Is this the official E-Math formula list?

The first half has every formula on SEAB's list for G3 Mathematics (K310), set out in our own layout with our own examples. The paper prints the list at the front, so the second half, what it leaves out, is the part to learn. Scholar Tests is not connected with MOE, SEAB or Cambridge.

Did the formula list change with the SEC?

No. From 2027 the O-Level becomes the Secondary Education Certificate, and the subject is called G3. SEAB's 2027 syllabus has the same topics and the same formula list as the 2026 O-Level one, so this sheet serves both.

How should answers be given?

To 3 significant figures unless the question says otherwise, and angles in degrees to 1 decimal place. Use your calculator's π or 3.142, unless the answer is wanted in terms of π. Show the working: essential working left out loses marks.

Yes. The print button gives both halves on plain paper, without this page's buttons or questions. Keep it beside you while you do past-year and practice papers until you no longer need to look.

G3 Mathematics (K310), was O-Level E-Math (4052)

O-Level E-Math formula sheet

The E-Math paper prints a short list of formulas on its second page. Below is every formula on that list, with a worked example for each, and then the longer list the paper does not give you: the quadratic formula, every area and volume outside the list, gradients, indices, probability and the circle properties.

What to learn by heart A-Math sheet

Given in the exam

SEAB prints these at the front of every paper. Know what each letter means and when to use each one, so you are not reading the list for the first time on the day.

Compound interest

Total amount
$A = P\left(1 + \dfrac{r}{100}\right)^{n}$
r is the rate for one period and n the number of periods.
Example: $5000 at 3% a year for 2 years: 5000 × 1.03² = $5304.50.

Mensuration

Curved surface area of a cone
$\pi r l$
Example: r = 3 cm, slant height l = 5 cm: 15π ≈ 47.1 cm².
Surface area of a sphere
$4\pi r^{2}$
Example: r = 2 cm: 16π ≈ 50.3 cm².
Volume of a cone
$\dfrac{1}{3}\pi r^{2} h$
Example: r = 3 cm, h = 4 cm: 12π ≈ 37.7 cm³.
Volume of a sphere
$\dfrac{4}{3}\pi r^{3}$
Example: r = 3 cm: 36π ≈ 113 cm³.
Area of a triangle
$\dfrac{1}{2}ab\sin C$
C is the angle between sides a and b.
Example: a = 8 cm, b = 5 cm, C = 30°: ½ × 8 × 5 × 0.5 = 10 cm².
Arc length
$r\theta$
θ in radians.
Example: r = 6 cm, θ = 1.2 rad: 7.2 cm.
Sector area
$\dfrac{1}{2}r^{2}\theta$
θ in radians.
Example: r = 6 cm, θ = 1.2 rad: ½ × 36 × 1.2 = 21.6 cm².

Trigonometry

Sine rule
$\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$
Use it when you know a side and the angle opposite it.
Example: a = 10 cm, A = 40°, B = 65°: b = 10 sin 65° ÷ sin 40° ≈ 14.1 cm.
Cosine rule
$a^{2} = b^{2} + c^{2} - 2bc\cos A$
Use it for two sides and the angle between them, or for three sides.
Example: b = 5 cm, c = 7 cm, A = 60°: a² = 25 + 49 − 35 = 39, so a ≈ 6.24 cm.

Statistics

Mean
$\bar{x} = \dfrac{\sum fx}{\sum f}$
For grouped data, x is the mid-value of each class.
Example: Scores 1, 2, 3 with frequencies 2, 5, 3: Σfx = 21, Σf = 10, mean = 2.1.
Standard deviation
$\sqrt{\dfrac{\sum fx^{2}}{\sum f} - \left(\dfrac{\sum fx}{\sum f}\right)^{2}}$
Example: Same data: Σfx² = 49, so √(4.9 − 2.1²) = √0.49 = 0.7.

Not given: learn these by heart

The paper does not print any of these, and the questions expect you to know them.

