1. GCSE MATHS EXAM
• Paper 1
– Non- Calculator Tuesday 11th am
• Paper 2
– Calculator Friday 14th am

2. Make sure you understand how
to do all the following questions.
These topics are very likely to
come up in Paper 1.

3. 1. The diagram shows some solid shapes and some mathematical names.
An arrow has been drawn from one solid shape to its mathematical name.
Draw an arrow from each of the other solid shapes to its mathematical
name.
The cube has been done for you.
pyramid
triangular prism
cube
cylinder
cuboid
(3 marks)
PYRAMID
TRIANGULAR PRISM
CUBE
CYLINDER
CUBOID

4. FACTORISE :
PUT INTO BRACKETS
EXPAND:
MULTIPLY EVERYTHING
INSIDE BY WHATS
OUTSIDE

5. 2.
(a) Factorise 15x – 10
.....................................
(1)
(b) Expand 5(x + 4)
.....................................
(1)
(c) Factorise x2 − 7x
.....................................
(1)
(d) Expand 3x(x + 2)
.....................................
(1)
(e) Expand and simplify 3(x + 5) + 2(5x – 6)
.....................................
(2)
5( 3x – 2)
5x + 20
x(x – 7)
3x2 + 6x
3x + 15 + 10x - 12
13x + 3

6. BIDMAS :
BRACKETS
INDICES
DIVISION
MULTIPLICATION
ADDITION
SUBTRACTION

7. 3.
(a) Work out 4 × 3 + 2
.....................................
(1)
(b) Work out 20 − 12 ÷ 4
.....................................
(1)
(c) Work out (18 ÷ 3) + (20 ÷ 5)
.....................................
(1)
(d) Work out (3 + 5)2
.....................................
(1)
B I D M A S
12 + 2
14
20 - 3
17
6 + 4 10
82
64

8. ALGEBRA NOTES :
• p + p + p + p = 4p
• p x p x p x p = p4
• p5 x p9 = p14
• p7 ÷ p3 = p4
• 5p2 x 2p9 = 10p11

9. = x4+5 x9
= p8-3 p5
= 4x3ef 12ef
6e
5pq
= k5-2 k3
a3
= 3x5p7+2 15p9

10. NOTES : FORMING EQUATIONS
• Angles in a triangle add to 180
• Angles in a Quadrilateral add to 360
• Perimeter: Add all the sides

11. x + 10 + 2x + 2x + 50 = 360
5x + 60 = 360
5x + 60 = 360
5x = 360 - 60
5x = 300
x = 300 ÷ 5
60

12. NOTES :
• Round to 1 Significant figure
• Remember
• ÷ by 0.5 same as x2
• ÷ by 0.2 same as x5
• ÷ by 0.1 same as x10

13. 50
300x6
. 50
1800
.
= 3600=

14. NOTES :
• Gradient: Measures STEEPNESS
RISE OVER RUN
• Draw the triangle: Height ÷ Base

15. ( 0, 3 )
( 2, 7 )
( 1, 5 )
RISE OVER RUN 2
4
= 2=
4
2

16. NOTES :
• TESSELATE: Tile leaving no
gaps in between

18. 9.(a)Express the following numbers as products of their prime factors.
(i) 60,
.............................
(ii) 96.
.............................
(4)
(b) Find the Highest Common Factor of 60 and 96.
.............................
(1)
(c) Work out the Lowest Common Multiple of 60 and 96.
............................
(2)
302
152
3 5
96
482
242
2 12
2 6
2 3
60 =2 x 2 x 3 x 5
96 =2 x 2 x 2 x 2 x 2 x 3
HCF = 2 x 2 x 3 =12
LCM = 12 x 2 x 2 x 2 x 5 =480

19. NOTES :
• EDGES: LINES
• VERTICES: CORNERS
• FACES: SURFACES

20. 6
12
8

21. NOTES : SCATTER GRAPHS
• POSITIVE CORRELATION
• NEGATIVE CORRELATION
• NO CORRELATION
•When drawing a line of best fit
try to have an equal number of
points above and below the line

22. x
x
Negative Correlation
200

23. NOTES :
• Perimeter: distance round the
edge of the shape
• Area: count the squares inside
• Volume: Count the number of
cubes in the front layer and
times by the number of layers

24. 16cm2
18
10

25. NOTES : STEM AND LEAF
• Draw a KEY
• Median: Middle Number (Order)
• Mode: Most Common
• Range: Biggest - Smallest

26. 43
45 – 8 = 37
27

27. NOTES :
• y = 3x + 1
means: y is 3 times x add 1
• Draw a table:
x
y

28. 14. (a) On the grid, draw the graph of y = 2x + 1
(b)Use your graph to find
(i) the value of y when x = –1.5
y = ..................
(ii) the value of x when y = 6
x = ..................
(2)
x
y
x
x
x
x
x
x-2
2.5
x –2 –1 0 1 2 3
y
x –2 –1 0 1 2 3
y 7
x –2 –1 0 1 2 3
y 5 7
x –2 –1 0 1 2 3
y 3 5 7
x –2 –1 0 1 2 3
y 1 3 5 7
x –2 –1 0 1 2 3
y -1 1 3 5 7
x –2 –1 0 1 2 3
y -3 -1 1 3 5 7

29. NOTES : VOLUME OF PRISM
• Area of the Front Face times
how far back it goes
• If necessary break up the shape into
simpler shapes
• Area of Triangle = ½ x Base x Height

30. Area of the Front =
7 x 5 = 35
6
6 x 4 = 24
35 + 24 = 59
Volume of Prism = 59 x 20 = 1180
1180

31. Area of Triangle =
½ x 8 x 15 = 60cm2
Volume of Prism = 60 x 10 = 600
600cm3
x

32. NOTES : TWO WAY TABLE
• Draw a table
• Tick off all the information you
use
• Read the question: WHAT DO
THEY WANT YOU TO FIND?

