Maths Summer Revision Ark Elvin Academy 2019-20 7 Maths Booklet.… · 3 . Learning Schedule . W/B...

Year 7

Maths Summer Revision

Ark Elvin Academy

2019-20

Name: __________________________________________

Teacher: _______________________________________

Teacher’s e-mail: ______________________________

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2

How to Use

If you are in set 3 or 4

1. Complete the numeracy skills challenges

2. Complete all of Section A

3. Try Section B

If you are in set 1 or 2

1. OPTIONAL to complete the numeracy skills challenges

2. Complete all of Section A

3. Complete all of Section B

If you are stuck on a question

1. What topic is it? E.g. fractions

2. Can you be more specific? E.g. adding fractions

3. Turn to page 3 and 4 and find the topic from the list

4. Look at what skill number it is

5. Go to Hegarty Maths and log in

6. In top search bar, type the skill number

7. Watch the video and complete the task

8. Try the question from the booklet again

3

Learning Schedule

W/B Set 3/4 ✓ Set 1/2

Wee

k 1

Numeracy Skills pg. 6 - 8 Section A pg. 24 - 25

Section A pg. 24 - 25 Section B pg. 42 - 45


Wee

k 2

Section A pg. 26 - 27 Section B pg. 46 - 49

Numeracy Skills pg. 12 - 14

Section A pg. 28 - 29


Section B pg. 50 - 53

Wee

k 3







Wee

k 4






Str

etch





6

Numeracy Skills

24

Section A Part 1: Understand place value to order integers and decimals 1) Look at these numbers:

a) In which number does the digit 1 have the greatest value?

……..……………… (1) b) In which number does the digit 4 have the least value?

……..……………… (1) 2) What number is 2000 more than 68 080?

…………………...…….. (1) 3) Compare using > or <

3 632 781 ……..…….. 3 632 178 (1)

4) Work out the following:

(a) 306 × 10 ……..…………………… (1)

(b) 6300 ÷ 100 ……..…………………… (1)

5) Write these numbers in ascending order:

0.99 0.09 0.9 …..……………………………………………………………….. (1)

6) Fill in the missing number: 23.67 x …………………………. = 236 700

(1)

Part 2: Use approximation and rounding 9) Round 0.78 to the nearest tenth.

……..……..……..…….. (1)

25

12) Round 68 532 to the nearest thousand

……..…………………………………… (1)

Part 3: Understand and use addition and subtraction in context 12) Add:

548 + 329

……..……..……..…….. (1) 13) Subtract:

732 –417

……..……..……..…….. (1) 18) Subtract 37.29 from 70

……..…………………………………… (1) 19) Calculate 54.2 – 2.87

……..…………………………………… (1)

Part 4: Mixed questions 20) Write 9 thousands, 70 tens and 4 ones as a single number

…………..…………………….. (1) 21) Ben writes the number three hundred and two thousand, four hundred and sixty-two as 32 462.

Explain why this is wrong.

26

(1)

Part 5: Multiply and divide multi-digit integers and decimals 1) Multiply

623 × 3

……..……………… (1) 2) Calculate

74.4 ÷ 4

……..……………… (1)

3) Calculate

518 × 83

……..……………… (2) 4) What is the product of 35 and 7?

……..……………… (1)

27

Part 6: Understand and use factors and multiples, including HCFs and LCMs 7)

a) List the first five multiples of 3.

(1)

b) List the first five multiples of 8.

(1)

c) What is the lowest common multiple of 3 and 8?

……..……………… (1)

8) Find the highest common factor of 9 and 27.

……..……………… (2)

Part 7: Understand and use the formulae for area of a rectangle, triangle and parallelogram 9) Calculate the area of this rectangle. 4 cm 9 cm

……..……………… cm2 (1)

28

10) Calculate the area of this parallelogram.

……..……………… cm2 (2) 11) Find the area of this triangle.

……..……………… cm2 (2)

Part 8: End of term review questions 16) Work out the following:

(a) 3.06 × 10

……..……………… (1)

(b) 630 ÷ 1000

……..……………… (1)

17) Calculate 11.46 – 7.6

……..……………… (1)

4.9 cm cm

4.3 cm cm

8 cm

8 cm cm

5 cm cm

10 cm cm

29

18)

(a) What is the value of the 3 in the number 537 129?

……..……………… (1)

(b) Round the number 5.786 to the nearest hundredth

……..……………… (1)

19) On a tour, there are 47 passengers on every coach. There are 684 coaches. Use rounding to estimate the total number of passengers.

……..……………… (2)

20) Match the description to the time. Fill in the blank spaces where needed.

(2)

30

Part 9: Accurately draw, measure and identify types of angles

1) a) Measure the marked angle. b) Measure angle YZX.

…………….. (1) ……………..

(1)

2) Draw an angle that measures 136.

(1) 3) Match the angles below to the correct name.

(2)

Reflex Acute Right angle Obtuse

31

Part 10: Use facts to solve problems involving unknown angles on a line and at a point

4) AC is a straight line. Work out the size of angle a giving a reason for your answer

Angle a = ……………..

