Paper 1 is non-calculator. The formula sheet is there for some boards — but not all. OCR does not provide one at all, and even where a sheet is provided, a significant number of the things students drop marks on are not included. Before relying on anything listed here, check your exam board's specification to confirm what is and is not given to you in the exam. Some of these, such as compound interest, may already be on your sheet. Know the difference before Thursday.
Circles and sectors
Area of a circle and circumference — confirm with your spec whether these are given:
Area of a sector and arc length — these are almost never provided and are regularly tested:
Where \(\theta\) is the angle of the sector in degrees and \(r\) is the radius. Both formulas use the same fraction of the full circle — get that fraction right first, then multiply.
Interior angles of polygons
Where \(n\) is the number of sides. For a regular polygon, divide that total by \(n\) to get each interior angle.
Straight line graphs
Gradient
You need two coordinates that sit on the line. Pick points that are easy to read exactly off the grid.
Midpoint of a line segment
Both coordinates get averaged. A common error is dividing only one of them.
Distance between two points
This is Pythagoras applied to coordinates. The square root wraps the whole expression — do not forget it at the end.
Parallel and perpendicular lines
- Parallel lines have the same gradient
- Perpendicular lines have gradients that are negative reciprocals: if one gradient is \(m\), the perpendicular is \(-\dfrac{1}{m}\)
Example: gradient \(\frac{1}{3}\) gives a perpendicular gradient of \(-3\).
Completing the square
For a quadratic \(x^2 + bx + c\), the completed square form is:
The turning point of the curve \(y = x^2 + bx + c\) is directly read from the completed square form as:
The x-coordinate of the turning point is \(-\dfrac{b}{2}\) — note the sign change. The y-coordinate is the constant left over after completing the square.
Graph transformations
Do not try to picture the whole graph shifting. Think about what happens to individual coordinates. Every transformation below describes how a point \((x,\ y)\) on \(f(x)\) moves.
Point \((x,\ y)\) moves to \((x + a,\ y)\)
Translates right by \(a\)
Point \((x,\ y)\) moves to \((x - a,\ y)\)
Translates left by \(a\)
Point \((x,\ y)\) moves to \((x,\ y + a)\)
Translates up by \(a\)
Point \((x,\ y)\) moves to \((x,\ y - a)\)
Translates down by \(a\)
Point \((x,\ y)\) moves to \((x,\ ay)\)
Vertical stretch, scale factor \(a\)
Point \((x,\ y)\) moves to \(\left(\dfrac{x}{a},\ y\right)\)
Horizontal stretch, scale factor \(\dfrac{1}{a}\)
\(f(x - a)\) moves the graph right, not left. \(f(x + a)\) moves it left, not right. Think about the coordinate effect rather than the sign.
Exact trigonometric values
These are not provided on the formula sheet. You are expected to know all of them for Paper 1. The full set required by the specification is below.
| 0° | 30° | 45° | 60° | 90° | |
|---|---|---|---|---|---|
| sin | \(0\) | \(\dfrac{1}{2}\) | \(\dfrac{\sqrt{2}}{2}\) | \(\dfrac{\sqrt{3}}{2}\) | \(1\) |
| cos | \(1\) | \(\dfrac{\sqrt{3}}{2}\) | \(\dfrac{\sqrt{2}}{2}\) | \(\dfrac{1}{2}\) | \(0\) |
| tan | \(0\) | \(\dfrac{1}{\sqrt{3}}\) | \(1\) | \(\sqrt{3}\) | undefined |
If you are not confident with these, the triangle method is a reliable way to derive them quickly from two triangles. Stick to whichever method you have learnt and practised. If you want a quick recap, this short video covers it well — but do not try to learn a new method the night before the exam.
Compound interest, growth and depreciation
Check your formula sheet — this may be provided. If it is not, the formula is:
- \(A\) = final amount
- \(P\) = principal (starting amount)
- \(r\) = percentage rate
- \(n\) = number of years or time periods
Recurring decimals to fractions
Let \(x\) equal the recurring decimal first. Multiply to shift one full recurring cycle to the left of the decimal point, subtract to eliminate the recurring part, then solve for \(x\).
Example: \(x = 0.\overline{3}\). Multiply both sides by 10: \(10x = 3.\overline{3}\). Subtract: \(9x = 3\), so \(x = \dfrac{1}{3}\). For a two-digit recurring block like \(0.\overline{27}\), multiply by 100 instead.
Probability rules
- All probabilities sum to 1
- AND (both events occur) — multiply the probabilities
- OR (at least one event occurs, mutually exclusive) — add the probabilities
For tree diagrams: multiply along the branches, add between branches when combining outcomes.
Index laws
- \(a^m \times a^n = a^{m+n}\)
- \(a^m \div a^n = a^{m-n}\)
- \((a^m)^n = a^{mn}\)
- \(a^0 = 1\) for any non-zero \(a\)
- \(a^{-n} = \dfrac{1}{a^n}\)
- \(a^{\frac{1}{n}} = \sqrt[n]{a}\)
- \(a^{\frac{m}{n}} = \left(\sqrt[n]{a}\right)^m\) — root first, then power
Surds
- \(\sqrt{a} \times \sqrt{b} = \sqrt{ab}\)
- \(\sqrt{a} \div \sqrt{b} = \sqrt{\dfrac{a}{b}}\)
- To rationalise a denominator with \(\sqrt{b}\): multiply numerator and denominator by \(\sqrt{b}\)
- To rationalise \(a + \sqrt{b}\): multiply by the conjugate \(a - \sqrt{b}\)
Always simplify first. \(\sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3}\). Working with unsimplified surds through a multi-step question almost always leads to errors.
Final exam reminders
- Show all working, even when uncertain. A wrong answer with correct method can still earn marks.
- Do not leave blanks. An attempt is always better than nothing.
- Check negative signs carefully in every step of a calculation.
- Re-read the question before writing your final answer to make sure you have answered what was actually asked.
- One mark can be the difference between grade boundaries.
Time management in the exam
When you reach a question, spend roughly 30 seconds reading it before writing anything. If the method is clear, begin and keep one eye on the time relative to the marks available. A 4-mark question should not take ten minutes. If you are on track, stay with it.
If within that first 30 seconds the question does not feel like your strongest area, mark it and move on immediately. Do not start a question half-committed. Come back to it once the rest of the paper is done.
If you have started a question and find yourself spending more time than the mark allocation suggests without clear progress, leave it and return later. A fresh look later in the session will often unlock something that felt stuck the first time round.
The goal is always to secure every mark you are capable of across the whole paper, not to spend all your time on the questions that feel hardest.
