MATHEMATICS“If a man's wit be wandering, let him study the mathematics.” Francis Bacon

Foundation L1/2 RevisionCirclesRatio

Percentages

L1 Finding the percentage of a quantity/Ratio, proportion, simple interest and formulaL2 Ratio, simple and compound interest and formula.L2 Area and perimeter of circles/percentage problems

Name:

Date:

Circles Area = πr2 Circumference = πd To find the relationship between radius and diameter.

To find circumferences of circles and areas enclosed by circles.

To recall and use the formulae for the circumference of a circle and the area enclosed by a circle.

To Use π ≈ 3.142 or use the π button on a calculator.

To find the perimeters and areas of semicircles and quarter circles.

To find the volume of a cylinder.

Q1. Diameter of a circle is 51 mm. Find out circumference and area of the circle giving your answer correct to 2 decimal places.

(4 marks)

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Q2. The circumference of a circle is 18cm. Work out the diameter and radius of the circle correct to 2 decimal places. (2 marks)

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L1 Finding the percentage of a quantity/Ratio, proportion, simple interest and formulaL2 Ratio, simple and compound interest and formula.L2 Area and perimeter of circles/percentage problems

Q3. Find the volume of a cylinder with height 5 cm and radius 3.9 cm to 1 decimal place. (2 marks)

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Q4. Given the following semi-circle with diameter. Find out its perimeter and area correct to 2 decimal

places. (5 marks)

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Q5. Omar is using weed killer to treat his circular lawn, which has a diameter of 12 m. The weed killer instructions say to use 20 ml for every square metre of lawn to be treated. How much weed killer does he need to use? Give your answer to the nearest ml.

(3 marks)

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L1 Finding the percentage of a quantity/Ratio, proportion, simple interest and formulaL2 Ratio, simple and compound interest and formula.L2 Area and perimeter of circles/percentage problems

Ratios To understand the meaning of ratio and to use ratios. To write a ratio in its simplest form and find an equivalent ratio. To solve a ratio problem in context, e.g. recipes. To share a quantity in a given ratio. To do proportional division. To solve problems based on best buys.

Q6. Write down each of the following ratios in its simplest form.

a) 15 : 21

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b) 14: 42

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c) 72: 45

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d) 42p : £1.36

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e) 350g : 2 kg

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f) 36 : 12

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(6

marks)

Q7. To make salad dressing you mix olive oil and vinegar in the ratio 5 : 3. How much olive oil is needed with 42ml of vinegar?……………………………………………………………………………………………………………………………………………………………….

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(2 marks)

Q8. The ratio of men to women at a conference was 11 : 4. How many men were there if there were 200 women?

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(2 marks)

Q9. Share £150 between Jane, Alan and Ann in the ratio 2:3:7. How much did each one of them get?……………………………………………………………………………………………………………………………………………………………….

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L1 Finding the percentage of a quantity/Ratio, proportion, simple interest and formulaL2 Ratio, simple and compound interest and formula.L2 Area and perimeter of circles/percentage problems

(3 marks)

Q10. Robin works as a waitress. Each week, she splits her wage into spending money and savings in the ratio 7:3.

a) If she earns £130 per week. How much will go to her savings?

b) One week Robin added £42 into her savings. How much did she earn that week?

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(4 marks)

Q11. Large tin of tuna weighs 400 g and costs £1.05. The small tin weighs 220 g and costs 57p. Which tin is better value for money?……………………………………………………………………………………………………………………………………………………………….

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(3 marks)

L1 Finding the percentage of a quantity/Ratio, proportion, simple interest and formulaL2 Ratio, simple and compound interest and formula.L2 Area and perimeter of circles/percentage problems

Percentages To find percentage of a quantity in order to increase or decrease

To use percentages in real-life situations:

– VAT– value of profit or loss– simple interest– income tax calculations

To use percentages as multipliers

Q12. Ben bought a car for £12000. Each year the value of the car depreciated by 10%. Work out the value of the car two years after he bought it.……………………………………………………………………………………………………………………………………………………………….

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(3 marks)

Q13. Wayne bought an engagement ring for Tracy. The total cost of the ring was £420 plus VAT at17 ½ %.

a) Work out the cost of the ring.

b) Wayne invited 96 people to an engagement party. Only 60 people came to the party. Express 60 as a percent of 96.