I know this because………………………………………………………….………………………………………… …………………………………..………………………………………………………………………….……………… (2)

Part 11: Understand and use the properties of triangles and quadrilaterals

7) The diagram shows an irregular hexagon drawn on a square grid. Draw four more irregular hexagons to show how they tessellate.

(1)

Diagram not drawn to scale

32

8) Give the mathematical name for each of these triangles.

…………………………………. …..……………………………. .………………………………. (2) 9) Draw all the lines of symmetry on the shape below.

(1)

11) Calculate the value of angle g giving a mathematical reason for your answer.

Angle g = ……………...



33

Part 12: Mixed Questions 12) Convert the units to fill in the gaps below 2 500 g = …………….. kg 7.35 m = …………….. cm (2)

13) Construct a triangle that has one angle of 55°, one angle of 38°, and a side of length 7 cm between

these two angles.

(3)

Part 13: End of term review questions 17) Round this number to 1 decimal place:

18.448

................................ (1)

18) Calculate:

a) 28 − 3.6

................................ (1)

b) 37 × 28

34

20) Work out the area of the rectangle shown.

................................ m2 (2)

21) Six friends win £2538 in a raffle. They decide to split the prize evenly between them. How much do they each receive?

£ ................................ (1)

22) Below is a sketch of triangle ABC. Make an accurate drawing of triangle ABC in the space below.

(3)

Not drawn to scale

Not drawn to scale

35

24) Work out the area of the triangle below.

…………….. cm2 (2)

25) Look at this list of numbers:

24, 5, 3, 18, 28, 6, 40 From the list, choose:

a) a factor of 20 …………………. (1)

b) a multiple of 7

…………………. (1)

c) the highest common factor of 6 and 9 …………………. (1)

(3)

27) Give the mathematical names for the shapes below.

Not drawn to scale

36

28) Find the value of angle 𝑦 in the image below giving a reason for your answer.

𝑦 = …………….. °

(2)

Part 14: Carry out combined calculations using all four operations with brackets 1) Work out the answers to the following calculations:

a) 8 × (1 + 3)

....................... (1) b) 4 + 5 × 3

....................... (1) c) 9 + 8 ÷ 2 – 3 × 4

....................... (1)

Not drawn to scale

37

Part 15: Represent unknown values using letters, forming and manipulating algebraic expressions

4) Draw lines to match each expression to its correct description

(3)

5) a) Write these expressions as simply as possible. The first one is done for you.

𝑥 + 4 + 3 𝑥 + 7

7𝑥 + 2𝑥

(1)

8𝑥 + 5 + 3𝑥 − 2 (1)

4𝑥2 + 4𝑥 − 2𝑥2 − 𝑥

(1)

𝑥

5

Divide a

number by 5 𝑥 − 5

5𝑥

𝑥 + 5

5 − 𝑥

Multiply a

number by 5

Subtract 5

from a number

Add 5 to a

number

Subtract a

number from 5

38

7) Multiply out the brackets in the following expressions:

a) 3(𝑦 + 4)

………………………………………………………. (1) b) 𝑚(4𝑝 + 6)

………………………………………………………. (1)

Part 16: Evaluate algebraic expressions through substitution 10) Given that 𝑥 = 6, 𝑦 = 3 and 𝑧 = 4,work out the value of these expressions: a) 14 − 𝑧

………………………. (1)

b) 𝑥

3

………………………. (1)

c) 𝑥𝑦

………………………. (1)

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Section B

Part 1: Use approximation and rounding

7) Round each number to the nearest hundred and then estimate the value of: 725 + 512

……………… + ……………… = ................. (1)

8) Mr Smith is saving to buy a television. So far, he has saved £412. The television costs £689. Use rounding to estimate how much more money Mr Smith needs in order to buy the television.

……..……..……..…….. (1) 10) James has £33.20. Crystal has £89.85 more than James.

Use rounding to estimate how much money Crystal has.

£…..……..……..…….. (1)

Part 2: Understand and use addition and subtraction in context 14) Mr Jones washed 541 bowls in total over a two week period.

He washed 216 of the bowls in the first week. How many bowls did he wash in the second week?

……..……..……..…….. (1)

43

15) Calculate the perimeter of each of these rectangles. Rectangle A ……..…………………… Rectangle B ……..…………………… (1) Write a statement comparing the perimeter of the two rectangles

……..…………………………..…………………………..…………………………..…………………………..…………………………..……

……………………..…………………………..…………………………..……………………………(1)

16) Greg buys a game for £13.49 in the sale.

The original price was £18.50. How much money does Greg save?

Greg saves £............................. (1)

17) Rob buys a jumper for £23.45 and a pair of shoes for £14.95. He gave the cashier £50. How much change should Rob receive?

Rob receives £.............................in change (2)

Part 3: Mixed questions 22) Beverley and Sally collect stickers.

Beverley has collected 135 stickers. She has 48 more stickers than Sally. How many stickers do they have altogether?

A 15 m

6 m

B 13 m

7 m

44

……..……..……..…….. (2) 23) The figure is made up of two identical rectangles.

