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This home learning pack contains 3 parts.  Students are not expected to complete all three.  Each part gets progressively more difficult and students should attempt the questions they are able to.  Hegarty maths video clips have been included to support learning.  We would love to hear how you are getting 

along. PART 1 

   

Name: ______________________________ Class: ______________________________ Teacher: ______________________________

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A – Ratio and Proportion (Hegarty Clips 69, 48, 97, 149, 332) 1. Work out:

-

3 x 1 / 5

2. Work out 5.3 x 0.94

_____ / 3

3. The normal cost of a coat is £94 In a sale the cost of the coat is reduced by 36% Work out the sale price of the coat.

£________ / 3

4. Write these numbers in order of size. Start with the smallest number.

53% 0.7

____ ____ ____ ____ ____ / 2

5. Rosa prepares the ingredients for pizzas. She uses cheese, topping and dough in the ratio 2 : 3 : 5. Rose uses 70 grams of dough. Work out the number of grams of cheese and the number of grams of topping Rosa uses.

Cheese ____gTopping ____g

/ 3

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B – Number (Hegarty Clips 295, 129, 102) 6. Use the information that 257 × 34 = 8738 to find the value of

2.57 × 34 = _______ 873.8 ÷ 2.57 = _______ / 2

7. Work out

Write down all the figures on your calculator display. ___________________ Give your answer to 3 significant figures. _______ / 3

8. Simplify t × t2 _______ Simplify m5 ÷ m3 _______ / 2

9. Write the reciprocal of 2. _______ / 1

C – Algebra (Hegarty Clips 161, 186, 151, 265, 207) 10. Expand

mn(n – m) __________ / 1

11. Solve 5p + 7 = 12 – 3p

p = _______ / 2

12. Compasses cost c pence each. Rulers cost r pence each. Write down an expression for the total cost, in pence, of 2 compasses and 4 rulers. ____________ / 2

78.6–765.8

50.356.2  

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13. Show the inequality x > 1 on the number line below.

/ 1

14. Complete the table of values for y = 4x + 3

x −2 −1 0 1 2 y −1 11

On the grid, draw the graph of y = 4x + 3

/ 4

12

11

10

–6

–5

–4

–3

–2

–2

–1

–1

8

9

7

6

5

4

3

2

2

1

1O x

y

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D – Shape, Space and Measure (Hegarty Clips 490, 492, 555, 571, 716) 15.

Write down the size of the angle marked x. ______º Give a reason for your answer. ____________________________________________________ Write down the size of the angle marked y. ______º Give a reason for your answer. ____________________________________________________ / 4

16. The diagram shows the positions of two ships, A and B.

A ship C is on a bearing of 064° from ship A. Ship C is also on a bearing of 290° from ship B. In the space above, draw an accurate diagram to show the position of ship C. Mark the position of ship C with a cross . Label it C. / 3

48°

xy

A

D

B

EF

C

G

30°

N

N

A

B

Diagram NOT accurately drawn 

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17.

The diagram shows a shape. Work out the area of the shape.

________ cm² / 3

18. Calculate the volume of this cuboid.

________ cm³ / 2

19. A car travels for 3 hours. Its average speed is 75 km/h. Work out the total distance the car travels.

__________ km / 2

20 cm

9 cm

4 cm

8 cm

Diagram NOT accurately drawn 

 

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E – Data Handling (Hegarty Clips 427, 359) 20. Sandra carries out a survey of 90 Year 11 students. She asks

them their favourite snack. She draws this accurate pie chart.

Use the pie chart to complete the table. Snack Frequency Angle Burger 20 Chips 45 180º Hot dog Kebab Total 90

/ 3

KebabBurger

Hot dog

Chips

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F – Probability (Hegarty Clip 359) 21. 2 coins are thrown and their scores are added together. Copy

and complete this sample space.

Coin

Dice

1 2 3 4 5 6

1 2 6

2

3 5

4

5 11

6 9 Use the diagram to find the probability scoring a 6. _____ / 3

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PART 2 A – Ratio and Proportion (Hegarty Clips 97, 707) 1. The average number of school dinners taken by

children fell from 180 to 165. What is the percentage decrease in the number taking school dinners?

