Download Maths Revision PP grade G to D questions

GCSE Maths
Facts To Remember
Multiplying and Dividing by 10, 100……
Multiplying by 10 moves the decimal point one to the right.
6 x 10 = 60
6.2 x 10 = 62
0.03 x 10 = 0.3
Multiplying by 100 moves the decimal point two to the right.
3 x 100 = 300
3.1 x 100 = 310
0.2 x 100 = 20
Dividing by 10 moves the decimal point one to the left.
60 / 10 = 6
6.2 / 10 = 0.62
0.3 / 10 = 0.03
Dividing by 100 moves the decimal point two to the left.
30 / 100 = 0.3
310 / 100 = 3.1
2 / 100 = 0.02
•
•
•
•
•
7.3 x 10
2.8 x 100
53 ÷ 10
0.5 ÷ 100
1.9 x 100
=
=
=
=
=
Equivalent fractions, decimals and percentages.
Fractions
Decimals
Percentages
1/4
0.25
25%
1/2
0.5
50%
3/4
0.75
75%
1/10
0.1
10%
3/10
0.3
30%
1/100
0.01
1%
1/5
0.2
20%
•
•
•
•
•
What is 0.8 as a fraction, in its
simplest form?
What is 3/5 as a percentage?
Want is 4% as a decimal?
What is 30% as a fraction?
What is 7/10 as a decimal?
Metric
• 1 kilogram (kg)
•1.6 kilometres (km)
•4.5 litres (l)
•1 litre (l)
•2.5 centimetres (cm)
=
=
=
=
=
=
Imperial Conversions
2.2 pounds (lb)
1 mile
1 gallon
1.75 pints
1 inch
Metric Conversions
•10 millimetres (mm)
•100 centimetres (cm)
•1000 millimetres (mm)
•1000 metres (m)
•1000 milligrams (mg)
•1000 grams (g)
•1000 millilitres (ml)
=
=
=
=
=
=
=
1 centimetre (cm)
1 metre (m)
1 metre (m)
1 kilometre (km)
1 gram (g)
1 kilogram (kg)
1 litre (l)
Speed, Distance, Time
Speed =
Distance
Time
Time = Distance
Speed
Distance = Speed x Time
Distance
Speed
Time
•
•
•
•
•
What is 3kg approximately in pounds?
What is 10 miles approximately in km?
What is 4 gallons in litres?
What is 2 litres approximately in pints?
A car travelled 250 km in 5 hours what is
the speed? Give the correct units.
Square Numbers
1x1 = 1
1
1 1
2x2 = 4
2
2 4
3
3
9
4
4
16
5
5
25
Cube Numbers
3x3 = 9
8
2 2
4x4 = 16
27
5x5 = 25
6x6 = 36
7x7 = 49
8x8 = 64
9x9 = 81
1x1x1 = 1
1 1
11
2x2x2 = 8
2
3x3x3 = 27
3
4x4x4 = 64
3
3
5x5x5 = 125
4
64
4
7x7x7 = 343
5
125
5
6x6x6 = 216
4
5
8x8x8 = 512
9x9x9 = 729
10x10 = 100
10x10x10 = 1000
11x11 = 121
11x11x11 = 1331
12x12 = 144
12x12x12 = 1728
Powers
Powers of 2:
21
22
The same as: (2x2)
23
(2x2x2)
24
(2x2x2x2)
25
(2x2x2x2x2)
Powers of 10:
101
102
The same as: (10x10)
103
(10x10x10)
104
(10x10x10x10)
105
(10x10x10x10x10)
Multiples and Factors
Multiples:
The multiples of a number are simply its Times Tables
e.g. the multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 40 ………
the multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, ………
Factors:
e.g.
The factors of a number are numbers that can divided exactly into it.
the factors of 30 are 1,2,3,5,6,10,15,30
the factors of 12 are 1,2,3,4,6,12
1 x 30 = 30
2 x 15 = 30
3 x 10 = 30
5 x 6 = 30
1 x 12 = 12
2 x 6 = 12
3 x 4 = 12
LCM – “Lowest Common Multiple”
the SMALLEST number that will DIVIDE BY ALL the numbers in question.
e.g. – Find the lowest common multiple (LCM) of 6 and 7
Answer – Multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, ……
Multiples of 7 are: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, ……
LCM of 6 and 7 is 42
HCF – “Highest Common Factor”
the BIGGEST number that will DIVIDE INTO ALL the numbers in question.
e.g. – Find the highest common factor (HCF) of 36, 54 and 72
Answer– Factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36, ……
Factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54, ……
Factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, ……
HCF of 36, 54 and 72 is 18
Triangle Numbers
1
3
2
6
3
10
4
15
5
21
6
28
7
36
8
45
9
55 …………………
10
Prime Numbers
Prime numbers are only divisible by 1 and themselves.