33. Walked Bicycle Car Total
Boys
Girls
Total 100
4910
16 21
41
5114
2435
35

34. NOTES : INEQUALITIES
• > greater than
• > greater than or equal to
• < less than
• < less than or equal to
• INTEGER: Whole Number

35. o
7y < 8 + 34
7y < 42
y < 42 ÷ 7
y < 6
-2, -1, 0, 1, 2

36. NOTES : QUESTIONNAIRES /
DATA COLLECTION
• Questionnaire or Data Collection
Table
• Look out for
Time frame: day, week, month
Overlapping intervals
Is there an option for 0 or none
Is there an option for More than..

37. There is no time frame in the question
The intervals are over lapping,
e.g. 1 to 5 and 5 to 10.
How many hours do you spend listening to
music in a week?
None 1-5 6-10 11-15 > 15

38. 44.8
4.48
0.0448
1.4

39. NOTES : PROPORTION
• If you know the ingredient for 18
“Cakes”; how much of each ingredient
do you need for 27 “Cakes”
•Half of 18 is 9
•Work out how much you need for 9
•Then add it to how much you need for
18;
•This gives the ingredients for 27

40. 270
60
165
45

41. NOTES : NEGATIVE NUMBERS
• Draw a number line to help you with
these questions.
• + x + = +
• - x - = +
• + x - = -
• - x + = -

42. 90
540
Jupiter
-230

43. NOTES : ANGLES
• Angles in a triangle Add to 180
• Angles in a Quadrilateral Add to 360
• Angles around a point Add to 360
• Angles on a Straight line Add to 180
• The base angles in an ISOSCELES
Triangle are Equal

44. x = 180 - 70
110
Angles on a straight line add up to 180
= 180 - 70 – 70 = 180 - 140
= 40 40
The two base angles in an isosceles triangle
are equal. Angles in a triangle add up to
180

45. NOTES : FRACTIONS
• of 55 means ÷ by 5 and x by 3
• So 55 ÷ 5 = 11
• and 11 x 3 = 33
5
3

46. Boys = 1200 – 575 = 625
= 575 x 2 ÷ 5 = 1150 ÷ 5
= 230
= 625 x 3 ÷ 5 = 1875 ÷ 5
= 375
230 + 375 = 605

47. NOTES : SHARING IN A RATIO
• Share £240 in the ratio 2: 3: 7
• Add the parts:
 2 + 3 + 7 = 12
• Find the value of 1 part
 240 ÷ 12 = 20
• Find the value of each part
 2 x 20 = £40
 3 x 20 = £60
 7 x 20 = £140

48. 2 + 3 = 5
5
3
=
1 + 3 = 4
300 ÷ 4 = 75
75 x 1 =
75

49. NOTES : EXTERIOR ANGLES
• Exterior Angle: Outside
• Interior Angle: Inside
• Exterior Angles = 360 ÷ Number of Sides
• Exterior Angle + Interior Angle = 180

50. Exterior
angle of
Hexagon
= 360 ÷ 6
= 60
Exterior
angle of
Octagon
= 360 ÷ 8
= 45
x = 60 + 45 = 105

51. NOTES :TIME TABLES
• Read the question very Carefully
• Look at the tables and use a ruler to
follow columns and rows
• Remember:
 1 hour = 60 minutes
365 days in a year

52. 1123
1125
43
67 - 43
24

53. NOTES : MONEY CALCULATIONS
• Read the question carefully, UNDERLINE
important bits
• Show all your workings
• Change pence into pounds,
 e.g. 27 pence is £0.27
• Line up the decimal pints when adding and
taking away

54. 5.95
1.62
0.25
0.96
8.78
10.00
8.78
1.22
1.22
-
+
Number of Boxes = 160 ÷ 12 = 13.....
14

55. NOTES :SEQUENCES
 5 11 17 23 29 35
 These are going up by 6 so 6n
 The term before 5 would be -1
 So the nth term formula is: 6n – 1
 Could 54 be a number in the sequence?
 No. Because all the numbers in the
sequence are odd and 54 is even

56. 23 27 31
31
4n - 1
Yes, because 4n – 1 = 319; so 4n = 320;
and so n = 80; 319 is in the sequence.

57. NOTES :SOLVING EQUATIONS
 REMEMBER: DO THE OPPOSITE
1. 5x = 45
x = 45 ÷ 5
x = 9
2. y = 6
7
y = 6 x 7
y = 42
3. 4n = 8
5
4n = 8 x 5
n = 40 ÷ 4
n = 10
4. 3x – 12 = 27
3x = 27 + 12
3x = 39
x = 39 ÷ 3
x = 13

58. x = 12 3 4
y = 7 + 5 12
x = - 5 2
-2.52t = 3 - 8
y = 20 2
102y = 4 x 5

59. NOTES : x ON BOTH SIDES
 REMEMBER:
x’s on one side and numbers on the other
E.g. 3x + 12 = 11x - 4
SWAP SIDES
11x - 4 = 3x + 12
11x – 3x = + 12 + 4
8x = 16
x = 16 ÷ 8
x = 2

60. 13x - 11x= +9 - 1
2x = 8
x = 8 2
x = 4
4

61. 5t - 3t = +6 + 4
2t = 10
t = 10 2
t = 5
5

62. GOOD LUCK