1. GCSE LINEAR GRADE C STARTER QUESTIONS
(FOUNDATION)
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Which ones are you using? 1) 2)
Write 32 as a product of prime factors 32 8 4 4 7 10 13
(a) Work out the nth term for the pattern of matches
3n + 1 4 2 2 2
(b) How many matches will the 100th pattern have?
ANSWER = 2 X 2 X 2 X 2 X 2
3 x = 301 2 2 = 3) 4)
Calculate the area of the semi-circle
Calculate the perimeter of the semi-circle
Perimeter of semi-circle =
Perimeter of semi-circle = 25.7cm 2

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3cm
4cm a
120°
120°
Work out angles a and b and give reasons for your answers
a = 120° (Alternate angles)
b = 60° (Angles on a straight line) 4)
4cm
10cm 3)
Work out the volume
Volume of cylinder = area of cross section x length
Volume of cylinder = area of circle x length
Volume of cylinder = 3.14 x 16 x 10 3

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The price of fuel goes up from £1.36 per litre to £1.45 per litre. What is the percentage increase? 2)
The price of a car depreciates from £3500 to £2100. What is the percentage decrease?
136p
145p
Increase = 9p
£3500
£2100
Decrease = £1400
Percentage Increase = 6.6% (1d.p.)
Percentage Decrease = 40% (1d.p.) 3) 4)
5cm
13cm
30cm
4cm
20cm
Both triangles are similar. Work out the missing length marked 4

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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? 2)
11 red 4)
Red ball = 44 times 3)
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?
Total frequency = 160 =
(b)
Write the vector that would translate the shape back. 5

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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? 2)
Divide 77kg in the ratio 2:4:5
SQUASH : WATER 4 : 5
x 7
x 7
28cl :
35cl ?
Therefore, 35cl of water needs to be added to make the drink. 4)
Construct an angle bisector to the angle below: 3)
Construct an perpendicular bisector to the line below: 6

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Which ones are you using? 1) 2) x
High or Low
+ 7
+ 7 2𝑥
Replace x with 3
< 16 3
x 3 = 12 3
Too low
÷ 2
÷ 2 4
x 4 = 44 3
Too high 𝑥
< 8
3.5
x 3.5 = 25.38 3
Too low
3.8
x 3.8 = 35.87 3
Too low 5 6 7 8 9 10
3.9
x 3.9 = 39.82 3
Too low
3.95
x 3.95 = 41.88 3
Too high
ANSWER = 3.9 (closest to 40) 4)
(a) 8 3)
(a)
Round 8.43 to 1s.f.
Round 8.43 to 1d.p.
8.4
(b)
(b)
Round 570 to 1s.f.
600
Round to 2d.p.
7.85
(c)
Round to 3d.p.
11.833
(c)
Round to 1s.f.
0.7
(d)
Round 8.98 to 1d.p.
9.0 7

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Solve the equation: 2)
Rotate the original shaded flag by a quarter turn clockwise about (0,2)
4𝑥 + 5 = 3(𝑥 + 4)
4𝑥 + 5 = 3𝑥 + 12
- 3𝑥
- 3𝑥 𝑥 + 5 = 12
- 5
- 5 𝑥 = 7 3)
Fully describe the single transformation that will map triangle P to Q.
A reflection in the line y = x 4)
Circle the recurring fractions from the list below:
0.5
0.6
0.625 8

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Name the type of correlation below:
Positive Correlation
Negative Correlation
No Correlation 4)
Find the volume of the prism
Draw on the line of best fit and estimate the number of typos for 6 chapters.
Cross section
9 typos 3)
Find the reciprocal of:
(a) 7
(b)
Volume = area of cross section x length
Volume = area of triangle x length 9

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Describe fully the single transformation that maps triangle A onto triangle B 2)
Enlarge the shape by scale factor 2 with (0,0) as the centre of enlargement. 3) 4)
Score
Frequency
Midpoint fx
1-5 9
6-10 10
11-15 13
16-20 7
21-25 1
Total
Score
Frequency fx 1 5 2 4 3 9 8 6
Total 5 3 27 8 8 80 27 13
169 32 18
126 40 23 23 36 40
148 40
425
Calculate the estimated mean and modal group from the table above.
Calculate the mean, mode and range from the table.
Mean =148/40 = 3.7
Mode = 3
Range = 6 – 1 = 5
Estimated Mean = 425/40 = 10.6
Modal Group = 11-15 10

