NCEA Numeracy flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Order of operations

A fixed sequence for evaluating expressions: work through brackets first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.

Percentage change formula

Change expressed relative to the original: (new value − old value) ÷ old value × 100. A positive result is an increase, a negative result a decrease.

Ratio sharing

To split an amount in a given ratio, add the ratio numbers to get total parts, divide the amount by total parts to find one share, then multiply by each ratio number.

nth term of linear pattern

For a sequence with constant difference d, the nth term is d·n + c, where c equals the first term minus d. Substitute n to check the formula.

Multiplying by reciprocal

Dividing by a fraction equals multiplying by its reciprocal, so a/b ÷ c/d becomes a/b × d/c. Flip the second fraction, then multiply numerators and denominators.

Standard form notation

A number written as a × 10^n where 1 ≤ a < 10 and n is an integer. Multiplying such numbers adds the powers of ten; dividing subtracts them.

Adding fractions rule

Fractions can only be added or subtracted once they share a common denominator. Convert each fraction, combine the numerators, then simplify the result.

Substitution into formulas

Replace every variable with its given value, placing negative values in brackets, then evaluate using order of operations to get a single numerical result.

Area of a triangle

Area equals one half times base times perpendicular height: A = ½ × b × h. The height must meet the base at right angles, not along a slanted side.

Circle circumference and area

Circumference is the distance around a circle, C = πd = 2πr. Area is the space inside, A = πr². Use π ≈ 3.14 unless told otherwise.

Volume of a prism

A prism's volume equals its cross-sectional area multiplied by its length. A cylinder is a circular prism, so its volume is πr²h.

Pythagoras theorem

In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c², with c opposite the right angle.

Angle sum facts

Angles on a straight line add to 180°, angles around a point add to 360°, and the three interior angles of any triangle add to 180°.

Speed distance time

Distance equals speed multiplied by time. Rearranged, time equals distance divided by speed and speed equals distance divided by time. Keep units consistent.

Metric unit conversions

Length: 1 m = 100 cm = 1000 mm, 1 km = 1000 m. Area: 1 hectare = 10 000 m². Capacity: 1 L = 1000 mL = 1000 cm³.

Scale factor on drawings

A scale of 1:100 means one unit on the drawing represents 100 of the same units in reality. Multiply drawing lengths by the scale factor to find real lengths.

Mean median mode

Mean is the sum of values divided by how many values there are. Median is the middle value once data is ordered. Mode is the most frequent value.

Interquartile range

IQR equals the upper quartile minus the lower quartile. It measures the spread of the middle 50% of data and is not distorted by extreme values.

Complement probability rule

The probability that an event does not happen equals 1 minus the probability that it does: P(not A) = 1 − P(A), since all outcomes sum to 1.

Independent events multiplication

When two events do not affect each other, the probability both occur is the product of their separate probabilities: P(A and B) = P(A) × P(B).

Mutually exclusive events

Events that cannot happen at the same time. For these, the probability of either occurring is the sum: P(A or B) = P(A) + P(B).

Relative frequency

An estimate of probability from data: the number of times an event occurred divided by the total number of trials, expressed as a fraction or decimal.

Median with even count

When a data set has an even number of values, the median is the mean of the two middle values after the data has been ordered from smallest to largest.

Identifying outliers

A common rule labels a value an outlier if it lies more than 1.5 times the interquartile range below the lower quartile or above the upper quartile.

Best-buy unit price

Divide the price by the quantity to get the cost per unit, for example per 100 g or per litre. Convert to matching units before comparing products.

Simple interest formula

Interest equals principal × rate × time, I = P × r × t, with the rate written as a decimal per year and time in years. Add interest to principal for the total.

Compound interest formula

Amount equals principal × (1 + r)^n, where r is the interest rate per period as a decimal and n is the number of compounding periods.

Adding GST to a price

To add 15% GST, multiply the price by 1.15. To remove GST from a GST-inclusive price, divide by 1.15 rather than subtracting 15% of the total.

Wages with overtime

Total pay equals the normal hourly rate times normal hours, plus overtime hours multiplied by the overtime rate, which is often 1.5 times the normal rate.

Budget surplus or deficit

Subtract all fixed and variable costs from total income. A positive result is a surplus; a negative result is a deficit that must be covered or reduced.

Discount then GST order

Apply the discount first by multiplying the price by (1 − discount rate), then add GST to the discounted amount. The order changes the final price.

Estimating to check answers

Round numbers to convenient values, compute an approximate answer mentally, then compare it with the exact result to catch place-value or unit errors.