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.
30 Students were asked if they play Rugby or Football.
All the students play at least one of these sports.
19 Play Football
17 Play Rugby
11 Play Rugby but not Football
What is the probability that they only play football?
x
30°
Find the value of x, give reasons for your answer.
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 Chris
Jo has 6 more than Sally
How many sweets do they each have?
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
Find the shaded area.
2 pens and 3 pencils cost 63p
3 pens and 2 pencils cost 67p
Work out the cost of 5 pens and 4 pencils.
1.5 cm
12 cm
6 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 cm
6 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?