Work out the length marked 𝑎. 4m 13m

𝑎

……..……..……..…….. (2)

Part 4: Understand and use the formulae for area of a rectangle, triangle and parallelogram 12) Find the total area of this shape.

……..……………… cm2 (3)

Part 5: Mixed Questions 13) Mr Payne wants to bake enough mince pies for 50 children.

He uses 6 baking trays with 8 mince pies on each tray. Will Mr Payne have enough mince pies? Explain your answer.

(2)

12 cm

8 cm

7 cm

45

14) Find the length of a rectangle that has a perimeter of 44 metres and a width of 3 metres.

……..……………… m (2)

15) A computer game costs twice as much as a board game. The board game costs twice as much as a toy. All three items cost £238 altogether. Work out the cost of the board game.

……..……………… (3)

21) Sam bought 4 kilograms of raisins for £6.24 per kilogram and 5 apples for 65p each.

How much did he pay for the raisins and the apples altogether?

……..……………… (3)

46

22) The diagram below shows a shaded shape inside a rectangle

(a) Work out the perimeter of the rectangle

……..……………… cm (1) (b) Calculate the shaded area

……..……………… cm2 (2)

Part 6: Use facts to solve problems involving unknown angles on a line and at a point 5) Work out the size of angle p giving a reason for your answer

Angle p = ……………..


20 cm cm

12 cm cm 8 cm

cm

14 cm cm


47

6) The image shows three straight lines that intersect at a point. Tick true or false for each of the statements below.

True False

Angle f is vertically opposite angle d

f + a = 180

c + d = a + f

f + e + b = 180

(2)

Part 7: Understand and use the properties of triangles and quadrilaterals

10) a) Write the name of the quadrilateral described:

……..….............................….. (1)

b) Decide if the following statements are true or false. For false statements explain why they are false.

i) A parallelogram has one pair of parallel sides

…………………………………………………………….…………………………………………………………………….. (1)

ii) A kite has exactly two pairs of equal sides

…………………………………………..………………………………………………………………………………… (1)

iii) The interior angles of a trapezium add up to 180°

……………………………………………………………………………………………………………………….…… (1)

Diagram not

drawn to scale

Two of my sides are 5 cm long

and the other two are 6 cm long.

Two of my interior angles are

45°, and the other two are 135°.

48

14) Work out the size of angle a, giving reasons for your answer.

Angle a = ……………..

I know this because …………………………………………………….…………………………………………….. ……………………………………………….….…………………………………………………………………………..(2) 15) Look at the diagram below. Give the mathematical reason for each of the facts. a = b because……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………... (1) b = c because ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………... (1)

................................ (2)



49

Part 8: End of term review questions

Q19) The shape below is made by joining square A and rectangle B. Calculate the perimeter of the compound shape.

................................ cm (3)

23) The perimeter of a square is 5.2 cm. Find the length of one of the sides of the square.

…………….. cm (2)

26) Calculate the size of angle 𝑥. Give reasons for your answer.

𝑥 = …………….. °

Not drawn to scale

Not drawn to scale

50

29) The diagram below shows square C with an additional line meeting one vertex. Find the value of angle z giving reasons for your answer.

𝑧 = …………….. °

(2)

Part 9: Carry out combined calculations using all four operations with brackets 2) John works out the answer to 3 + 42. John thinks the answer is 49. Explain why John is wrong.

....................... (1)

3) Put brackets in the calculation below to make the answer 36

4 × 5 + 3 + 4

Not drawn to scale

51

(1)

Part 10: Represent unknown values using letters, forming and manipulating algebraic expressions

6) Write an expression for the perimeter of this isosceles triangle.

…………………………………………………………. (1)

8) Factorise the following expressions

a) 7𝑔 + 14

……………………………………………………… (1)

b) 3𝑘𝑛 − 9𝑘𝑚

…………………………………………………….. (2)

Part 11: Evaluate algebraic expressions through substitution 9) The formula shows how much you pay for a hotel room.

P = 30 × N

a) Maria pays for a room for 10 days. How much must she pay?

………………………. (1)

b) Later, Dan pays £210 for a room. For how many days does book the room?

………………………. (1)

N represents for

the number of days

P represents the total price

you pay in pounds (£)

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11) Using the equation above, work out:

a) the value of 𝟔𝟎𝒏

...................... (1) b) the value of 𝟔(𝒏 + 𝟏)

...................... (1)

Part 12: Mixed Questions

13) Jay makes a sequence of patterns with black and grey rectangular tiles.

The rule for finding the number of tiles in pattern number N in Jay's sequence is:

number of tiles = 𝟏 + 𝟒𝐍

a) The 1 in this rule represents the black tile. What does the 𝟒𝐍 represent?

………………………………………………………………………………………………………………………… (1)

b) Jay makes pattern number 9 in his sequence. How many black tiles and how many grey tiles does he use?

............................... black and ............................... grey tiles (1)

6𝑛 = 108

Maths Summer Revision Ark Elvin Academy 2019-20 7 Maths Booklet.… · 3 . Learning Schedule . W/B...

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Transcript of Maths Summer Revision Ark Elvin Academy 2019-20 7 Maths Booklet.… · 3 . Learning Schedule . W/B...