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Score
Frequency 1 5 2 4 3 9 8 6 cf 5 9 18 h 26 34 40
Find the median score from the table. w l
= 20.5th value
Surface Area = 2lw + 2hw + 2lh
= 4
Surface Area = 2 x 8 x 3 + 2 x 5 x 3 + 2 x 8 x 5
Surface Area = 48 + 30 + 80 4)
The line slopes down from left to right, so it’s a negative gradient.
Surface Area =
Surface Area = 6 3)
Find the gradient of the line. 1
Find the gradient of the line. 2 2 -6 1
GRADIENT =
GRADIENT = 2 2
GRADIENT = -3 11

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Find the equation of the line below: 2)
Find the equation of the line below:
The line slopes down from left to right, so it’s a negative gradient. 8
GRADIENT = 4
y - intercept = 3
y - intercept = 3
GRADIENT = 2 8 8 10 4 -8
GRADIENT = 10 -4
GRADIENT = 5 12

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Find the HCF of 12 and 30 2)
Find the LCM of 6 and 8 6
6, 12, 18, 24, 30 12
1, 2, 3, 4, 6, 12 8
8, 16, 24, 32, 40 30
1, 2, 3, 5, 6, 10, 15, 30
Lowest Common Multiple = 24
Highest Common Factor = 6 3) 4)
Find the co-ordinates of the midpoint of the line segment
Rotation of 180° from centre (0,0)
Name the single transformation that moves triangle P to R
= (2.5,2) 13

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Which ones are you using? 1) 2)
Expand and simplify:
-8 < 2n =
- 21
- 2
÷ 2
÷ 2
÷ 2
÷ 2 =
- 23 -4
< n n 3 n
> -4 4)
Integer solutions= -3, -2, -1, 0, 1, 2, 3 3)
Construct a frequency polygon x x
(a) x
Draw a line of best fit on your scatter graph. x
(b) x
Use your line of best fit to estimate the number of pages in a book of weight 280g.
138 pages 14

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Draw all the points which are 5cm equidistant from the point below: 1) 5 1 -1
-1.25 -1 1 5 X X X X X X X 3)
Estimate the answer to:
(a)
(b)
-0.6
1.6 y
= 2000
= 7500 15

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Construct an equilateral triangle below: 2)
Construct a rhombus below: 16

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The distance–time graph below represents a car journey from Barnsley to Nottingham, a distance of 50 km, and back again.
15km
20mins
D-E
50km
Represents a stop for 20 minutes
19km
16km
20mins
60mins
10mins
20mins
(c) Work out the average speed for each of the five stages of the journey.
A-B
B-C
C-D
E-F
20mins = 16km
10mins = 19km
20mins = 15km
60mins = 50km x3 x3 x6 x6 x3 x3
60mins =
48km
60mins =
114km
60mins =
45km
50km/h
48km/h
114km/h
45km/h 17

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The graph shows Amy’s progress on a sponsored walk.
19km
Stop
Stop
(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)
2 times
11:30 – 12:30
This is where the line is steepest
20p x 19 =
£3.80
30p x 19 =
£5.70
9.50 18

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Which ones are you using? 1) 2) = = = = = = 15 + + + + 3) 4) x x x x x3 x5 x7 x3 = = x3 x5 x7 x3
Common denominator of 15
Common denominator of 21 = = = = = = 19

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95°
155°
80° 2)
Pentagon (5 sides)
Sum of interior = (n – 2) × 180
= (5 – 2) × 180
= 3 × 180
= 540°
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°
2x + 3x x = 540°
8x = 540°
8x = 320°
x = 40° - - - -
540°
90°
155°
95°
80°
120° 20

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Calculate the size of the exterior and interior angle for a regular dodecagon 2)
The diagram shows the exterior angle of a regular polygon.
18º
162º
Dodecagon
12 sides
(a)
What is the value of the interior angle?
(b)
How many sides does it have?
Number of sides = 20
(c)
What is the sum of interior angles? 3)
Isosceles Triangle
Base angles the same
67.5º
45º
Interior angle
135º
Exterior angle
67.5º
Angles in a triangle add to 180º 21