Week 36 · Maths Practice Paper

Fill in the blanks with one number:

If 9 oranges cost GBP 1.08, how much change would I get from GBP 20 if I buy 15 oranges?

Look at the diagram below (dark squares are shaded).

Which of the following are equivalent to 38 ? Circle all the correct answers:

0.375        914        3×28×2        37.5%        964        35

A bakery sells 150 items, some of which are gluten-free. 40% of the items are cakes; the rest are pastries. Of the cakes, 20 are gluten-free. In total there are 45 gluten-free items. How many pastries are NOT gluten-free?

The 6x6 grid below has both diagonals drawn on it, and two squares are already shaded. For both diagonals to be lines of symmetry, more squares need to be shaded. Using (column, row) with (1,1) at the bottom-left square, which extra squares need shading, and how many are there?

Ali and Ben share a bag of sweets. Ali is greedy: for every 4 sweets Ben eats, Ali eats 7. Between them they eat 121 sweets. How many more sweets did Ali eat than Ben?

The diagram below shows a triangle on top of a square. The base of the triangle is the same length as a side of the square, and the height of the triangle is the same as its base. The total area of the shape is 54 cm². What is the height of the triangle?

To make enough soup for 12 people, 900g of tomatoes is needed. What weight of tomatoes would be needed to make enough soup for 20 people?

A staircase is built from unit cubes: one column of 1 cube, the next column of 2 cubes stacked on top of each other, and the next column of 3 cubes stacked on top of each other, all standing side by side (the staircase is only 1 cube deep, as shown below). I want to paint all the visible faces of the staircase, including the bottom. How many cube faces do I need to paint?

There are 210 pupils at a school: 66 pupils play the guitar and 45 pupils play the drums. 13 of the guitarists also play the drums. How many pupils at the school play neither the guitar nor the drums?

The sum of two angles in a triangle is four times the third angle. The largest angle is 20 degrees greater than the second largest angle. Find the angles of the triangle.

Maria won the quiz round of a competition, for which she got 16 of the total prize money. She also won the bonus round, for which she got 110 of the total prize money. Maria got GBP 320 altogether. How much was the total prize money?

Zara has two identical rectangular strips of card. She experiments by laying the strips on a table in two different arrangements, shown below.

A different area of table is covered by the strips in the two arrangements. The area in Arrangement 2 is 78 of the area in Arrangement 1. The length of each strip is 16 cm. What is the area of table covered in Arrangement 2?

At Elmfield Academy, 25% of the pupils normally at school are in Year 8. One day some Year 8 boys go on a school trip. The total number of pupils left at school is then 360, and the proportion of these who are in Year 8 is 15%. How many pupils are normally at school in total?