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Exam-Style Questions.Problems adapted from questions set for previous Mathematics exams. |
1. | GCSE Higher |
At a concert, the number of men, women and children can be expressed with the following ratio:
$$ 6 : 11 : 4 $$There were 6525 more women than men. How many children were at the concert?
2. | GCSE Higher |
Toystore sell model sheep in four different colours. In their newest warehouse there are currently 1760 sheep in stock. Three eighths of the sheep are yellow, 15% of the sheep are blue and the ratio of green to red sheep is 5:6.
Work out the number of sheep of each colour in the Toystore warehouse.
3. | GCSE Higher |
Rishi breeds fish in tanks. Some of the tanks are small and some are large.
There are 8 fish in each small tank and 28 fish in each large tank.
Rishi currently has 560 fish and the ratio of the number of fish in small tanks to the number of fish in large tanks is 4:1
Rishi says that less than 10% of the tanks are large tanks.
Is Rishi correct?
You must show all your working.
4. | GCSE Higher |
(a) Find the ratio \(a:b \) given the equation:
$$ 7a + 2b = 4(a+b) $$(b) Find the ratio \( c:d \) given the following equation where \( c \gt 0 \text{ and } d \gt 0 \).
$$ 2c^2 = 5cd - \dfrac{25d^2}{8} $$5. | GCSE Higher |
At a summer camp the campers can choose one of three programmes: camp craft, water sports or hiking.
During the first week of camp the campers chose the programmes in the ratio 7 : 5 : 8
During the second week of camp the same number of campers chose the programmes in the ratio 7 : 6 : 4
Show that there were more campers on the camp craft programme in the second week than the first.
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