AUTHOR GCSE LINEAR GRADE C STARTER QUESTIONS (FOUNDATION)

AUTHOR

GCSE LINEAR GRADE C STARTER QUESTIONS

(FOUNDATION)

www.mistrymaths.co.uk

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

LINEAR GRADE C STARTERS

Effective Participator

Self Manager

Independent Enquirer

Creative Thinker

Team Worker

Reflective Learner Which ones are you

using?PLT Skills

1) 2)

3) 4)

(a) Work out the nth term for the pattern of matches

(b) How many matches will the 100th pattern have?

Write 32 as a product of prime factors

Calculate the area of the semi-circle Calculate the perimeter of the semi-circle

4 7 10 13

3n + 1

3 x 100 + 1 = 301

32

8 4

4 2 2 2

2 2ANSWER = 2 X 2 X 2 X 2 X 2

=

Perimeter of semi-circle = 15.7 + 10

Perimeter of semi-circle = 25.7cm



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using?PLT Skills

3cm

4cm

120°

a

b

Work out angles a and b and give reasons for your answers

4cm

10cm

1) 2)

3)4)

a = 120° (Alternate angles)b = 60° (Angles on a straight line)

120°

Volume of cylinder = area of cross section x lengthVolume of cylinder = area of circle x length

Volume of cylinder = 3.14 x 16 x 10

Work out the volume



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Team Worker


using?PLT Skills

1) 2)

3) 4)

The price of fuel goes up from £1.36 per litre to £1.45 per litre.

What is the percentage increase?

The price of a car depreciates from £3500 to £2100. What is the

percentage decrease?

Both triangles are similar. Work out the missing length marked

4cm 20cm

30cm

5cm

13cm

136p 145p Increase = 9p

Percentage Increase = 6.6% (1d.p.)

£3500 £2100 Decrease = £1400

Percentage Decrease = 40% (1d.p.)



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Team Worker


using?PLT Skills

1) 2)

3)

4)

A bag contains 20 balls. 9 balls are blue and the rest are red. A ball is drawn at random from the bag, it’s colour is noted and then it is put back in the bag. This is repeated 80 times. How many time would you expect a red ball to be drawn?

The frequency table shows the speeds of 160 vehicles that pass a radar speed check on a dual carriageway.

What is the experimental probability that a car is travelling

faster than 70 mph?

Write the vector that would translate the shape back.

(b)

11 red

Red ball = 44 times

Total frequency = 160

=



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Team Worker


using?PLT Skills

1) 2)

3)4)

A fruit drink is made by mixing lemon squash with water in the ratio 4:5. How

much water needs to be added to 28cl of lemon squash to make the drink?

x 75

4

SQUASH : WATER

28cl x 7

:

: ?35cl Therefore, 35cl of water needs to be added to make the drink.

Divide 77kg in the ratio 2:4:5

Construct an perpendicular bisector to the line below:

Construct an angle bisector to the angle below:

Too low



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Team Worker


using?PLT Skills

1) 2)

3) 4)

x High or Low3 3 - 5 x 3 = 123

4053 xxToo low

4 4 - 5 x 4 = 443 Too high

3.5 3.5 - 5 x 3.5 = 25.38 3

Too low

3.8 3.8 - 5 x 3.8 = 35.87 3

3.9 3.9 - 5 x 3.9 = 39.82 3 Too low

Replace x with 3

3.95 3.95 - 5 x 3.95 = 41.88 3 Too high

ANSWER = 3.9 (closest to 40)

+ 7 + 7

2 𝑥 < 16÷ 2 ÷ 2𝑥 < 8

5 6 7 8 9 10

(a) Round 8.43 to 1d.p.

(b) Round 7.845 to 2d.p.

(c) Round 11.8327 to 3d.p.

(d) Round 8.98 to 1d.p.

8.4

7.85

11.833

9.0

(a) Round 8.43 to 1s.f. 8

(b) Round 570 to 1s.f. 600

(c) Round 0.723 to 1s.f. 0.7



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using?PLT Skills

1) 2)

3)

4)

Solve the equation: 4 𝑥 + 5 = 3( + 4)𝑥 4 𝑥 + 5 = 3 + 12𝑥- 3𝑥 - 3𝑥 𝑥 + 5 = 12

- 5 - 5𝑥 = 7

Rotate the original shaded flag by a quarter turn clockwise about (0,2)

Fully describe the single transformation that will map triangle P to Q.

A reflection in the line y = x

Circle the recurring fractions from the list below:

0.5 0.6 0.333.. 0.625 0.777..



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Team Worker


using?PLT Skills

1) 2)

3)

4)

Draw on the line of best fit and estimate the number of typos for 6 chapters.

9 typos

Name the type of correlation below:

Positive Correlation

Negative Correlation

No Correlation

Find the reciprocal of:(a) 7 (b) Volume = area of cross section x length

Volume = area of triangle x length

Cross section

Find the volume of the prism



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Team Worker


using?PLT Skills

1) 2)

3) 4)

Describe fully the single transformation that maps triangle A onto triangle B

Enlarge the shape by scale factor 2 with (0,0) as the centre of enlargement.

Score Frequency Midpoint fx

1-5 96-10 10

11-15 1316-20 721-25 1Total

Score Frequency fx1 52 43 94 85 86 6

Total

Estimated Mean = 425/40 = 10.6

Modal Group = 11-15

Mode = 3 Range = 6 – 1 = 5 Calculate the mean, mode and range from the table. Calculate the estimated mean and modal

group from the table above.

