year 10 spring work pack maths (h) - city heights€¦ · year 10 spring work pack – maths (h)...

YEAR 10 SUMMER MATHS PACK- HIGHER

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City Heights E-ACT Academy

Year 10 Spring work pack – Maths (H)

Topics Activity/Task

Worksheet 1 – Statistics;

Interpreting Data

Use Hegarty Maths Clips 430- 431, 453- 454, 417 and 418 for Revision of the content

link to help: https://hegartymaths.com

Complete Worksheet 1

Worksheet 2 – Fractions Ratio

and Percentages

Use Hegarty Maths Clips 52, 55, 74, 76, 82-83 and 149, 332- 334 for Revision of the content



Worksheet 3 – Polygon,

Trigonometry, Polygon

Use Hegarty Maths Clips 487, 565, 481- 483, and 561 -564 for Revision of the content



Worksheet 4- Area and Volume

Use Hegarty Maths Clips 555 - 559, 536, 541, 537, 538, 542, and 543 for Revision of the content



Worksheet 5 – Equations and

Inequalities

Use Hegarty Maths Clips 154, 179-183, 184-186 for Revision of the content



Worksheet 6 - Probability

Use Hegarty Maths Clips 349- 367 Revision of the content



https://hegartymaths.com/







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Worksheet 1 – Statistics; Interpreting Data

1 The time series graph shows the rate of inflation in the UK in 2014.

a What was the rate of inflation in September 2014?

Give your answer correct to 1 decimal place.

(1 mark)

b Which month experienced the greatest rise in the rate of inflation?

(1 mark)

c Describe what this time series suggests about the trend in inflation over 2014.

(1 mark)


@ Pearson Education Ltd 2015. Copying permitted for purchasing institution only. This material is not copyright free. 3

2 The back-to-back stem-and-leaf diagram shows the numbers of male and female students who

study A-level Maths in a sample of colleges.

a How many males students are there?

(1 mark)

b Find the range of the number of female students.

(1 mark)

c Find the median number of male students.

(1 mark)



3 The table shows the time spent waiting at a doctor’s surgery for 120 patients.

a Estimate the mean waiting time.

(3 marks)

b In which group is the median time?

(1 mark)

c One of the patients waited for 7 minutes but their time was incorrectly recorded as 16 minutes.

Without doing any calculations, state whether your answers to parts a and b will increase,

decrease or stay the same.

(2 marks)

Time t (minutes) Frequency

0 ≤ t < 5 23

5 ≤ t < 10 46

10 ≤ t < 15 35

15 ≤ t < 20 9

20 ≤ t < 25 3

25 ≤ t < 30 2

30 ≤ t < 35 2



4 The table shows the maximum and minimum temperatures for seven cities recorded on

1 September 2014.

Athens Edinburgh Rome Reykjavik Orlando Doha Moscow

Maximum

temperature (°C) 30 19 25 12 34 41 17

Minimum

temperature (°C) 20 13 17 10 25 31 8

a Plot this data on a scatter diagram.

(3 marks)

b Describe the correlation and explain what it means in this context.

(2 marks)

c Draw a line of best fit on your diagram.

Use the line to estimate the minimum temperature of a city when the maximum

temperature is 15°C.

(2 marks)

d Is it sensible to use the graph to estimate the maximum recorded temperature in a desert where

the minimum recorded temperature is –4°C? Give a reason for your answer.

(1 mark)



5 A box office keeps a record of the types of shows they take bookings for in a one-hour period.

a Explain why it is not possible to present this information using a frequency polygon.

(1 mark)

b Draw a pie chart for this data.

(3 marks)

c The bookings taken in the next hour are also displayed on a pie chart.

The angle for the sector representing musicals is 90°.

Does this show that more bookings have been taken for musicals than in the previous hour?

Explain your answer.

musical comedian play concert comedian concert

musical concert concert play concert

musical concert comedian play concert

musical comedian concert comedian



(1 mark)



6 180 Year 10 students all study one language from a choice of French, Spanish or Italian.

89 of the students are male. 12 of the male students study Italian.

46 of the female students study Spanish. 29 of the 55 students who study French are male.

a Draw a two-way table for this data.

(3 marks)

b What fraction of the students study Spanish?