Numbers, percentage and rate

Simple interest
$I = \dfrac{PRT}{100}$
Example: $2000 at 4% a year for 3 years: I = $240.
Percentage change
$\dfrac{\text{change}}{\text{original}} \times 100\%$
Example: 80 rises to 92: 12 ÷ 80 × 100% = 15% increase.
Reverse percentage
$\text{original} = \dfrac{\text{new}}{1 \pm \text{rate}}$
Example: $64 after 20% off: 64 ÷ 0.8 = $80 before.
Standard form
$A \times 10^{n}, \quad 1 \le A < 10$
Example: 0.000 52 = 5.2 × 10⁻⁴.
Laws of indices
$a^{m} \times a^{n} = a^{m+n}, \quad a^{m} \div a^{n} = a^{m-n}$
$(a^{m})^{n} = a^{mn}, \quad a^{0} = 1, \quad a^{-n} = \dfrac{1}{a^{n}}$
$a^{\frac{1}{n}} = \sqrt[n]{a}, \quad a^{\frac{m}{n}} = \left(\sqrt[n]{a}\right)^{m}$
Example: 8^(2/3) = (∛8)² = 2² = 4.
Speed
$\text{speed} = \dfrac{\text{distance}}{\text{time}}$
$\text{average speed} = \dfrac{\text{total distance}}{\text{total time}}$
Example: 72 km/h ÷ 3.6 = 20 m/s.
Direct and inverse proportion
$y = kx \quad\text{and}\quad y = \dfrac{k}{x}$
Example: y = k/x and y = 6 when x = 2, so k = 12; when x = 3, y = 4.
Map scale
$\text{area scale} = (\text{length scale})^{2}$
Example: 1 : 50 000 means 1 cm to 0.5 km, so 1 cm² to 0.25 km².

Algebra

Special products
$(a + b)^{2} = a^{2} + 2ab + b^{2}$
$(a - b)^{2} = a^{2} - 2ab + b^{2}$
$a^{2} - b^{2} = (a + b)(a - b)$
Example: 51² − 49² = (51 + 49)(51 − 49) = 200.
Quadratic formula
$x = \dfrac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$
Not on the E-Math list. The A-Math list has it; this paper does not.
Example: x² − 3x − 1 = 0: x = (3 ± √13) ÷ 2, so x ≈ 3.30 or −0.303.
Completing the square
$x^{2} + px + q = \left(x + \dfrac{p}{2}\right)^{2} - \left(\dfrac{p}{2}\right)^{2} + q$
Example: x² + 6x + 1 = (x + 3)² − 8, so the minimum point is (−3, −8).
nth term of a linear sequence
$T_{n} = a + (n - 1)d$
Example: 5, 8, 11, ...: a = 5, d = 3, so Tₙ = 3n + 2.

Coordinates and graphs

Gradient
$m = \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}$
Example: (1, 2) and (4, 11): m = 9 ÷ 3 = 3.
Length of a line segment
$\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$
Example: (1, 2) and (4, 6): √(9 + 16) = 5.
Straight line
$y = mx + c$
c is where the line crosses the y-axis.
Example: Gradient 3 through (0, −2): y = 3x − 2.

Angles, triangles and circles

Pythagoras' theorem
$a^{2} + b^{2} = c^{2}$
c is the side opposite the right angle.
Example: Sides 6 cm and 8 cm: hypotenuse = √100 = 10 cm.
Trigonometric ratios
$\sin\theta = \dfrac{\text{opp}}{\text{hyp}}, \quad \cos\theta = \dfrac{\text{adj}}{\text{hyp}}, \quad \tan\theta = \dfrac{\text{opp}}{\text{adj}}$
Right-angled triangles only.
Example: Hypotenuse 10 cm, angle 30°: opposite = 10 sin 30° = 5 cm.
Angles of a polygon
$\text{interior sum} = (n - 2) \times 180^{\circ}$
$\text{exterior sum} = 360^{\circ}$
Example: A regular hexagon: each exterior angle 360° ÷ 6 = 60°, each interior angle 120°.
Circle properties
$\angle AOB = 2\angle ACB$
$\text{angle in a semicircle} = 90^{\circ}$
$\text{tangent} \perp \text{radius}$
$\text{cyclic quadrilateral: } \angle A + \angle C = 180^{\circ}$
O is the centre and C is on the circle. Also: angles in the same segment are equal, and tangents from one point are equal.
Example: An angle of 35° at the circumference stands on the same arc as 70° at the centre.
Similar figures
$\dfrac{A_{1}}{A_{2}} = \left(\dfrac{l_{1}}{l_{2}}\right)^{2}, \quad \dfrac{V_{1}}{V_{2}} = \left(\dfrac{l_{1}}{l_{2}}\right)^{3}$
Example: Lengths 2 : 3 give areas 4 : 9 and volumes 8 : 27.

