LANTITE Numeracy cheat sheet

Order of operations: evaluate brackets first, then indices, then multiplication and division from left to right, then addition and subtraction from left to right.

Percentage change = (new value − old value) ÷ old value × 100%; an increase of p% multiplies the original amount by (1 + p/100).

To find a fraction a/b of an amount N, calculate (a/b) × N; to divide by a fraction, multiply by its reciprocal.

For a ratio a:b, the total number of parts is a + b, and each share equals (part ÷ total parts) × total amount.

Direct proportion has the form y = kx; inverse proportion has the form y = k/x or xy = k.

Expand brackets using a(b + c) = ab + ac, and simplify by collecting like terms.

Solve a linear equation by applying the same operation to both sides until the variable is isolated.

Index rules: a^m × a^n = a^(m+n), a^m ÷ a^n = a^(m−n), and a^−n = 1/a^n for a ≠ 0.

When rounding, identify the required place value and check the next digit; if it is 5 or more, round up.

Metric conversions: 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm, 1 kg = 1000 g, and 1 L = 1000 mL.

Area formulas: rectangle = length × width; triangle = ½ × base × perpendicular height; circle = πr².

Perimeter is the total boundary length, while area is measured in square units.

Volume of a prism = area of uniform cross-section × length; volume of a cylinder = πr²h.

Pythagoras' theorem: in a right-angled triangle, a² + b² = c², where c is the hypotenuse.

Angle facts: angles on a straight line sum to 180°, angles at a point sum to 360°, and interior angles of a triangle sum to 180°.

For similar figures with length scale factor k, areas scale by k² and volumes scale by k³.

Speed = distance ÷ time; ensure distance and time units match before calculating.

One hectare = 10,000 m², equivalent to a square with side length 100 m.

Mean = sum of values ÷ number of values; median = middle value when ordered; mode = most frequent value; range = maximum − minimum.

Probability of an event = favourable outcomes ÷ total equally likely outcomes, and every probability lies between 0 and 1.

Complement rule: P(not event) = 1 − P(event).

For independent events, P(A and B) = P(A) × P(B).

Relative frequency = number of occurrences ÷ total trials, and it can estimate probability.

Pie chart sector angle = (category frequency ÷ total frequency) × 360°.

The interquartile range = upper quartile − lower quartile and describes the spread of the middle 50% of data.

The mean is more affected by outliers than the median, so the median is often preferred for skewed data.

A random sample is more likely to represent the population than a biased or convenience sample.