G1 Mathematics revision reference

This is a selected revision lookup for 2027 G1 Mathematics (K110). It is a study reference, rather than a statement of the formulas supplied in an examination. Use the links to revisit the full teaching.

Number, ratio, percentages and rates

• Standard form: A × 10ⁿ, with 1 ≤ A < 10 and integer n for a positive number. For a negative number, put the minus sign in front.
• Decimal places count places after the decimal point. Significant figures begin with the first nonzero digit. Keep guard digits while working and round the final result as requested.
• In a ratio a:b, the shares of the total are a/(a + b) and b/(a + b) for positive a,b. Convert quantities to matching units first.
• Direct proportion: y = kx; inverse proportion: y = k/x, with x nonzero. Find the constant k from a known pair.
• For a scale factor k in length, the area scale factor is k².
• Percentage change: divide the change by the original value, then multiply by 100%.
• A percentage increase of p% uses multiplier 1 + p/100; a decrease uses 1-p/100. For a reverse percentage, divide the final amount by the appropriate nonzero multiplier.
• Average speed is total distance divided by total time. It is not usually the average of the separate speeds.
• To convert km/h to m/s, divide by 3.6; reverse the conversion by multiplying by 3.6.

Example: after a 20% discount, a price is $48. The original price was 48÷0.8 = 60 dollars. Adding 20% to $48 would use the wrong whole.

Read more: Number and proportion.

Algebra and graphs

Expression names a quantity; equation states that two expressions are equal. In 3a², square a before multiplying by 3.

• Expand a bracket by multiplying every term: -2(3x-5) = -6x + 10.
• Combine like terms. For example, 3x + 2x = 5x, while 3x + 2 stays as it is.
• Factorise by taking out a common factor, or by finding two brackets for a quadratic of the form x² + px + q.
• Cancel factors in a product of algebraic fractions, preserving exclusions from the original denominators. Do not cancel terms across addition.

For ax² + bx + c = 0, with a ≠ 0:

For simultaneous linear equations, use substitution, elimination or a graph and check both original equations. For a nonvertical line y = mx + c, m is gradient and c is the y-intercept. Gradient is vertical change divided by horizontal change; a vertical line has no finite gradient.

G1 does not require the special squared-binomial and difference-of-squares identities, prime factorisation, or adding and subtracting algebraic fractions. Use the G1 methods in the linked lessons.

Read more: Algebra and equations and Functions and graphs.

Geometry, right triangles and mensuration

Congruent figures have the same shape and size. Similar figures have equal corresponding angles and proportional corresponding lengths.

Angles on a straight line sum to 180°; angles at a point sum to 360°. Vertically opposite angles are equal. For parallel lines cut by a transversal, corresponding angles and alternate angles are equal; interior angles on the same side sum to 180°.

For a right triangle with hypotenuse c:

Relative to an acute angle θ:

Choose the sides relative to the stated angle. Use degree mode when the angle is given in degrees.

Plane figures, with perpendicular height h:

• Triangle: A = (1/2)bh.
• Parallelogram: A = bh.
• Trapezium, parallel sides a,b: A = (1/2)(a + b)h.
• Circle, radius r: C = 2π r, A = π r².
• Sector, angle θ in degrees: arc length = θ/360 2π r; area = θ/360 π r².

Solids, using perpendicular height h:

• Prism: V = cross-sectional area × length.
• Pyramid: V = 1/3 × base area × h.
• Cylinder: V = π r²h; curved surface area = 2π rh.
• Cone: V = (1/3)π r²h; curved surface area = π rl, where l is slant height.
• Sphere: V = (4/3)π r³; surface area = 4π r².
• Cuboid, length l, width w, height h: V = lwh; surface area = 2(lw + lh + wh).
• Cube, side s: V = s³; surface area = 6s².

Add exposed bases to a curved surface area when the question asks for total surface area. A cone’s slant height and perpendicular height do different jobs.

Units: 1 m² = 10 000 cm² and 1 m³ = 1 000 000 cm³. Square or cube the length conversion factor. Use any value of π or final precision stated in the question; otherwise follow your paper’s instructions.

Read more: Geometry, Mensuration and Trigonometry.

Statistics and probability

• Mean: total of the values divided by the positive number of values.
• Median: the middle value in order, or the mean of the two middle values when the number is even.
• Mode: a most frequent value.
• Range: maximum minus minimum; interquartile range: upper quartile minus lower quartile.
• A percentile describes position in ordered data, rather than a percentage increase in a value.

For equally likely outcomes, probability = number of successful outcomes ÷ total number of outcomes. Probabilities lie from 0 to 1, inclusive. A graph’s labels and scale matter: a bar height counts intervals on its axis, not just visible grid squares.

Read more: Statistics and probability.