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(4 marks)

Q14. There are 800 students at Prestfield School. 144 of these students were absent on Wednesday.

a) Find out how many students were not absent on Wednesday.

L1 Finding the percentage of a quantity/Ratio, proportion, simple interest and formulaL2 Ratio, simple and compound interest and formula.L2 Area and perimeter of circles/percentage problems

b) Trudy says that more than 25% of the 800 students were absent on Wednesday.Is she correct? Explain your answer.

c) 45% of these 800 students are girls. Work out 45% of 800.

d) Write 176 out of 800 as a percentage.……………………………………………………………………………………………………………………………………………………………….

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(8 marks)Q15. Loft insulation reduces annual heating cost by 20%. After he insulated his loft, Dean’s annual heating cost was £520. Work out Dean’s annual heating cost would have been, if he has not insulated his loft. ……………………………………………………………………………………………………………………………………………………………….

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(3 marks)Q16. A shopkeeper buys shoes at £20 and sells them at £25. Find out the profit as a percentage.

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(2 marks)

Q17. Jim expected 24 people to turn up for a job interview, but only 18 did. What was the percentage error?

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(3 marks)

Q18. Calculate the percentage savings of the following:

a) Jeans was £75 now £35.………………………………………………………………….…………………………………………………………………………………………….

L1 Finding the percentage of a quantity/Ratio, proportion, simple interest and formulaL2 Ratio, simple and compound interest and formula.L2 Area and perimeter of circles/percentage problems

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(2 marks)

b) Shirt was £30.50 now £22.75.………………………………………………………………….…………………………………………………………………………………………….

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(2 marks)

c) Microwave was £150 Now £99.………………………………………………………………….…………………………………………………………………………………………….

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(2 marks)

Q19. Use your calculator to find the amount of interest earned on the following amounts:

a) On £4500 for 8 years at 10.2% per annum.b) On £5000 for 7 years at 5.5% per annum.

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(4 marks)

Q20. Sian invests £7000 for 3 years at 4% per annum compound interest. Find the compound interest earned in 3 years.

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(3 marks)

Q21. Calculate the amount of depreciation and the final value of an item that have initial value of £6000 over 5 years at 7% per annum.

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(3 marks)

L1 Finding the percentage of a quantity/Ratio, proportion, simple interest and formulaL2 Ratio, simple and compound interest and formula.L2 Area and perimeter of circles/percentage problems

(Total: 75 Marks)

MARKING GRID

Question Marks Breakdown Solutions1 4 Method for circumference + correct answer

Method for area + correct answer160.24mm2043.8mm2

2 2 DiameterRadius

5.73cm2.86cm

3 2 Method and correct answer 238.95cm3

4 5 1 for circumference1 for division1 for rounding1 for perimeter1 for area

Perimeter = 46.28cmArea = 127.25cm2

5 3 1 for method1 for rounding1 for the correct answer

2262ml

6 6 Mark for each correct answer a. 5:7 b. 1:3c. 8:5 d. 21p:68pe. 7:40 f. 3:1

7 2 Calculation + correct answer 70ml8 2 Calculation + correct answer 550 men9 3 3 correct amounts Jane £25

Alan £37.50Ann £87.50

10 4 a. Calculation and correct answerb. Calculation and correct answer

a. Savings £39b. £140

11 3 Correct working (2)Correct choice (1)

Small tin

12 3 Method (2)Answer (1)

£9720

13 4 Method (2)Answer (2)

a. £493.50b. 62.5%

14 8 Method and answer x 4 a. 656b. No 18% ˂ 25%c. 360 girlsd. 22%

15 3 Method (2)Answer (1)

£650

16 2 Method + answer 25%17 3 Method (2)

Answer (1)25%

18 6 3 x Method + 3 x correct answers a. 46%b. 25%c. 34%

19 4 Simple interest method and answer x 2 a. £8172b. £5275

20 3 Compound interest method (2)Answer (1)

£874

21 3 Method (2) £3610

L1 Finding the percentage of a quantity/Ratio, proportion, simple interest and formulaL2 Ratio, simple and compound interest and formula.L2 Area and perimeter of circles/percentage problems

Answer (1)

Total marks = 75

L1 Finding the percentage of a quantity/Ratio, proportion, simple interest and formulaL2 Ratio, simple and compound interest and formula.L2 Area and perimeter of circles/percentage problems