NCEA Level 1 Pāngarau 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.

Significant figures

A count of meaningful digits starting from the first non-zero digit. Used to show the precision of a measurement or rounded answer.

Standard form

Writing a number as a × 10ⁿ where 1 ≤ a < 10 and n is an integer. Useful for very large or very small values.

Percentage change

Calculated as (new value − old value) ÷ old value × 100. A positive result is an increase, a negative result a decrease.

Ratio sharing

To divide an amount in a given ratio, add the ratio parts, divide the total by that sum, then multiply by each part.

Negative index

A power written with a negative exponent equals the reciprocal of the base raised to the positive exponent: x⁻ⁿ = 1/xⁿ.

Fraction multiplication

Multiply numerators together and denominators together: a/b × c/d = ac/bd. Cancel common factors first to keep numbers small.

Fraction division

Dividing by a fraction is the same as multiplying by its reciprocal: a/b ÷ c/d = a/b × d/c.

Rounding rule

To round to a given place, check the next digit. If it is 5 or more, round up; if 4 or less, keep the digit unchanged.

Estimation check

Round each value to one significant figure and compute mentally to confirm the order of magnitude of a calculator answer.

Expanding brackets

Multiply each term inside the bracket by the term outside. For two brackets, (x + a)(x + b) = x² + (a + b)x + ab.

Difference of two squares

A factorising pattern: a² − b² = (a − b)(a + b). Recognise it when two perfect squares are subtracted.

Solving linear equations

Keep the equation balanced by applying the same operation to both sides until the variable is isolated on one side.

Gradient of a line

The steepness of a straight line, calculated as rise ÷ run, or (y₂ − y₁)/(x₂ − x₁) for two points on the line.

Equation of a straight line

Written as y = mx + c, where m is the gradient and c is the y-intercept, the point where the line crosses the y-axis.

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.

Area of a triangle

Area = ½ × base × perpendicular height. The height must be measured at right angles to the chosen base.

Circumference of a circle

The distance around a circle: C = 2πr, or C = πd, where r is the radius and d is the diameter.

Volume of a prism

Volume = area of the uniform cross-section × length. A cylinder is a prism with circular cross-section: V = πr²h.

Trigonometric ratios

In a right triangle: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent. Used to find sides or angles.

Angles in a triangle

The three interior angles of any triangle always add up to 180°. This rule lets you find a missing angle.

Angles on a straight line

Angles that sit together on a straight line sum to 180°. Angles meeting at a full point sum to 360°.

Co-interior angles

When two parallel lines are crossed by a transversal, co-interior angles (same side of the transversal) add to 180°.

Mean, median, mode

Mean is the sum divided by the count; median is the middle value in order; mode is the most frequent value.

Range of data

The difference between the largest and smallest values. It measures spread, not the centre of the data.

Probability of an event

Number of favourable outcomes divided by the total number of equally likely outcomes. Always between 0 and 1.

Complementary probability

The probability an event does not happen is 1 minus the probability it does: P(not A) = 1 − P(A).

Compound interest formula

A = P(1 + r)ⁿ, where P is the principal, r the decimal interest rate per period and n the number of periods.

Reverse percentage

To find an original amount before a percentage change, divide the final amount by the decimal multiplier, not multiply.

Scale factor

The multiplier relating corresponding lengths in similar shapes or on a scale drawing. Areas scale by the square of it.

Unit rate method

Find the value for one unit by dividing, then multiply by the required quantity. Reliable for proportional reasoning problems.

Speed, distance, time

Distance = speed × time. Rearranged, speed = distance ÷ time and time = distance ÷ speed. Keep units consistent.