Week 50 · Maths Practice Paper

Work out:

Fill in the missing numbers in these sequences:

A farmer has 300 animals. 25 of them are sheep. 30% of them are cows.

A shape is made of a 10cm by 8cm rectangle, with a right-angled triangle attached to the right-hand side (legs 6cm and 8cm, sharing the rectangle's taller side as one leg).

Fill in the blanks to make the calculation correct.

The table shows the train timetable from Kings Cross to Cambridge. Departures: 9:05, 9:35, 10:10, 10:40. Arrivals: 9:58, 10:28, 11:03, 11:33. To get to work John has to walk 10 minutes to the station, get the train to Cambridge, and then walk 20 minutes to his office. If John has to get to work before 11:00 today, what is the latest time he can leave the house?

Two straight lines cross to form a triangle with a base angle of 35°. The angle vertically opposite the triangle's apex angle is 87°.

On the grid, points A(-2,-3), B(2,2) and C(7,2) are plotted.

Ava, Bella, Chloe, Dina and Ella play a ball game. Their ages are 6, 8, 9, 10 and 12.

Mark drives a 120-mile journey in 3 hours. How much faster would he have to drive if he wanted to complete the journey in 2.5 hours?

A shape has vertices at (2,8), (2,6), (4,6) and (5,8).

Benny is making pancakes for a party and needs to buy flour and eggs. A bag of flour costs £1.25 and a box of 6 eggs costs £1.05.

A sequence of patterns of dots has Shape N made up of N × (N+1) dots (Shape 1 has 1×2=2 dots, Shape 2 has 2×3=6 dots, and so on). What is the first shape to be made up of more than 300 dots, and how many dots does it have?

In a magic triangle, each of the numbers 1 to 6 is placed once — three at the corners and three at the midpoints of the sides — so that each side of the triangle adds up to the same total. The corners hold the numbers 1, 3 and 5, as shown.

The instruction x ⊕ y means subtract x from y and then divide 480 by the result. For example, 6 ⊕ 70 = 480 ÷ (70 − 6) = 7.5.

An L-shaped figure can be split into two rectangles: a rectangle x cm wide by 10cm tall, sitting on top of a second rectangle (x+4) cm wide by 6cm tall, aligned to the left (total height 16cm). The total area is 88 cm².

A quadrilateral has vertices at (0,0), (1,7), (4,5) and (1,1) on a centimetre grid. Find its area.

Wilfred lists all the factors of an even number. He finds that the second largest factor of the number is 78 bigger than the second smallest factor of the number. What was the even number?

3 bricklayers take 6 hours to build 4 walls. Assuming the bricklayers work at the same pace and the walls are the same size,

A large cube is made up of a number of smaller cubes. The number of small cubes that touch exactly four other small cubes face-to-face is 108. How many small cubes make up the large cube?