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NCEA Level 2 Maths formula sheet (formulae sheet)

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Formula sheet

The card below opens today's Level 2 Maths paper with the sheet in the drawer. The contents follow in our own layout. This is the 2025 sheet, the latest NZQA has published, and NZQA's Mathematics and Statistics subject page links a Level 2 formulae sheet. NZQA's 2026 specification for the three standards does not mention the sheet, so check it in the room.

Formula sheet

NCEA Level 2 Maths

Open formula sheet

Quadratic equations

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}Quadratic formula, for ax² + bx + c = 0
\Delta=b^2-4acDiscriminant

Logarithms

y=b^x\Rightarrow x=\log_byDefinition
\log_b(xy)=\log_b(x)+\log_b(y)Log of a product
\log_b\left(\frac{x}{y}\right)=\log_b(x)-\log_b(y)Log of a quotient
\log_b\left(x^n\right)=n\log_bxLog of a power
y=e^x\Rightarrow x=\log_ey=\ln yNatural logarithm

Calculus

\frac{d}{dx}\left(x^n\right)=nx^{n-1}Derivative of a power
f'(x)=x^n\Rightarrow f(x)=\frac{x^{n+1}}{n+1}+cAntiderivative of a power

Standard normal table

The right-hand half of the sheet is the standard normal table, with z from 0.0 to 3.9 down the side and the second decimal place across. Each entry gives the probability that the standardised normal variable Z lies between 0 and z, and a block of differences on the right helps with a third decimal place. The formula z = (x − μ) ÷ σ is printed with it.

What is not on the sheet

  • Areas and volumes. NZQA's 2026 specification says candidates should be familiar with common 2D and 3D shapes and their formulae, for 91261 and 91262. None is printed.
  • The product, quotient and chain rules. The calculus section has only the derivative of x to the power n and its reverse.
  • Exponential growth and compound interest. NZQA says you may have to form and solve exponential equations for growth, decay and compound interest. No formula is given.
  • Change of base for logarithms. The sheet has the product, quotient and power laws, but not the change of base rule that the Level 3 booklet prints.
  • Probability rules. There is no addition rule or conditional probability line at Level 2. You must know the probability tree method.
  • Which formula to use. The sheet does not say when to use the discriminant or when a log law applies.

NZQA also says candidates must bring an approved calculator, that algebraic techniques must be shown rather than just the correct answer, and that probability working should be given to a minimum of three decimal places.

How to use the sheet in the exam

  1. Say which standard the question is from, so you know which half of the sheet to look at.
  2. Write down the formula before you substitute, so a slip in the arithmetic still earns the method.
  3. Show algebraic working, as NZQA asks, instead of going straight to an answer on the calculator.
  4. Check the answer against the context: a negative length is not a solution.

Algebra: the quadratic formula and the discriminant

Solve 2x² − 3x − 5 = 0. Here a = 2, b = −3 and c = −5, and the discriminant tells you how many solutions to expect:

\Delta=b^2-4ac=(-3)^2-4(2)(-5)=9+40=49
x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{3\pm7}{4}\quad\text{so}\quad x=2.5\ \text{or}\ x=-1

A positive discriminant means two real solutions, and 49 is a perfect square, so both are rational. Practise this in our Algebra course, then press Mark to check your answer there:

Use the quadratic formula to find both roots.

Press Mark to have your answer marked in the Algebra course.

Calculus: finding a function from its gradient

A curve has gradient function f′(x) = 6x² − 4x + 1 and passes through (1, 3). Use the line that reverses x to the power n on each term:

f(x)=\frac{6x^3}{3}-\frac{4x^2}{2}+x+c=2x^3-2x^2+x+c

Substitute the point: f(1) = 2 − 2 + 1 + c = 3, so c = 2. The curve is f(x) = 2x³ − 2x² + x + 2.

Probability: the normal table

Heights are normal with a mean of 165 cm and a standard deviation of 10 cm. Find the probability that a height is between 165 and 177.8 cm. Standardise first: z = (177.8 − 165) ÷ 10 = 1.28. The table gives 0.3997 at z = 1.28, which is the row for 1.2 under the column 8. So the probability is 0.400 to three decimal places.

The Level 2 sheet and the others

The Level 1 Maths sheet is the opposite: areas, volumes, trigonometry in right-angled triangles and unit conversions, with no algebra. The Level 3 Calculus booklet has the trigonometry, the calculus rules and numerical methods. For how the Level 2 standards work, see the NCEA Level 2 Maths guide.

Exam answers

The answers and a worked mark scheme come with today's paper once it is marked. Sit the paper with the sheet open beside you, mark it, and the worked answers show which line or table each question wanted. We do not publish official or past paper answers. Every question on the daily paper is our own.

Use the sheet with today's paper

Uni-Sine publishes a free daily paper on the NCEA Level 2 Maths track. It is a short timed paper of 8 questions worth 25 to 35 marks, not a full NCEA exam, and it is not written by NZQA. Open the sheet from the paper itself, so the normal table and quadratic formula are one click away.

Common mistakes with the Level 2 Maths sheet

  • Forgetting the ± in the quadratic formula. You lose a solution.
  • Dropping the + c when you reverse a derivative.
  • Reading the normal table as the area to the left. It gives the area from 0 to z, so add 0.5 to get the area below a positive z.
  • Using the power line on 1/x. The reverse rule does not work when n = −1.

Common questions

Do you get a formula sheet in NCEA Level 2 Maths?
Yes. NZQA supplies a Formulae Sheet, L2-MATHF, with the exam for 91261, 91262 and 91267. It has the quadratic formula, logarithm laws, two calculus lines and a standard normal table.
When is the 2026 Level 2 Maths exam?
Thursday 19 November 2026, in the morning session, which starts at 9.30 am.
Are area and volume formulae on the Level 2 Maths sheet?
No. NZQA says candidates should already be familiar with common 2D and 3D shapes and their formulae.
Is the normal distribution table in the Level 2 exam?
Yes. The sheet prints a standard normal table with a block of differences.

Revision cards

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