Problem Solving Questions

All questions were written by teachers at the Newcastle Developing Resources for

the new GCSE (9-1) CPD event run by OCR in 2015.

4 cm

8 cm

4 identical right angled triangles are arranged as shown. Find the perimeter of the shape produced.

50 Students were asked if they play Rugby or Football.All the students play at least one of these sports.

19 Play Football17 Play Rugby11 Play Rugby but not Football

What is the probability that they only play football?

Find the value of x, give reasons for your answer.

30°

x

A rectangle has an area of 24 cm2

What is the greatest possible perimeter of the rectangle if the sides are all integers?

Sally, Chris and Jo have 70 sweets.

Sally has 8 more than ChrisJo has 6 more than Sally

How many sweets do they each have?

Find the shaded area.

A circle is drawn inside an equilateral triangle such that the circumference of the circle touches the midpoint of the sides of the triangle.

10 cm

2 pens and 3 pencils cost 63p3 pens and 2 pencils cost 67p

Work out the cost of 5 pens and 4 pencils.

12 cm

6 cm

1.5 cm

4.5 cm

The area of the triangle is four times the area of the trapezium, show that the perpendicular height of the trapezium is 3 cm.

10 cm6 cm

Find the area of the triangle.

The product of 3 numbers is 1020.

Two of the numbers are 5 and 17. What is the third number?

Tom owns a music shop. In January he made a profit of £10 000. In February his profit was 10% higher.

Each month his profit was 10% higher than the previous month. When he makes £15 000 profit in a single month, he is going to buy himself a new car. In which month will Tom buy his new car?

The point P has coordinates (0, 3) and the point R has coordinates (12, 9).

Q is on the line PR such that the ratio of PQ : QR is 1 : 2.

What are the coordinates of Q?

Ben earns £10 in March, this increases by £2 every month.

How much does he earn in the nth month?

How much has he earned in total after n months?