AUTHOR GCSE LINEAR GRADE E STARTER QUESTIONS (FOUNDATION)

AUTHOR

GCSE LINEAR GRADE E STARTER QUESTIONS

(FOUNDATION)

www.mistrymaths.co.uk

http://www.mistrymaths.co.uk/

LINEAR GRADE E STARTERS

Effective Participator

Self Manager

Independent Enquirer

Creative Thinker

Team Worker

Reflective Learner Which ones are you

using?PLT Skills

1) 2)

3) 4)

Write the term to term rule of the following sequences:

(a) -3, -5, -7, -9, ….., ….Subtract 2 from the previous term each

time

Write down the next two terms of the following sequences:

-2 -2 -2

(a) 1, 3, 6, 10, 15, ….., ….

(b) 2, 3, 5, 9, 17, ….., ….

+2 +3 +4 +5 +6

21

+7

28

+1 +2 +4 +8 +16

33

+32

65

Work out the area and perimeter of:

Replace 𝑥 with 2 and y with 3

= 2 x 2 – 3 x 3

= 4 – 9

= -5

Replace 𝑥 with -3 and y with -4

= 2 x -3 – 3 x -4

= -6 + 12

= 6

8.3cm

2.6cm

Area of a rectangle = length x widthArea of rectangle = 8.3 x 2.6

Perimeter of a rectangle = length + width + length + widthPerimeter of rectangle = 8.3 + 2.6 + 8.3 + 2.6Perimeter of rectangle = 21.8cm



Self Manager


Creative Thinker

Team Worker


using?PLT Skills

1) 2)

3) 4)

Work out the following:

= 1 x 1 x 1

= 1

= 2 x 2 x 2

= 8

= 5 x 5 x 5

= 125

What number multiplies by itself 3 times to make

27?= 3

What number multiplies by itself 3 times to make

64?= 4


(a) 10% of £40= £4

10% means ÷10

(b)10% of £57 10% means ÷10

= £5.70


(a) 30% of 90mm

x3 10% = 9mm30% =

x327mm

(b)90% of 40years

x9 10% = 4years90% =

x936years

(c) 35% of 80cl

x3 10% = 8cl30% =

x324cl

5% = 4cl 35% = 28cl

Add 30% and 5% answers

(d)17.5% of 60litres

÷2 10% = 6litres 5% =

÷23litres

÷2 ÷22.5% =1.5litres17.5% = 10.5litres Add 10%, 5%

and 2.5% answers

On the map, how many km would 5cm be?

x5 1cm = 160km5cm =

x5800km



Self Manager


Creative Thinker

Team Worker


using?PLT Skills

1) 2)

3)

(b) His speed for the first hour?

(c) How long did he stop for?

(d) How long did it take him to run 40km?

15min

s

30min

s

45min

s

8km

10km/h

15mins

15mins2hours 45mins

P = 2L + 2W

Use the formula to find W when L= 2 and P = 20

Replace L with 2 and P with 20

20 = 2 x 2 + 2 x W20 = 4 + 2W

- 4- 4

16 = 2W÷ 2÷ 2

8 = WW = 8

Work out the value of each of the angles below:

Angles in a triangle add to

180º40º 60º60º 60º

75º 75ºIsosceles triangle

so base angles are the same



Self Manager


Creative Thinker

Team Worker


using?PLT Skills

1) 2)

5)4)

NOT THE SAME

F = 1.8C + 32

Use the formula to find F when C= 4

Replace C with 4

F = 1.8 x 4 + 32F = 7.2 + 32F = 39.2

2 𝑥 + 3 = 11𝑥6

+ 2 = 9 𝑥 + 2 6

= 9 6 𝑥 - 5 = 34- 3 - 3

2 𝑥 = 8÷ 2 ÷ 2𝑥 = 4

+ 5 + 5

6 𝑥 = 39÷ 6 ÷ 6𝑥 = 6.5

- 2 - 2𝑥6

= 7x 6 x 6𝑥 = 42

x 6 x 6

𝑥 + 2 = 54- 2 - 2𝑥 = 52

3) 6)



Self Manager


Creative Thinker

Team Worker


using?PLT Skills

1) 2)

3)

5)

(a) 2y + 3y – 7y

(b) 7x + 9 + 3x - 6

(c) 5m – 6n + 4m – 3n

= -2y

= 10x

Simplify by collecting like terms:

+ 3

= 9m – 9n 40º

70º

(Exterior angle is equal to the sum of the opposite interior angles)

= 110º

Round the following to 1d.p.:

(a) 4 . 8 3 (b) 7 . 2 8

= 4 . 8 = 7 . 3

4) Round the following to 2d.p.:

(a) 6 . 8 3 2 (b) 3 . 6 6 8

= 6 . 8 3 = 3 . 6 7

Round the following to 1s.f.:

(a) 7 . 1 (b) 6 7 (c) 3 8 2

= 7 = 70 = 400

(d) 0 . 0 3 4

= 0.03



Self Manager


Creative Thinker

Team Worker


using?PLT Skills

1) 2)

3) 4)

Reflect the shape in the y-axis Reflect the shape in the x-axis

y-axis

Write down all the prime numbers below 30

2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 29

Which is the only even prime number?