_______% / 3

2. Margaret goes on holiday to Switzerland. The exchange rate is £1 = 2.10 francs. She changes £450 into francs. How many francs should she get?

__________ francs / 2

B – Number (Hegarty Clips 774, 131, 105, 122, 123) 3. The length of a piece of string is 16 cm, correct to the nearest

cm. What is the greatest possible length the piece of string could be? Circle the correct answer.

15.95 15.5 16.05 16.4 16.5 / 1

4. Work out an estimate for the value of

__________ / 3

5. Evaluate (a3)4 _______

/ 16. Write 40 000 000 in standard form.

_______________Write 3 x 10–5 as an ordinary number.

_______________ / 2

523.0

31279.5

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C – Algebra (Hegarty Clips 169, 162, 186, 281) 7. Factorise fully 5xy + 10x²

_______________Expand and simplify (x + 4)(x – 3)

_______________ / 4

8. Solve 7r + 2 = 5(r – 4)

r = _______ / 3

9. Make t the subject of the formula v = u + 5t

t = ______ / 2

10. Solve the inequality 6x – 3 < 9

/ 2

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D – Shape, Space and Measure (Hegarty Clips 560, 683, 642, 501, 880, 570) 11. Work out the value of x.

x = ________º / 3

12. Here is a sketch of a triangle. In the space below, use ruler and compasses to construct this triangle accurately. You must show all construction lines. / 2

Diagram NOT accurately drawn 

5.7 cm 4.2 cm

6.3 cm

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13.

Enlarge shape A by scale factor 3 from centre (4, 3). Label it B. Reflect shape A in the x axis. Label it C. / 5

14.

ABCD is a rectangle. AC = 17 cm. AD = 10 cm. Calculate the length of the side CD. Give your answer correct to one decimal place.

__________ cm / 3

5

4

3

2

1

–1

–2

–3

–4

–5

5 6 74321–1–2–3–4–5

A

Ox

y

10 cm17 cm

A B

CD

Diagram NOT accurately drawn 

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15. Anil cycled from his home to the park. Anil waited in the park. Then he cycled back home. Here is a distance-time graph for Anil’s complete journey.

At what time did Anil leave home? __________ What is the distance from Anil’s home to the park? ________km How many minutes did Anil wait in the park? _______mins / 3

16.

Here is a triangular prism. Calculate the volume of the prism.

__________ cm³ / 3

8

6

4

2

00900 0910 0920 0930 0940 0950 1000 1010

Time of day

Distancefromhome(km)

4.5 cm

10 cm

6 cm

Diagram NOT accurately drawn 

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E – Data Handling (Hegarty Clips 395, 396, 453, 401) 17. Explain what is meant by a random sample.

____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ Explain what is meant by a stratified sample. ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ / 2

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18. The scatter graph shows the Science mark and the Maths mark for 15 students.

What type of correlation does this scatter graph show? ____________________________________________________ Draw a line of best fit on the scatter graph. Sophie’s Science mark was 42. Use your line of best fit to estimate Sophie’s Maths mark.

_____________ / 3

60

50

40

30

20

10

10 20 30 40 50 60Science mark

Mathsmark

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19. Phillip is going to carry out a survey of the football teams supported by each of his friends. In the space below, draw a suitable data collection sheet that Phillip could use.

/ 3F – Probability (Hegarty Clip 361) 20. Amy has 10 CDs in a CD holder. Amy’s favourite group is Edex.

She has 6 Edex CDs in the CD holder. Amy takes one of these CDs at random. She writes down whether or not it is an Edex CD.She puts the CD back in the holder. Amy again takes one of these CDs at random. Complete the probability tree diagram.

/ 2

0.6

..........

Second choice

..........

First choice

..........

..........

..........

EDEXCD

EDEXCD

EDEXCD

NOT-EDEXCD

NOT-EDEXCD

NOT-EDEXCD

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PART 3  A – Ratio and Proportion (Hegarty Clips 94, 346) 1. Toby invested £4500 for 2 years in a savings

account. He was paid 4% per annum compound interest. How much did Toby have in his savings account after 2 years?