(1 mark)



7 The frequency polygon shows the distribution of the waiting times for patients in a hospital.

a How many patients were there in total?

(1 mark)

b How many patients waited between 20 and 30 minutes to be seen?

(1 mark)

c State the modal class.

(1 mark)

Overall mark /32



Worksheet 2 – Fractions Ratio and Percentages

1 Work out.

a 1 23 25 3

(3 marks)

b 3 74 –14 9

(3 marks)

2 Shane has a winning lottery ticket.

He gives some money to his daughter, some money to charity and invests the rest,

in the ratio 3 : 1 : 11

He gives £7221 to his daughter.

a Work out how much money he invests.

(2 marks)

b Work out how much he won in total.



(1 mark)


3 A local council is concerned that there are too many students for staff to look after in schools.

There are 18 staff and 225 students in school A.

a Write the staff : student ratio in the form 1 : n.

(1 mark)

School B has 23 staff and 322 students.

b Which school has the better staff : student ratio according to the council?

Explain your answer.

(2 marks)

4 Chris is going on holiday to the United States of America.

The exchange rate is £1 = $1.55

Chris has up to £720 to change into dollars but he can only get $20 or $50 notes.

What is the maximum number of dollars Chris can get?

(3 marks)

5 a X is directly proportional to Y.

Work out the missing values, p and q, in the table.

b Write a formula for X in terms of Y.

(4 marks)

X Y

60 35

36 p

q 17.5


6 Mia makes cupcakes and sells them to raise money for charity.

She spends £6.82 on ingredients.

Mia sells all the cupcakes and takes £37.51 during the sale.

What percentage profit does Mia make on the cupcakes?

(2 marks)

7 A store experienced a 14.2% fall in takings in February, compared to the previous month.

Their takings in February were £742 513.20

How much did they take in January?

(3 marks)

8 The diagram shows triangle ABC.

The base of the triangle decreases by 30% and

the height increases by 20%.

What is the overall percentage change to the area of the triangle?

State clearly if this is an increase or a decrease.

(6 marks)

Overall mark /30


Worksheet 3 – Polygon, Trigonometry, Polygon

1 ABCDEFGHIJ is a regular decagon.

a What is the sum of the interior angles?

b Work out the size of angle IJK.

(3 marks)

2 XYZ is a right-angled triangle.

Calculate the length of XZ.

Give your answer correct to 2 decimal places.

(3 marks)

3 PQR and XYZ are straight lines.

PR is parallel to XZ.

PY = QY.

Work out the value of a.

Give reasons for your answer.

(3 marks)


4 PQRS and XYZ are straight lines.

PS is parallel to XZ.

Prove that the angle sum of any triangle is 180°.

(4 marks)

5 Write down the value of

a cos 90°

b sin 0°

c sin 45°

d tan 0°

e cos 30°

(5 marks)

6 PQR is a right-angled triangle.

Calculate the size of the angle marked x.

Give your answer correct to 1 decimal place.

(3 marks)


7 Dave builds a wheelchair ramp with 1 metre of wood.

He wants the vertical height of the ramp to be 50 centimetres.

What does the angle of elevation need to be?

(3 marks)

8 Josie spots her brother Dan from the roof of a block of flats.

The angle of depression from Josie to Dan is 45°

The distance from Josie directly to Dan is 80 metres.

Calculate the height of the block of flats.

Give your answer correct to 2 decimal places.

(3 marks)

9 A rectangular gate has a diagonal bar running across it.

The gate is 80 cm high and 2 m wide.

Work out the length of the bar.

Give your answer in surd form.

(3 marks)

Overall mark /30


Worksheet 4- Area and Volume

1 A circle has diameter of 120 cm.

Work out the circumference of the circle. Give your answer correct to 3 significant figures.

(2 marks)

2 a Work out the area of the trapezium.

b Work out the perimeter of the trapezium.

(4 marks)

3 A cylindrical can holds 355 ml when full.

The can is 12 cm tall.

Work out the radius of the can to 2 decimal places.

(4 marks)


4 This triangular prism has volume 15 510 cm3.

Work out

a the length of the prism (x)

b the surface area of the prism.

(5 marks)

5 a What is the area of a circle with radius 6 cm?