2

x y = 3x - 5

-1

0

1

2

Fill in the table above for y.

3 x -1 - 5-8

3 x 0 - 5-5

3 x 1 - 5-2

3 x 2 - 51

14



Self Manager


Creative Thinker

Team Worker


using?PLT Skills

1) 2) 3)

(a)

- 8 X +4 =

+7 X - 6 =

+3 X +5 =

- 11 X - 2 =

-32

-42

15

22

-15 +3 =

+12 - 4 =

+80 +10 =

- 28 - 2 =

-5

-3

8

14

(a)

(b)

(c)

(d)

(a)

(b)

(c)

(d)

1

2

3

1 7 9

1 2 5 8

2 3 5 5 8 9

2 7

KEY:

3 2 means 32

Stem-and-leaf to show the ages of people at a table tennis club

How many people were asked their age?

(b)What is the range of ages?

(c)What is the median age?

Count the amount of leaves16

47 - 11= 36

Find the middle age32.5

4) Find the volume of the cuboid below:

Volume = length x width x height

Volume = 12cmx6cmx9cm

Volume = 648cm3

5)

5cm 100cm

60cm

÷20

÷20



Self Manager


Creative Thinker

Team Worker


using?PLT Skills

1) 2)

3) 4)

Find the missing numbers below:

(a) -7, -5. -3, …., ….

(b) -6, -9. -12, …., ….

(c)

-1 1

-15 -18

a)

U T th H th

b)

60100

7100 =

0 0 7.U T th H th

0 6.7% 6

10 = 60%=

Change the decimals to fractions and percentages:

Estimate the answers below:(a) 3.9 x 2.2

(b) -4.11 x 6.82

(c) -19.75 ÷ -4.91

4 x 2 = 8

-4 x 7 = -28

-20 ÷ 5 = -4

Enlarge the triangle by scale factor 2:



Self Manager


Creative Thinker

Team Worker


using?PLT Skills

1) 2)

3) 4)

1m = 1cm

Draw an accurate scale drawing of the triangle above:3m

2m

3m

2m

Draw the lines with equations y=2 and y =-5:

Draw the lines with equations x=3 and x =-7:

Draw the lines with equations y=x and y =-x:

x=3x=-7

y=2

y=-5

y=xy=-x

(b) 48 ounces to pounds



Self Manager


Creative Thinker

Team Worker


using?PLT Skills

1) 2)

3)

Draw a 4 by 6 by 3 cuboid below:

(c) 4 feet to inches(a) 36 feet to yardssmaller to bigger (÷)

36 ÷ 3 = 12 yards

smaller to bigger (÷)

48 ÷ 16 = 3 pounds

bigger to smaller (x)

4 x 12 = 48 inches

Convert the following units:

Convert the following units:(a) 732cm to m (b) 450cl to litres

(c) 1.2m to cm (d) 3m to mm

smaller to bigger (÷) 732 ÷ 100 = 7.32m

smaller to bigger (÷)

450 ÷ 100 = 4.5 litres

bigger to smaller (x) 1.2 x 100 = 120cm

bigger to smaller (x)

3 x 1000 = 3000mm

y = 180º - 95º



Self Manager


Creative Thinker

Team Worker


using?PLT Skills

1)

2)

3)

Construct a pie chart for the table below:

Musical Instruments

Guitar 35

Violin 10

Recorder 15

Drum 5

Keyboard 25

TOTAL = 90

35Guitar angle = 360 0

9014 ox

10Violin angle = 36 00

904 ox

15Recorder angle = 36 00

906 ox

5Drum angle = 360 0

902 ox

25Keyboard angle = 360 0

9010 ox

Guitar

Violin

Recorder

Dru

m

Keyboard

Find the averages and range for the data below:

2, 5, 6, 3, 1, 1, 15, 7Ordered: 1, 1, 2, 3, 5, 6, 7, 15

Mode = 1 (most common)

Median = 4 (middle when in order)Mean = = = 5

Range = Biggest - Smallest = 15 -1 = 14

y

Work out the value of x and y above.

x = 360º - 100º - 60º - 95º = 105º(Angles in a quadrilateral add to 360º)

= 85º(Angles on a straight line add to 180º)

4



Self Manager


Creative Thinker

Team Worker


using?PLT Skills

1) 2)

6) 7)

7.9 + 4.7 28.6 + 3.12 3) 7.52 - 4.45 4) 10.2 - 6.19 5) 5.8 x 9.8

7 . 9

4 . 7+6

1

. 12

2 8 . 63 . 1 2+

00

27.11

3

7 . 5 24 . 4 5-

1

70.3

1 0 . 2 00 6 . 1 9-

1 1

10.

1

4

0 5 8 x9

8

45

72

40

64

48

6

15

..

.56.84

2

5x

4

6

2 x 4

5 x 6=

8

30=

4

15=

1

12+

1

6 X 2

X 2

12+

12

1 2=

3

12=

1

4=

1

3- 1

6X 2

X 2

6-

6

2 1=

1

6=

8)

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AUTHOR GCSE LINEAR GRADE E STARTER QUESTIONS (FOUNDATION)