MUST KNOW QUICK FACTS
MEMORISE
The following are the mathematical facts you need to memorise.
In order to learn how to use numbers, algebra, geometry and statistics you will need to have a basic recall of facts that can
then be applied. The UK curriculum in mathematics is now focussed on Mastery approaches to ensure that the best
students genuinely are so, and that more students get the best grades.
With this in mind the first step to mastery
comes from knowing the basic facts so that in school you can apply these facts.
Time maths facts
-
60 seconds in a minute
-
60 minutes in a hour
-
24 hours in a day
-
7 days in a week
-
52 weeks in a year
-
4 weeks in a month
-
365 days in a year
-
A leap year happens every 4 years: February has 29 days on a leap year
30 days hath September, April, June and November, All the rest have 31, Excepting February alone. Which only has but 28 days clear, And 29 in each leap year.
Example questions:
​
How many days are there in a leap year?
How many weeks are there in 3 months?
How many days in 3 weeks?
How many days are there in June and July combined?
What is quarter past 6 in the evening in 24hr clock time?
What is 21:19 in 12 hr am/pm time?
You need to recognise percentage, fraction and decimal equivalents.
​
50% = 1/2 = 0.5
10% = 1/10 = 0.1
30% = 3/10= 0.3
70% = 7/10 = 0.7
80% = 4/5 = 0.8
90% = 9/10 = 0.9
20% = 1/5 = 0.2
40% = 2/5= 0.4
60% = 3/5= 0.6
25% = 1/4 = 0.25
75% = 3/4 = 0.75
1% =1/100 = 0.01
3% =3/100 = 0.03
7% =7/100 = 0.07
A prime numbers has exactly 1 factor pair.
The pair is always 1 and the number itself.
1 is not a prime number, as it only has one factor: 1 x 1 = 1
​
2 is the only even prime number.
You should be able to list the first 10 prime
numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
A square number is a number multiplied by itself.
These are the first 10 square numbers: memorise them.
12 = 1 x 1= 1
22 = 2 x 2 = 4
32 = 3 x 3 = 9
42 = 4 x 4 =16
52 = 5 x 5 = 25
62 = 6 x 6 = 36
72 = 7 x 7 = 49
82 = 8 x 8 = 64
92 = 9 x 9 = 81
102 = 10 x 10 =100
A cubed number is a number multiplied
by itself twice, for example: 3³= 3 x 3 x 3
These are the first 10 cubed numbers: memorise them.
1³ = 1 x 1 x 1 = 1
2³ = 2 x 2 x 2 = 8
3³ = 3 x 3 x 3 = 27
4³ = 4 x 4 x 4 = 64
5³ = 5 x 5 x 5 = 125
6³ = 6 x 6 x 6 = 216
7³ = 7 x 7 x 7 = 343
8³ = 8 x 8 x 8 = 512
9³ = 9 x 9 x 9 = 729
10³ = 10 x 10 x 10 = 1000
Convert between commonly used imperial and metric measurements.
Learn by heart:
​
1 km = 5/8 mile
​
1 m = 39.37 inches
1 foot = 30.5 cm
1 inch = 2.54 cm
​
1 kg = 2.2 lb
1 gallon = 4.5 litres
1 litre = 1. 75 pints
Know all the number bonds to 100 that include multiples of 5:
e.g., 15+85, 45+55, 40+60, 25+75.
​
Number bonds to 10
(1+9, 3+7, 2+8, 3+7, 4+6, 5+5)
number bond to 1
0.1+0.9,
0.3+0.7,
0.2+0.8,
0.3+0.7,
0.4+0.6,
0.5+0.5
​
Must know how to convert between metric units:
10mg = 1cg
1000mg = 1g
100cg = 1g
100000cg = 1kg
1000g = 1kg
1000kg = 1 tonne
10mm = 1cm
1000mm = 1m
100cm = 1m
100000cm = 1km
1000m = 1km
10ml = 1cl
1000ml = 1l
100cl = 1l
100000cl = 1kl
1000l = 1kl
1/2 of a litre is 500ml
3/4 of a litre is 750 ml
1/4 of a litre is 250 ml
​
1/2 of a kilometre 500m
3/4 of a kilometre 750m
1/4 of a kilometre 250m
​
1/2 of a kilogram 500g
3/4 of kilogram 750g
1/4 of kilogram 250g
​
1/2 of a metre 50cm
3/4 of a metre 75cm
1/4 of a metre 25cm
Fraction addition and subtraction.
Know, off by heart, the following fraction addition and subtraction facts:
​
½ + ¼ = ¾
¾ - ½ = ¼
​
1/5 + 2/10 = 2/5
1/3 + 2/6 = 2/3
¼ + 2/8 = ½
¾ - ½ = ¼
¾ - 2/8 = ½
2/5 – 2/10 = 1/5
2/3 – 2/6 = 1/3
½ - 2/8 = ¼
Memorise simple conversions between percentages and degrees in a pie chart.
Must know conversions:
10% = 36°
​
25% = 90°
50% = 180°
75% = 270°
33% = 120° (roughly)
66% = 240° (roughly)
20% = 72°
Regular Polygons
​
A polygon is a plane (2D) shape with straight sides.
To be a regular polygon all the sides and angles must be the same:
​
Triangle - 3 Sides - Interior angle 60°
Square - 4 Sides - Interior angle 90°
Pentagon - 5 Sides - Interior angle 108°
Hexagon - 6 sides - Interior angle 120°
Heptagon - 7 Sides - Interior angle 128.57°
Octagon - 8 Sides - Interior angle 135°
Nonagon - 9 Sides - Interior angle 140°
Decagon - 10 Sides - Interior angle 144°
​
Any polygon - interior angle = (n-2) × 180° / n
Tricks and Tips for Doing Math in Your Head
​
Division tricks
​
Here’s a quick way to know when a number can be evenly divided by these certain numbers:
-
10 if the number ends in 0
-
9 when the digits are added together and the total is evenly divisible by 9
-
8 if the last three digits are evenly divisible by 8 or are 000
-
6 if it is an even number and when the digits are added together the answer is evenly divisible by 3
-
5 if it ends in a 0 or 5
-
4 if it ends in 00 or a two digit number that is evenly divisible by 4
-
3 when the digits are added together and the result is evenly divisible by the number 3
-
2 if it ends in 0, 2, 4, 6, or 8