Give your answer in terms of π.

b Sarah draws a circle with double the area of the circle in part a.

What radius does she use?

Give your answer to a suitable degree of accuracy.

(3 marks)

6 Calculate the surface area of a sphere of radius 7.3 cm.

Give your answer to 3 significant figures.

Surface area of a sphere = 4πr2

(2 marks)


7 This solid is made from a cone and a cylinder of radius 5 cm.

Find the total surface area of the solid, including the base, in terms of π.

Curved surface area of a cone = πrl

(4 marks)

8 Find the angle of this sector.

(3 marks)

9 The lengths of this square-based pyramid are given to 1 decimal place.

Calculate the upper and lower bounds for its volume.

(3 marks)


Overall mark /30

Worksheet 5 – Equations and Inequalities

1 Solve the quadratic equation 14 = 3x2 – 19x

(3 marks)

2 Factorise 10x2 – 13x – 3

(2 marks)

3 Solve the equation 5x2 – 6x – 7 = 0

Give your solutions to 3 significant figures.


(3 marks)


4 Solve these simultaneous equations.

a 7x – 2y = 4

3x + 2y = 16

(3 marks)

b 5x + 2y = 17

4x + 3y = 8

(4 marks)

5 Emma buys 3 gingerbread men and 2 cupcakes in a bakery and pays £4.05

James buys 2 gingerbread men and 5 cupcakes from the same bakery and pays £6

What is the cost of 1 gingerbread man? What is the cost of 1 cupcake?

(5 marks)


6 Solve these inequalities.

a 4x + 1 > 6x + 5

(3 marks)

b –6 ≤ 4(x – 5) < 7 – x

(3 marks)

7 A curve with equation y = x2 – 7x – 3 crosses a straight line with equation y = 4x – 3 in two places.

Find the coordinates of the points where the lines intersect.

(4 marks)

Overall mark /30


Worksheet 6 - Probability

1 Jack spins a five-sided spinner. Each side of the spinner is a different colour.

The table shows the probability that the spinner will land on red, green, blue or yellow.

Colour red green blue yellow purple

Probability 0.25 0.20 0.15 0.13

a Work out the probability that the spinner will land on purple.

(2 marks)

Jack spins the spinner 200 times.

b Work out an estimate for the number of times the spinner will land on blue.

(2 marks)

2 A fast-food chain launches a new milkshake range.

The milkshakes are sold in three different sizes and there are four different flavours.

a How many combinations of flavour and size are there?

(2 marks)

b One of the milkshakes is a large strawberry milkshake.

A milkshake is picked at random. What is the probability it is this combination?

(2 marks)

3 X and Y are two mutually exclusive events.

P(X) = 0.55 and P(X or Y) = 0.7

Work out P(not Y).

(2 marks)


4 State whether each pair of events is independent or dependent.

a Rolling two six-sided dice.

(1 mark)

b Randomly taking a counter from a bag, replacing it, and then taking another one.

(1 mark)

c Randomly taking a chocolate from a box, eating it, and then taking another.

(1 mark)

d Randomly taking two pencils from a packet of 12 coloured pencils.

(1 mark)

5 Tom has a fair six-sided spinner. He spins it three times.

The probability that the spinner will land on white is 1

6.

a Calculate the probability that the spinner will land on white for all three spins.

(2 marks)

b Calculate the probability that the spinner will land on white for at least one of the spins.

(3 marks)


6 There are 12 sweets in a bag.

7 of the sweets are strawberry flavour.

5 of the sweets are lime flavour.

Harriet takes 2 sweets at random.

Work out the probability that she takes at least one strawberry sweet.

(4 marks)


7 The Venn diagram shows the numbers of people who chose cream (C) and ice cream (I) on

their dessert in a restaurant.

Use the Venn diagram to find

a P(C)

(1 mark)

b P(I')

(1 mark)

c P(C I)

(1 mark)

d P(C I)

(1 mark)


8 A tennis club has 100 members. The members are males and females in the ratio of 2 : 3.

Work out the probability that two members chosen at random are both female.

(4 marks)

Overall mark /32

year 10 spring work pack maths (h) - city heights€¦ · year 10 spring work pack – maths (h)...

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