Every numerical rule, conversion and identity across the 7 MYP1 units. No worked examples — pure reference for last-minute revision.
4 532 = 4 thousands + 5 hundreds + 3 tens + 2 ones
= 4 000 + 500 + 30 + 2
I=1 V=5 X=10 L=50 C=100 D=500 M=1000
Hindu-Arabic = 10 · Babylonian = 60 · Mayan = 20 · Binary = 2
÷2: last digit even (0,2,4,6,8)
÷3: digit-sum divisible by 3
÷4: last 2 digits divisible by 4
÷5: ends in 0 or 5
÷6: divisible by 2 AND 3
÷8: last 3 digits divisible by 8
÷9: digit-sum divisible by 9
÷10: ends in 0
A prime number has exactly TWO factors: 1 and itself.
Write a number as a product of primes only.
12 = 2 × 2 × 3 = 2² × 3
60 = 2 × 2 × 3 × 5 = 2² × 3 × 5
72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²
To find the GCF of two numbers:
1. Write the prime factorisation of each.
2. Pick the primes they SHARE,
each at its LOWEST power.
3. Multiply.
12 = 2 × 2 × 3
18 = 2 × 3 × 3
Shared: 2 × 3 = 6 → GCF = 6
To find the LCM of two numbers:
1. Write the prime factorisation of each.
2. Take EVERY prime that appears in either,
each at its HIGHEST power.
3. Multiply.
12 = 2 × 2 × 3
18 = 2 × 3 × 3
All: 2 × 2 × 3 × 3 = 36 → LCM = 36
5³ means 5 × 5 × 5 = 125
2⁴ means 2 × 2 × 2 × 2 = 16
In 5³ : 5 is the BASE, 3 is the EXPONENT (or INDEX).
√81 = 9 because 9 × 9 = 81
√144 = 12 because 12 × 12 = 144
1³=1 2³=8 3³=27 4³=64 5³=125
6³=216 7³=343 8³=512 9³=729 10³=1000
1. Brackets
2. Indices (powers and roots)
3. Division & Multiplication (left → right)
4. Addition & Subtraction (left → right)
% = decimal × 100 (move decimal point 2 places RIGHT)
decimal = % ÷ 100 (move decimal point 2 places LEFT)
% = (numerator ÷ denominator) × 100
1/2=50% 1/3≈33.3% 1/4=25% 1/5=20%
1/8=12.5% 1/10=10% 3/4=75% 2/3≈66.7%
amount = (percent ÷ 100) × quantity
= decimal × quantity
10 % of x = x ÷ 10
5 % = half of 10 %
1 % = x ÷ 100
20 % = double 10 %
whole = part ÷ (percent ÷ 100)
% change = ((new − old) ÷ old) × 100 %
To INCREASE 50 by 20 %:
→ multiply by 1.20
→ 50 × 1.20 = 60
To DECREASE 80 by 25 %:
→ multiply by 0.75 (because 100 % − 25 % = 75 %)
→ 80 × 0.75 = 60
$120 with 30 % off:
Way 1 — subtract: discount = 30 % of $120 = $36
sale price = $120 − $36 = $84
Way 2 — short way: pay 100 % − 30 % = 70 % of $120
$120 × 0.70 = $84
$20 with 15 % tax added:
Way 1 — add: tax = 15 % of $20 = $3
final price = $20 + $3 = $23
Way 2 — short way: pay 100 % + 15 % = 115 % of $20
$20 × 1.15 = $23
Backpack $30, with 10 % off, then 15 % tax:
After discount: $30 − 10 % = $30 × 0.90 = $27
After tax: $27 + 15 % = $27 × 1.15 = $31.05
3, 7, 11, 15, 19, … (+4 each step)
75, 68, 61, 54, 47 (−7 each step)
Position: 1 2 3 4 … n
Term: 3 5 7 9 … ?
Each term is 2 more than the last → pattern adds 2.
Rule for the n-th term: 2n + 1
7 × h is written as 7h
n × 3 is written as 3n (number first)
y × y is written as y²
a × b is written as ab
"5 more than n" → n + 5
"5 less than n" → n − 5
"5 times n" → 5n
"n divided by 5" → n ÷ 5 (or n/5)
"twice n, plus 7" → 2n + 7
Evaluate 2x + 3 when x = 5:
2(5) + 3
= 10 + 3
= 13
Whatever you do to one side of an equation,
you MUST do the same thing to the other side.