£__________ / 3

2. The shutter speed, S, of a camera varies inversely as the square of the aperture setting, f. When f = 8, S = 125. Find a formula for S in terms of f.

__________Hence, or otherwise, calculate the value of S when f = 4

__________ / 4

B – Number (Hegarty Clips 109, 125) 3. Work out the value of 163/4

____________ / 2

4. Work out (3.2 × 105) × (4.5 × 104) Give your answer in standard form correct to 2 significant figures. / 2

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C – Algebra (Hegarty Clips 251, 214, 22, 191, 286, 271) 5. Complete this table of values for y = x3 + x – 2

x –2 –1 0 1 2 y –12 0

On the grid, draw the graph of y = x3 + x – 2

/ 4

–2

–12

–10

–8

–6

–4

–2

2

4

6

8

10

y

x–1 1 2O

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6. The straight line L1 has equation y = 2x + 3. The straight line L2 is parallel to the straight line L1. The straight line L2 passes through the point (3, 2). Find an equation of the straight line L2.

________________ / 3

7. Factorise x² - 7x + 12

________________Solve the equation x² - 7x + 12 = 0

________________ / 3

8. Solve the simultaneous equations 3x – 4y = 13 2x + 3y = 3

x = _____y = _____

/ 4

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9. Rearrange the formula to make a the subject.

a = ____________ / 4

10. Solve the inequality 5x – 7 < 2x – 1

____________ / 2

D – Shape, Space and Measure (Hegarty Clips 690, 669, 509, 656, 544, 577, 614) 11.

ABCD and DEFG are squares. Prove that triangle CDG and triangle ADE are congruent. / 3

A

B

C

D E

FG

an

anP

2

Diagram NOT accurately drawn 

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12.

Scale: 1 cm represents 10 km

Here is a map. The map shows two towns, Burford and Hightown. A company is going to build a warehouse. The warehouse will be less than 20 km from Burford and less than 30 km from Hightown. Shade the region on the map where the company can build the warehouse. / 3

13.

Work out the length of AB. Give your answer correct to 3 significant figures.

AB = __________ cm / 3

Diaaccu

A

B C8.5 cm

38°

Diagram NOT accurately drawn 

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14.

Enlarge A by scale factor ½ from centre (-3, -3). Label it B. Translate A by vector 5

3. Label it C.

/ 515.

Work out the length of the arc AB. Give your answer to 3 significant figures.

___________ cm / 3

7

6

5

4

3

2

1

–1

–2

–3

–4

–1–2–3–4

y

x321 7654 8

O

Diagram NOT accurately drawn 

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16.

A cone has a base radius of 5 cm and a vertical height of 8 cm. Calculate the volume of the cone. Give your answer correct to 3 significant figures.

___________ cm³ / 3

17.

Shapes ABCD and EFGH are mathematically similar. Calculate the length of BC.

_________ cmCalculate the length of EF.

_________ cm / 4

100°100°

AE

B F

CG

DH

6 cm

5 cm

8 cm

4 cm

Diagram NOT accurately drawn 

Diagram NOT accurately drawn 

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E – Data Handling (Hegarty Clips 417, 396) 18. 20 students scored goals for the school hockey team

last month. The table gives information about the number of goals they scored.

Goals scored Number of students

1 9 2 3 3 5 4 3

Work out the mean number of goals scored. __________ / 3

19. The table shows the number of boys in each of four groups. Jamie takes a sample of 40 boys stratified by group. Calculate the number of boys from group B that should be in his sample.

Group A B C D Total Number of boys 32 43 38 19 132

____________ / 2

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F – Probability (Hegarty Clip 364) 20. There are 3 boys and 7 girls at a playgroup. Mrs Gold selects

two children at random. Complete the probability tree diagram below.

Work out the probability that Mrs Gold selects two girls. ______ / 4

1st child 2nd child

boy

girl

boy

girl

boy

girl

............

............

............

3

10

............

............

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