(1 is not a prime number)
2 3 5 7 11 13 17 19 23 29 31 37 …………………
From the following list of numbers
1 , 2 , 5 , 8 ,15 , 25 , 36 , 49 , 51
• 1) What are the factors of 45?
• 2) What are the multiples of 5?
• 3) What are the prime numbers?
• 4) What are the square numbers?
• 5) What are the cube numbers?
Mean, Median, Mode and Range
(1,5,2,17,4,8,12,3,8)
MODE: Most common
1,5,2,17,4,8,12,3,8 = 8 is the most common number
MEDIAN: Middle value (put in order first)
1,2,3,4,5,8,8,12,17 = 5 is the middle number
MEAN: Total of items / number of items
1+5+2+17+4+8+12+3+8 = 60
60/9 = 6.6 is the mean number
RANGE: Difference between smallest value and biggest value
17 – 1 = 16 is the range
For the following data
5, 11 , 7 , 1 , 4 , 7 , 3 , 2
• 1) What is the mean?
• 2) What is the median?
• 3) What is the mode?
• 4) What is the range?
Circle Words
g
f
c
e
d
a
b
a= Centre of circle
b= Radius
c= Diameter
d= Circumference
e= Chord
f= Arc
g= Tangent
• What are the correct circle words
for?
• A=
A
• B=
D
B
• C=
C
• D=
E
• E=
Area = mm2, cm2, m2………
Volume = mm3, cm3, m3………
x
Square: Area = x2
x
w
Rectangle: Area = lw
l
h
Triangle: Area = ½ bh
b
Circle: Area = p r2
Circumference = 2pr
Parallelogram: Area = bh
r
h
b
h
Cuboid: Volume = l x w x h
l
w
•
•
•
What is the area of a circle of diameter 8cm?
What is the circumference of a circle radius
5m?
What is the area of the following triangle?
13cm
•
12cm
13cm
10cm
What is the volume of the cuboid?
2m
2m
5m
•
Find the area of the parallelogram?
5m
4m
10m
Triangles
Equilateral triangle (3 sides equal)
Isosceles triangle (2 sides equal)
Scalene triangle (all sides different)
Quadrilateral (4 sided shapes)
Trapezium
Rhombus
Parallelogram
Name of shape
Number of sides
Pentagon
5
Hexagon
6
Heptagon
7
Octagon
8
Nonagon
9
Decagon
10
Duo Decagon
12
Picture
Name the given shapes
Angles and Bearings
Angle around a complete circle = 360o
Angle around a point on a straight line = 1800
Bearings – are always measured clockwise from the North
- are expressed as three digits e.g. 090o
Acute angles are between 0o and 90o
Obtuse angles are between 90o and 180o
Reflex angles are between 180o and 360o
N
130o
• Give the special names of these
angles.
a
b
c
Angles
Corresponding angles are equal,
shown as (a) in diagram.
Alternate angles are equal, shown
as (b) in diagram.
Supplementary angles add up to
180o, shown as (c) and (d) in
diagram.
Find the missing angles in these
2
diagrams
130o
1
70o
b
c
a
4
3
g
35o
f
200o
d
h
Shapes
A Regular shape has equal sides and equal angles
The sum of interior angles in a triangle is 180o
The sum of interior angles in a quadrilateral is
2 x 180o = 360o
The sum of interior angles in a pentagon is
3 x 180o = 540o
The exterior angle of an n sided regular shape = 360o / n
The interior angle and exterior angle = 180o
•
•
•
•
•
What is a regular shape?
What do all the interior angles of a
triangle sum to?
What do all the interior angles of a
quadrilateral sum to?
Work out is the interior angle of a
regular pentagon?
Work out exterior angle of a regular
pentagon?
Rotation – rotates a shape through a
number of degrees about a point.
Reflection – gives a mirror image of a
shape along a line of reflection.
Enlargement – makes the shape bigger or
smaller by a scale factor from a point.
Translation – moves all points of an object
in the same direction and the same
distance.
Two shapes are congruent if they are identical in every way
Two shapes are similar if they have the same shape but
may be different in size
On graph paper
• Plot the points A ( 1,3) , B (1,5) and C( 4,3) and draw
the triangle ABC
• Reflect the triangle ABC in the line x=5. What are
the co ordinates of the reflected triangle?
• Rotate the triangle ABC about (0, 0) through 900
clockwise. What are the co ordinates of the
rotated triangle?
• Enlarge ABC by a scale factor of 2 from the point
(0, 0). What are the co ordinates of the enlarged
triangle?
• Translate ABC by the translation vector (-3, -5).
What are the co ordinates of the rotated triangle?