12 DAYS OF GCSE MATHEMATICS REVISION – HIGHER TIER

Day 1 / Day 2 / Day 3
Barney wants to invest an £8000 inheritance. He is choosing between two banks – Stokes’ Bank and Jones’ Bank. He intends investing his money for four years. The banks offer the following interest rates:
STOKES’ BANK
3.5% per year compound interest / JONES’ BANK
5% for 1st year
4% for 2nd year
3% for 3rd year
2% for 4th year
No withdrawals during the four year period / Withdrawals allowed at any time
(a) Which Bank should Barney choose? Explain your answer.
(b) Why might he NOT want to use Stokes’ Bank? / Rectangle ABCD has area cm2.
Length AB = cm. Find the perimeter of the rectangle.

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Day 4 / Day 5 / Day 6
Andrew chooses, at random, a counter from bag A which contains 3 red, 2 white and 4 black counters. He then places the counter in bag B which, before the counter is added, contains 6 red, 1 white and 3 black counters.
He then takes a counter, at random, from bag B. What is the probability that the counter drawn from bag B is red? / Ben and his family are visiting a theme park. He buys 3 adult and 5 child tickets and the total cost is £157.
Emma and her family are visiting the same theme park. She buys 4 adult and 3 child tickets and the total cost for her is £147. Using an algebraic method, work out the cost of a single adult ticket and a single child ticket. / The speed, in mph, of 50 cars on a road was measured. The results are shown in the table:
Speed, s, mph / Frequency
30 < s ≤ 40 / 7
40 < s ≤ 50 / 13
50 < s ≤ 55 / 10
55 < x ≤ 60 / 14
60 < x ≤ 80 / 6
(a) Draw a histogram to illustrate the table.
(b) Estimate the proportion of cars which travelled between 53 and 70 mph.
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Day 7 / Day 8 / Day 9
A circle with equation
x2 + y2 = 20
and a line with equation
y – x = 2
are plotted on the same graph.
They intersect at two places, A and B.
Find the length of the line AB. / (a) Find the area of rectangle ABCD.

(b) Expand and fully simplify (4x – 3)2
(c) Solve the equation x2 – x – 72 = 0 / (i) Make m the subject in the formula

(ii) Y is indirectly proportional to the cube root of X.
When X = 27, Y = 7.
(a) Find an equation for Y in terms of X.
(b) Find the value of X when Y= 1/7.
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Day 10 / Day 11 / Day 12
A bag has 8 red and 5 white counters in it. Paul takes a counter out of the bag at random, notes its colour and puts it back in the bag. He then takes another counter out and notes its colour.
(a) Draw a tree diagram to illustrate all the possible outcomes
(b) What is the probability that at least one of the counters is white? / / Class 11A sat a mathematics test. The result is shown in the table below
Mark, x / Frequency
0 < x ≤ 10 / 4
10 < x ≤ 20 / 9
20 < x ≤ 30 / 13
30 < x ≤ 40 / 6
The lowest score was 9 and the highest 38.
(a) Which group does the median lie?
(b) Estimate the mean score for class 11A.
(c) Class 11B sit the same test with a mean of 23 and range of 35. Compare and contrast the classes performance.
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If you need help with your revision over the Easter holiday either email your teacher or email Mr - remember the BEST way to LEARN mathematics is to DO mathematics!