58

2732403614840

Mean =148/40 = 3.7

3

8131823

27

80169

12623

42540



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Team Worker


using?PLT Skills

1) 2)

3)

4)

lw

h

Surface Area = 2lw + 2hw + 2lhSurface Area = 2 x 8 x 3 + 2 x 5 x 3 + 2 x 8 x 5

Surface Area = 48 + 30 + 80

Surface Area =

Surface Area =

Score Frequency1 52 43 94 85 86 6

cf5918263440

= 20.5th value= 4

Find the median score from the table.

21

GRADIENT =1

2

Find the gradient of the line.

2

6

The line slopes down from left to

right, so it’s a negative gradient.

GRADIENT =-62

GRADIENT = -3

Find the gradient of the line.



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Team Worker


using?PLT Skills

1) 2)

GRADIENT =84

GRADIENT = 2

4

8

y - intercept = 3

Find the equation of the line below: Find the equation of the line below:

10

8

The line slopes down from left to right, so it’s

a negative gradient.

5

GRADIENT = -810

GRADIENT = -4

y - intercept = 3



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Team Worker


using?PLT Skills

1) 2)

3) 4)

Find the HCF of 12 and 30 Find the LCM of 6 and 8

12 1, 2, 3, 4, 6, 12

30 1, 2, 3, 5, 6, 10, 15, 30

Highest Common Factor = 6

6 6, 12, 18, 24, 30

8 8, 16, 24, 32, 40

Lowest Common Multiple = 24

Name the single transformation that moves triangle P to R

Rotation of 180° from centre (0,0)

Find the co-ordinates of the midpoint of the line segment

= (2.5,2)

Expand and simplify:



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using?PLT Skills

1) 2)

3)

4)

-8 < 2n÷ 2 ÷ 2

n<-4n > -4

÷ 2 ÷ 2

n 3

Integer solutions= -3, -2, -1, 0, 1, 2, 3

= - 21 - 2= - 23

Draw a line of best fit on your scatter graph.

Use your line of best fit to estimate the number of pages in a book of weight 280g.

(a)

(b)

Construct a frequency polygon

x

x

x

x

x

138 pages



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Team Worker


using?PLT Skills

1) 2)

3)

5 1 -1 -1.25 -1 1 5

X

X

XX

X

X

X

y-0.6 1.6

0.5 -1.25

Draw all the points which are 5cm equidistant from the point below:

Estimate the answer to:(a) (b)

= 2000 = 7500



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Team Worker


using?PLT Skills

1) 2)Construct an equilateral triangle below: Construct a rhombus below:



Self Manager


Creative Thinker

Team Worker


using?PLT Skills

1)

(c) Work out the average speed for each of the five stages of the journey.

The distance–time graph below represents a car journey from Barnsley to Nottingham, a distance of 50 km, and back again.

16km

20m

ins

A-B20mins = 16km60mins =

x3 x348km

48km/h

10mins

19k

m

B-C10mins = 19km60mins =

x6 x6114km

114km/h

20mins

15km

C-D20mins = 15km60mins =

x3 x345km

45km/h

D-ERepresents a stop for 20

minutes

20mins

50km

60mins

E-F60mins = 50km

50km/h



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Creative Thinker

Team Worker


using?PLT Skills1) The graph shows Amy’s progress on a sponsored walk.

(a) How many times does Amy stop during her walk?Answer .......................................................................... (1 mark) (b) Between which times does Amy walk the fastest? Explain your answer.Answer ...............................................................Explanation .......................................................................................................................................................................................................................................... (2 marks)

(c) Bill sponsors Amy for 20 pence per kilometre.Kate sponsors Amy for 30 pence per kilometre.How much should Amy collect altogether from Bill and Kate after her walk?.................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... Answer £ ...................... (3 marks)

Stop

Stop

2 times

11:30 – 12:30This is where the line is steepest

19km

20p x 19 = £3.80 30p x 19 = £5.70

9.50



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Team Worker


using?PLT Skills

1) 2)

3) 4)

=

=

=

=

=

= 15

x

+

=

x

+

Common denominator of 15

=

x3

x3

x5

x5

=

=

x

+

x

+

=Common denominator of 21

=

x7

x7

x3

x3

=

=



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using?PLT Skills

1) 2)1)95°

155°

80° Pentagon (5 sides)

Sum of interior angles = (number of sides – 2) x 180°

Sum of interior angles = ( 5 – 2 ) x 180°Sum of interior angles = 3 x 180°Sum of interior angles = 540°

- 90°- 155°- 95°- 80°540°

120°

Sum of interior = (n – 2) × 180

= (5 – 2) × 180

= 3 × 180

= 540°

2x + 3x + 5 + 3x + 75 + 140 = 540°

8x + 220 = 540°

8x = 320°

x = 40°



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Team Worker


using?PLT Skills

1) 2)1) Calculate the size of the exterior and interior angle for a regular dodecagonDodecagon 12 sides

18º

The diagram shows the exterior angle of a regular polygon.

(a) What is the value of the interior angle?

(b) How many sides does it have?

(c) What is the sum of interior angles?Number of sides = 20

162º

3)

Exterior angleInterior angle 45º135º67.5º67.5º

Angles in a triangle add to 180º

Isosceles Triangle Base angles the same

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AUTHOR GCSE LINEAR GRADE C STARTER QUESTIONS (FOUNDATION)