are shaded, what fraction of the whole pattern's area is shaded?

A shape has vertices at (1,7), (1,5), (3,5) and (4,7).

Benny has £10 to spend on ingredients for a salad. He chooses to spend it on apples and carrots — each pack of apples costs £1.25 and each bag of carrots costs 65p.

A pie chart with 6 equal slices shows the favourite colours of a Year 7 class: Blue (3 slices), Red (2 slices), Yellow (1 slice).

The instruction x ⊕ y means divide x by y and then subtract the result from 120. For example, 6 ⊕ 2 = 120 − (6 ÷ 2) = 117.

An L-shaped figure can be split into two rectangles: a rectangle x cm wide by 8cm tall, sitting on top of a second rectangle (x+2) cm wide by 4cm tall, aligned to the left, giving a total height of 12cm.

Nina swims on every date that is a multiple of 2. Omar swims on every date that is a multiple of 3. Priya swims on every date that is a multiple of 4. Consider only dates 1 to 30 of a month.

Below are the first three shapes in a sequence, where each new shape is made by adding a ring of small squares around the outside of the last shape. Shape N has 2N² − 2N + 1 small squares (Shape 1 has 1 square, Shape 2 has 5, Shape 3 has 13).

6 decorators take 5 hours to paint 4 rooms. Assuming the decorators work at the same pace and the rooms are the same size,

The square ABCD consists of four identical rectangles arranged around a central square. Each rectangle has a perimeter of 40cm. The area of the central square is 4 times bigger than the area of each rectangle. What is the length of each side of the central square, to the nearest cm?