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

TOPIC QUESTIONS 7.3 x 10 = 2.8 x 100 = 53 ÷ 10 = 0.5 ÷ 100 = 53 ÷ 10 = 0.5 ÷ 100 = 1.9 x 100 =

Equivalent fractions, decimals and 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%

TOPIC QUESTIONS 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 = Imperial Conversions 1 kilogram (kg) = 2.2 pounds (lb) 1.6 kilometres (km) = 1 mile 4.5 litres (l) = 1 gallon 1 litre (l) = 1.75 pints 2.5 centimetres (cm) = 1 inch Metric Conversions 10 millimetres (mm) = 1 centimetre (cm) 100 centimetres (cm) = 1 metre (m) 1000 millimetres (mm) = 1 metre (m) 1000 metres (m) = 1 kilometre (km) 1000 milligrams (mg) = 1 gram (g) 1000 grams (g) = 1 kilogram (kg) 1000 millilitres (ml) = 1 litre (l) Speed, Distance, Time Speed = Distance Time Time = Distance Speed Distance = Speed x Time Distance Speed Time

TOPIC QUESTIONS 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 Cube Numbers 1 2 4 3 9 16 5 25 1x1 = 1 2x2 = 4 3x3 = 9 4x4 = 16 5x5 = 25 6x6 = 36 7x7 = 49 8x8 = 64 9x9 = 81 10x10 = 100 11x11 = 121 12x12 = 144 1x1x1 = 1 2x2x2 = 8 3x3x3 = 27 4x4x4 = 64 5x5x5 = 125 6x6x6 = 216 7x7x7 = 343 8x8x8 = 512 9x9x9 = 729 10x10x10 = 1000 11x11x11 = 1331 12x12x12 = 1728 1 1 1 1 2 8 2 2 3 27 3 3 4 64 4 4 5 125 5 5

Powers Powers of 2: 21 22 23 24 25 Powers of 10: 101 102 103 104 105 21 22 23 24 25 The same as: (2x2) (2x2x2) (2x2x2x2) (2x2x2x2x2) Powers of 10: 101 102 103 104 105 The same as: (10x10) (10x10x10) (10x10x10x10) (10x10x10x10x10)

The multiples of a number are simply its Times Tables 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: The factors of a number are numbers that can divided exactly into it. e.g. 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

Prime numbers are only divisible by 1 and themselves. Triangle Numbers 1 3 6 10 15 21 28 36 45 55 ………………… 2 3 4 5 6 7 8 9 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 …………………

TOPIC QUESTIONS 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

TOPIC QUESTIONS 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 b a d a= Centre of circle b= Radius c= Diameter d= Circumference e= Chord f= Arc g= Tangent

TOPIC QUESTIONS What are the correct circle words for? A= B= C= D= E=

Area = mm2, cm2, m2……… Volume = mm3, cm3, m3……… x Square: Area = x2 l w Rectangle: Area = lw h b Triangle: Area = ½ bh Circle: Area = p r2 Circumference = 2pr r h b Parallelogram: Area = bh h w l Cuboid: Volume = l x w x h

TOPIC QUESTIONS 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? What is the volume of the cuboid? Find the area of the parallelogram? 13cm 13cm 12cm 10cm 2m 2m 5m 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 Picture Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 Nonagon 9 Decagon 10 Duo Decagon 12

TOPIC QUESTIONS 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 N 130o Acute angles are between 0o and 90o Obtuse angles are between 90o and 180o Reflex angles are between 180o and 360o

TOPIC QUESTIONS 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.

TOPIC QUESTIONS Find the missing angles in these diagrams 2 1 4 3 130o b c a 4 3 g 35o h f 200o d

A Regular shape has equal sides and equal angles 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 Exterior angle Interior angle

TOPIC QUESTIONS 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

TOPIC QUESTIONS 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?