NCEA Pāngarau Co-requisite (NZQA Standard 32412) flashcards

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

Order of operations

The agreed sequence for evaluating expressions: brackets first, then exponents, then multiplication and division left to right, then addition and subtraction left to right.

Highest common factor

The largest whole number that divides exactly into two or more numbers. For 12 and 18 the HCF is 6, used to simplify fractions.

Ratio sharing

Dividing a total in a given ratio by adding the ratio numbers to find total parts, dividing the total by that, then multiplying each ratio number by the share.

Linear relationship

A relationship with a constant rate of change, written y = mx + c, where m is the gradient and c the y-intercept. Its graph is a straight line.

Index laws

Rules for powers: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, and a⁰ = 1 for any non-zero a.

Standard form

Writing a number as a × 10ⁿ with 1 ≤ a < 10. For example, 0.0035 is written as 3.5 × 10⁻³.

Percentage increase

Multiplying by 1 plus the rate as a decimal. A 20% increase is a multiply by 1.20; a 20% decrease is a multiply by 0.80.

Area of a triangle

Half the base multiplied by the perpendicular height: A = ½ × b × h. The height must be measured at right angles to the chosen base.

Circumference and area of a circle

Circumference C = 2πr or πd; area A = πr². The radius is half the diameter, and π is approximately 3.14.

Volume of a prism

The area of the uniform cross-section multiplied by the length of the prism. A cylinder is a prism with circular cross-section: V = 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.

Angle sum of a triangle

The three interior angles of any triangle add to 180°. This lets you find a missing angle when the other two are known.

Co-interior angles

Angles between two parallel lines on the same side of a transversal. They are supplementary, meaning they add to 180°.

Scale factor

The ratio between a drawing and the real object. A scale of 1:100 means 1 cm on the drawing represents 100 cm in reality.

Unit conversion for area

Area units square the length conversion: 1 m = 100 cm, so 1 m² = 100 × 100 = 10 000 cm². Volume units cube it.

Mean

The arithmetic average: add all the values and divide by how many there are. It is affected by extreme values more than the median is.

Median

The middle value when data is ordered from smallest to largest. With an even number of values, average the two middle values.

Range of a data set

The difference between the largest and smallest values. It measures the spread of the data but ignores everything between the extremes.

Probability of an event

The number of favourable outcomes divided by the total number of equally likely outcomes. Values lie between 0 and 1 inclusive.

Complementary probability

The probability that an event does not happen: P(not A) = 1 − P(A). The two probabilities always add to exactly 1.

Independent events

Events where one outcome does not affect the other. The probability of both occurring is P(A) × P(B).

Random sample

A sample in which every member of the population has an equal chance of being selected, reducing bias in conclusions drawn from the data.

Two-way table

A table showing frequencies for two categorical variables. Probabilities are found by dividing a cell or total by the grand total.

Correlation versus causation

Correlation means two variables change together in a pattern. Causation means one causes the other, which requires more evidence than a pattern alone.

Estimation before calculating

Rounding numbers to convenient values to get an approximate answer, then using it to check whether the exact calculated result is reasonable.

Working backwards

A strategy that starts from the final result and applies inverse operations step by step to find an unknown starting value.

Generalisation

Expressing a pattern found across several cases as a rule in words and then as an algebraic formula, such as nth term = 3n + 1.

Justifying an answer

Stating the calculated values, the rule or formula used, and any assumptions made, so the conclusion is supported by evidence rather than assertion.

Unit price

The cost of one unit of a product, found by dividing total price by quantity. Comparing unit prices identifies the best value among options.

GST calculation

New Zealand GST is 15%. Add GST by multiplying by 0.15; find a GST-inclusive price by multiplying by 1.15; remove GST by dividing by 1.15.

Speed, distance, time

Speed = distance ÷ time; distance = speed × time; time = distance ÷ speed. Units must be consistent, such as kilometres and hours for km/h.

Compound interest

Interest calculated on both the principal and previously earned interest: A = P(1 + r)ⁿ, where r is the rate per period as a decimal and n the number of periods.