MMa

Maths

Edexcel · 1MA1 · Higher tier · every topic

Every topic on the Higher GCSE. Rate each one red (don't get it), orange (getting there) or green (confident). Tap a MW clip to watch that MathsWatch video (you'll need your school login), or Practise for questions that change every time.

✱ Non-calc likely on the non-calculator paperGCSE only may not be in your school mock, but can be in the real exam

For 2026 and 2027 exams you're given a formulae sheet. Everything below in Learn these is not on it, so you have to memorise it. Check the exact sheet with your teacher.

Learn these: number and algebra

What	Formula / fact
Index laws	a^m × aⁿ = a^m+n · a^m ÷ aⁿ = a^m−n · (a^m)ⁿ = a^mn · a⁰ = 1
Negative and fractional indices	a⁻ⁿ = 1/aⁿ · a^1/n = ⁿ√a · a^m/n = (ⁿ√a)^m
Surds	√a × √b = √(ab) · √a ÷ √b = √(a/b) · rationalise: multiply top and bottom by the surd
Percentage change	(change ÷ original) × 100
Reverse percentage	original = new amount ÷ multiplier (e.g. ÷ 1.2 after a 20% rise)
Simple interest	interest = principal × rate × years
Depreciation	value = original × (1 − r/100)ⁿ
Straight line	y = mx + c · gradient m = (y₂ − y₁) ÷ (x₂ − x₁)
Perpendicular gradient	m₁ × m₂ = −1 (flip and change sign)
Circle centre origin GCSE only	x² + y² = r² · a tangent is perpendicular to the radius
Linear sequence nth term	dn + (first term − d)
Quadratic sequence	a = second difference ÷ 2, then find the linear part
Difference of two squares	a² − b² = (a + b)(a − b)
Completing the square GCSE only	x² + bx + c = (x + b/2)² − (b/2)² + c; the turning point is (−b/2, c − (b/2)²)
Bounds	Max of a ÷ b = max a ÷ min b · max of a − b = max a − min b

Learn these: ratio, proportion and rates

Speed	speed = distance ÷ time
Density	density = mass ÷ volume
Pressure	pressure = force ÷ area
Direct proportion	y = kx (or y = kx², y = k√x…)
Inverse proportion	y = k/x (or y = k/x²…)
Gradient of a graph GCSE only	gradient of a distance–time graph = speed; velocity–time = acceleration
Area under a graph GCSE only	area under a velocity–time graph = distance travelled

Learn these: geometry

Rectangle · triangle · parallelogram	l × w · ½ × b × h · b × h
Cuboid volume	l × w × h
Cylinder	V = πr²h · surface area = 2πrh + 2πr²
Pyramid	V = ⅓ × base area × h (learn it to be safe)
Sector ✱ often	area = θ/360 × πr² · arc length = θ/360 × 2πr
Angles	on a straight line 180° · around a point 360° · in a triangle 180° · in a quadrilateral 360°
Parallel lines	alternate and corresponding angles are equal; co-interior angles add to 180°
Polygons	interior sum = (n − 2) × 180° · regular exterior angle = 360° ÷ n · interior + exterior = 180°
Bearings	measured clockwise from north, 3 figures; back bearing = ± 180°
Similar shapes GCSE only	length × k · area × k² · volume × k³
Congruence GCSE only	SSS, SAS, ASA, RHS

Exact trig values ✱ non-calc

	0°	30°	45°	60°	90°
sin	0	1/2	√2/2	√3/2	1
cos	1	√3/2	√2/2	1/2	0
tan	0	√3/3	1	√3	–

Circle theorems GCSE only

Angle at the centre is twice the angle at the circumference.
Angle in a semicircle is 90°.
Angles in the same segment are equal.
Opposite angles of a cyclic quadrilateral add to 180°.
Tangent and radius meet at 90°; two tangents from a point are equal.
Alternate segment theorem: the angle between a tangent and a chord equals the angle in the alternate segment.
The perpendicular from the centre to a chord bisects the chord.

Learn these: statistics and probability

Mean from a table	Σfx ÷ Σf (use midpoints for grouped data: an estimate)
Range · IQR	largest − smallest · upper quartile − lower quartile
Frequency density	frequency ÷ class width
Probability	P = favourable outcomes ÷ total · P(not A) = 1 − P(A) · all outcomes add to 1
AND / OR	independent: P(A and B) = P(A) × P(B) · mutually exclusive: P(A or B) = P(A) + P(B)
Relative frequency	frequency ÷ total trials · expected = probability × trials
Pie chart angle	frequency ÷ total × 360°
Stratified sample	group size ÷ population × sample size

On the formulae sheet (2026/2027)

Quadratic formula · circumference and area of a circle · area of a trapezium · Pythagoras · sin, cos, tan ratios · sine rule · cosine rule · area of a triangle (½ab sin C) · volume of a prism · volume and curved surface area of a cone · volume and surface area of a sphere · compound interest. You still need to know when to use each one.

Edexcel Higher: the papers

Paper	Calculator?	Time	Marks
Paper 1	No	1 h 30	80
Paper 2	Yes	1 h 30	80
Paper 3	Yes	1 h 30	80

About 1 minute per mark, with 10 minutes spare to check. Topics marked ✱ are likely to come up on the non-calculator paper: practise them by hand.

Get the method marks

Show every step. A wrong answer with the right method can still score most of the marks.
Write the formula first, then substitute, then calculate.
Don't round until the end. Keep full numbers in your calculator.
Give units and round as the question says (e.g. "to 1 decimal place").
"Show that" questions: write every line, and finish with the exact value given.

Non-calculator tricks

Percentages: find 10%, 5% and 1%, then build up.
Fractions: ÷ means flip the second fraction and multiply.
Estimating: round each number to 1 significant figure first.
Long multiplication: use the grid or column method and check with an estimate.
Know your squares to 15², cubes to 5³, and the exact trig values.

Common mistakes

−3² = −9 but (−3)² = 9.
Bearings are measured clockwise from north.
Area scale factor is k², volume is k³.
In compound interest, use the multiplier to the power of the years: 1.05³, not 1.15.
Reverse percentages: divide by the multiplier; don't take the percentage off the new amount.
Frequency density = frequency ÷ class width, not the other way round.

MathsWatch and other practice

Each topic shows its MathsWatch clip number. Tap it to go straight to that clip (sign in with your school login if asked). Watch the video, then do the questions.

For more exam questions, try Corbettmaths (videos, worksheets and 5-a-day) and Physics & Maths Tutor (past papers by topic).