2. A train carriage has 80 seats. On my journey I noticed that all the seats in my carriage were taken and 7 people were standing.

At Banbury, 9 people left the carriage, 28 people entered it and all the seats were taken.

How many people now had no seat?

‍

3. The diagram shows an equilateral triangle, a square, and one diagonal of the square.

‍

What is the value of x ?

‍

4. The perimeter of the regular decagon P is 8 times the perimeter of the regular octagon Q.

Each edge of the regular octagon Q is 10 cm long.

‍
How long is each edge of the regular decagon P?

‍

5. My train left Southampton at 06:15 and arrived in Birmingham at 08:48 later that morning.

How many minutes did the journey take?

‍

6. The diagram shows a partially completed magic square, in which all rows, all columns and both main diagonals have the same total.

‍

What is the value of x + y?

7. How many integers are greater than 20 + 18 and also less than 20 × 18?

8. Gill scored a goal half way through the second quarter of a ‘teachers versus pupils’ netball match.

At that point, what fraction of the whole match remained to be played?

9. The approximate cost of restoring the Flying Scotsman was £4 million. This was about 500 times the cost of building the steam engine in 1923.

Roughly what did the engine cost to build?

Adding four of the five fractions $\frac{1}{2},\frac{1}{3},\frac{1}{6},\frac{1}{9}$ and $\frac{1}{18}$ gives a total of 1.

Which of the fractions is not used?

‍

‍

11. How many digits are there in the correct answer to the calculation 123 123 123 123 ÷ 123 ?

12. The diagram shows a quadrilateral PQRS in which PQ and QR have the same length. Also PR bisects ∠SPQ, the ratio of ∠SPR to ∠PRS is 2 : 3 and ∠PSR = 110°.

‍

How large is angle PQR?

‍

13. The diagram shows a shape made from four 3 cm × 3 cm × 3 cm wooden cubes joined by their edges.

What, in cm², is the surface area of the shape?

14. Billy has three times as many llamas as lambs. Milly has twice as many lambs as llamas.

They have 17 animals in total.

How many of the animals are llamas?

15. Beatrix places copies of the L-shape shown on a 4 × 4 board so that each L-shape covers exactly three cells of the board.

She is allowed to turn around or turn over an L-shape.

‍

What is the largest number of L-shapes she can place on the board without overlaps?