Mensuration

Plane figures
$\text{parallelogram} = bh, \quad \text{trapezium} = \dfrac{1}{2}(a + b)h$
$\text{circle: } A = \pi r^{2}, \quad C = 2\pi r$
Example: A trapezium with parallel sides 5 cm and 9 cm, height 4 cm: 28 cm².
Prisms and cylinders
$V = \text{cross-section area} \times \text{length}$
$\text{cylinder: } V = \pi r^{2}h, \quad \text{curved surface} = 2\pi rh$
Example: A cylinder with r = 2 cm, h = 5 cm: V = 20π ≈ 62.8 cm³.
Volume of a pyramid
$\dfrac{1}{3} \times \text{base area} \times h$
Example: A 6 cm square base, height 5 cm: ⅓ × 36 × 5 = 60 cm³.
Radians
$\pi \text{ rad} = 180^{\circ}$
Example: 1.2 rad = 1.2 × 180° ÷ π ≈ 68.8°.
Area of a segment
$\dfrac{1}{2}r^{2}\theta - \dfrac{1}{2}r^{2}\sin\theta$
Sector minus triangle. θ in radians, and the calculator in radian mode.
Example: r = 6 cm, θ = 1.2 rad: 21.6 − 18 sin 1.2 ≈ 4.82 cm².
Unit conversions
$1\text{ m}^{2} = 10\,000\text{ cm}^{2}, \quad 1\text{ m}^{3} = 1\,000\,000\text{ cm}^{3}$
Example: 3.5 m² = 35 000 cm².

Vectors

Magnitude
$\left|\begin{pmatrix} x \\ y \end{pmatrix}\right| = \sqrt{x^{2} + y^{2}}$
Example: The vector (3, −4) has magnitude 5.
Vector between two points
$\overrightarrow{AB} = \overrightarrow{OB} - \overrightarrow{OA}$
Example: A(1, 2) and B(4, 6): AB = (3, 4).

Statistics and probability

Median and quartiles
$\text{median: the } \tfrac{n+1}{2}\text{th value}, \quad \text{IQR} = Q_{3} - Q_{1}$
Example: 9 values in order: the median is the 5th.
Probability
$P(A) = \dfrac{\text{favourable outcomes}}{\text{all outcomes}}, \quad P(\text{not } A) = 1 - P(A)$
$\text{exclusive: } P(A \text{ or } B) = P(A) + P(B)$
$\text{independent: } P(A \text{ and } B) = P(A) \times P(B)$
Example: Two fair coins: P(two heads) = ½ × ½ = ¼.

Use the formulas on a paper

A free E-Math paper in the O-Level's two-paper shape for each year, with every answer, to print or sit online.

Sec 3 E-Math paper Sec 4 E-Math paper

Questions parents ask

Is this the official E-Math formula list?: The first half has every formula on SEAB's list for G3 Mathematics (K310), set out in our own layout with our own examples. The paper prints the list at the front, so the second half, what it leaves out, is the part to learn. Scholar Tests is not connected with MOE, SEAB or Cambridge.
Did the formula list change with the SEC?: No. From 2027 the O-Level becomes the Secondary Education Certificate, and the subject is called G3. SEAB's 2027 syllabus has the same topics and the same formula list as the 2026 O-Level one, so this sheet serves both.
How should answers be given?: To 3 significant figures unless the question says otherwise, and angles in degrees to 1 decimal place. Use your calculator's π or 3.142, unless the answer is wanted in terms of π. Show the working: essential working left out loses marks.
Can I print it?: Yes. The print button gives both halves on plain paper, without this page's buttons or questions. Keep it beside you while you do past-year and practice papers until you no longer need to look.