3rd Year Topics Maths revision – Autumn Term
Algebra skills – solve for x unless specified
3 1 2
1. (3𝑥 − 2) = 3𝑥 + 5 2. 𝑥 =𝑥−2 3. 2𝑥 − 6 = 𝑥 + 4
2 5 3
(4 + 3𝑥) (𝑥 + 4) 3 (𝑥 − 3) (2𝑥 + 4) 1
4. − = 5. + =5 6. 𝑦 = 3𝑥 +
5 2 2 3 2 2
Estimate the value of y when x = 1
7. 𝑦 − 6 = 2 − 4𝑥 8. −5𝑥𝑦𝑧 + 7𝑥𝑦 + 10𝑥𝑦 ! 𝑧 9. −48𝑎𝑏 ! 𝑐 " + 12𝑏 ! 𝑐 " − 18𝑎! 𝑏 " 𝑐 !
Estimate the value of x when y =2 Factorise Factorise
Change the subject of the formula – make x the subject
9𝑥 − 4 1−𝑥 𝑗 3x − 2 + 4x
1. 𝑦 = 2. 3 − 𝑦 = 3. =
13 − 𝑥 3 − 9𝑥 𝑡 4 − 2𝑥
4. 3√𝑥 + 𝑏 = 𝑎 + 𝑏 5. 𝑎! 𝑥 ! − 𝑏 ! = 𝑏 ! 𝑐 ! √2𝑥 + 1
6. =𝑐
𝑎+𝑏
Percentage increase and decrease and reverse percentages
1. On weekdays, it costs £5.50 per hour to rent a golf club. On Tuesdays the cost is
35% more. How much does it cost to rent a club for 3 hours on a Tuesday?
2. Adnan has a rectangular shed in his garden. He decides to enlarge the shed by
increasing both its length and width by 34%. What is the percentage increase in
the floor area of the shed?
3. Lynn works as a bus driver. She is paid £10.80 per hour for the first 38 hours she
works each week. She is paid 25% more per hour for each extra hour she works.
One week, Lynn was paid £491.40 . In total, how many hours did she work that
week?
, 4. Erik thinks of a prime number between 20 and 30. His number is x% of 125. Work
out one possible value of x.
5. A shop sells freezers and cookers. The ratio of the number of freezers sold to the
number of cookers sold is 5 : 2. The shop sells a total of 140 freezers and cookers
in one week.
a) Work out the number of freezers and the number of cookers sold that week
b) Jake buys a freezer with an original price of £145. The price of the freezer is
reduced by 20%. Work out how much Jake saves
6. What is the price of these tyres before VAT was added?
Tyre Sale
Dunlap tyres for Minis (including
valves and balancing)
£71.30
Including VAT at 15%
Compound and simple interest
1. Kylie wants to invest £20 000 for 3 years. She considers two investments,
Investment A and Investment B
Investment A Investment B
£20 000 £20 000
Earns 3.02% interest per annum Earns 2.98% compound interest
per annum
Interest paid yearly by cheque
Kylie wants to get the greatest return on her investment. Which of these investments
should she choose?
2. Jaspir invested £2400 for n years in a savings account. He was paid 7.5% per
annum compound interest. At the end of n years he had £3445.51 in the savings
account.
Work out the value of n.
3. The value of a car depreciates by 35% each year. At the end of 2007 the value of
the car was £5460. Work out the value of the car at the end of 2006.
Algebra skills – solve for x unless specified
3 1 2
1. (3𝑥 − 2) = 3𝑥 + 5 2. 𝑥 =𝑥−2 3. 2𝑥 − 6 = 𝑥 + 4
2 5 3
(4 + 3𝑥) (𝑥 + 4) 3 (𝑥 − 3) (2𝑥 + 4) 1
4. − = 5. + =5 6. 𝑦 = 3𝑥 +
5 2 2 3 2 2
Estimate the value of y when x = 1
7. 𝑦 − 6 = 2 − 4𝑥 8. −5𝑥𝑦𝑧 + 7𝑥𝑦 + 10𝑥𝑦 ! 𝑧 9. −48𝑎𝑏 ! 𝑐 " + 12𝑏 ! 𝑐 " − 18𝑎! 𝑏 " 𝑐 !
Estimate the value of x when y =2 Factorise Factorise
Change the subject of the formula – make x the subject
9𝑥 − 4 1−𝑥 𝑗 3x − 2 + 4x
1. 𝑦 = 2. 3 − 𝑦 = 3. =
13 − 𝑥 3 − 9𝑥 𝑡 4 − 2𝑥
4. 3√𝑥 + 𝑏 = 𝑎 + 𝑏 5. 𝑎! 𝑥 ! − 𝑏 ! = 𝑏 ! 𝑐 ! √2𝑥 + 1
6. =𝑐
𝑎+𝑏
Percentage increase and decrease and reverse percentages
1. On weekdays, it costs £5.50 per hour to rent a golf club. On Tuesdays the cost is
35% more. How much does it cost to rent a club for 3 hours on a Tuesday?
2. Adnan has a rectangular shed in his garden. He decides to enlarge the shed by
increasing both its length and width by 34%. What is the percentage increase in
the floor area of the shed?
3. Lynn works as a bus driver. She is paid £10.80 per hour for the first 38 hours she
works each week. She is paid 25% more per hour for each extra hour she works.
One week, Lynn was paid £491.40 . In total, how many hours did she work that
week?
, 4. Erik thinks of a prime number between 20 and 30. His number is x% of 125. Work
out one possible value of x.
5. A shop sells freezers and cookers. The ratio of the number of freezers sold to the
number of cookers sold is 5 : 2. The shop sells a total of 140 freezers and cookers
in one week.
a) Work out the number of freezers and the number of cookers sold that week
b) Jake buys a freezer with an original price of £145. The price of the freezer is
reduced by 20%. Work out how much Jake saves
6. What is the price of these tyres before VAT was added?
Tyre Sale
Dunlap tyres for Minis (including
valves and balancing)
£71.30
Including VAT at 15%
Compound and simple interest
1. Kylie wants to invest £20 000 for 3 years. She considers two investments,
Investment A and Investment B
Investment A Investment B
£20 000 £20 000
Earns 3.02% interest per annum Earns 2.98% compound interest
per annum
Interest paid yearly by cheque
Kylie wants to get the greatest return on her investment. Which of these investments
should she choose?
2. Jaspir invested £2400 for n years in a savings account. He was paid 7.5% per
annum compound interest. At the end of n years he had £3445.51 in the savings
account.
Work out the value of n.
3. The value of a car depreciates by 35% each year. At the end of 2007 the value of
the car was £5460. Work out the value of the car at the end of 2006.