x + 7 = 12 → subtract 7 → x = 5
m − 9 = 4 → add 9 → m = 13
5k = 20 → divide by 5 → k = 4
p ÷ 10 = 4 → multiply by 10 → p = 40
Solve 2x + 3 = 11
Step 1 — subtract 3: 2x = 8
Step 2 — divide by 2: x = 4
Check: 2(4) + 3 = 11 ✓
Acute — less than 90°
Right — exactly 90°
Obtuse — more than 90°, less than 180°
Straight — exactly 180°
Reflex — more than 180°, less than 360°
Complementary angles add to 90°
Supplementary angles add to 180°
Angles on a straight line add to 180°
Angles around a point add to 360°
Vertically opposite angles are EQUAL
Complement of 35° = 90° − 35° = 55°
Supplement of 110° = 180° − 110° = 70°
Acute — all three angles less than 90°
Right — one angle exactly 90°
Obtuse — one angle more than 90°
Equilateral — all 3 sides equal (all angles = 60°)
Isosceles — 2 sides equal (2 base angles equal)
Scalene — all sides different (all angles different)
The three interior angles of ANY triangle add to 180°.
If two angles are 50° and 60°,
the third angle = 180° − 50° − 60° = 70°.
The four interior angles of ANY quadrilateral add to 360°.
(Why: cut along a diagonal into 2 triangles → 2 × 180° = 360°.)
Square — 4 equal sides, 4 right angles
Rectangle — opposite sides equal, 4 right angles
Parallelogram — opposite sides parallel & equal
Rhombus — parallelogram with 4 equal sides
Trapezium — exactly 1 pair of parallel sides
Kite — 2 pairs of equal adjacent sides
Multiply (or divide) the TOP and the BOTTOM
by the SAME number.
1/2 = 2/4 = 3/6 = 5/10 = 50/100
12/18: GCF of 12 and 18 is 6
12 ÷ 6 = 2, 18 ÷ 6 = 3
12/18 = 2/3 (lowest terms)
Method 1 — common denominator:
3/4 vs 5/6 → 9/12 vs 10/12 → 5/6 is bigger
Method 2 — convert to decimal:
3/4 = 0.75, 5/6 ≈ 0.83 → 5/6 is bigger
2/7 + 3/7 = 5/7
7/9 − 4/9 = 3/9 = 1/3
1/2 + 1/4: common denom 4
1/2 = 2/4
2/4 + 1/4 = 3/4
2/3 + 1/4: common denom 12 (LCM of 3 and 4)
2/3 = 8/12, 1/4 = 3/12
8/12 + 3/12 = 11/12
(top × top)
———————————
(bottom × bottom)
2/3 × 4/5 = (2 × 4) / (3 × 5) = 8/15
1. KEEP the first fraction
2. CHANGE ÷ to ×
3. FLIP the second fraction (its reciprocal)
2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3
7/4 : 7 ÷ 4 = 1 remainder 3 → 1 ¾
11/3: 11 ÷ 3 = 3 remainder 2 → 3 ⅔
(whole × denom) + numerator
————————————————————————————
same denominator
2 ¾ : (2 × 4) + 3 = 11 → 11/4
Categorical — sorts into groups
(favourite colour, country, sport)
Numerical — measured as numbers
(height, age, price, score)
Bar chart — compare counts across categories
Pie chart — show parts of a whole (% or fraction)
Line graph — show change over time
Pictogram — counts shown with picture symbols
angle of a slice = (slice's % ÷ 100) × 360°
25% slice → 90° (a quarter)
50% slice → 180° (a half)
33⅓% slice → 120° (a third)
mean = (sum of all values) ÷ (number of values)
For 4, 7, 9, 6, 4:
sum = 30, count = 5
mean = 30 ÷ 5 = 6
1. Put the values in order.
2. Pick the middle one.
4, 7, 9, 6, 4 → 4, 4, 6, 7, 9 → median = 6
For an even count, average the two middle values.
Mode = value(s) that appear most often.
4, 7, 9, 6, 4 → mode = 4 (it appears twice)
A data set may have NO mode, ONE mode, or MORE THAN ONE.
range = biggest value − smallest value
12, 5, 18, 7, 11 → 18 − 5 = 13
Rectangle: P = 2 × (length + width)
Square: P = 4 × side
Equilateral △: P = 3 × side
Any polygon: add all the sides
Rectangle: A = length × width
Square: A = side × side (= side²)
Triangle: A = (base × height) ÷ 2
Parallelogram: A = base × height
1. Split the shape into rectangles / triangles.
2. Find each area.
3. ADD them up — or SUBTRACT, if a piece is cut out.
Rectangle 10 × 8 with a 3 × 3 hole cut out:
80 − 9 = 71 m²
Cube: V = side × side × side (= side³)
Rectangular prism: V = length × width × height
Any prism: V = (area of base) × height
Cube (side s):
SA = 6 × s² (6 identical square faces)
Rectangular prism (ℓ × w × h):
SA = 2(ℓ × w) + 2(ℓ × h) + 2(w × h)
Example 8 × 5 × 3:
SA = 2(40) + 2(24) + 2(15) = 80 + 48 + 30 = 158 cm²