KS3 Mathematics key terms

133 terms with short definitions you can learn for the exam. Type to filter the list.

Key terms 101

Acute angle: An angle less than 90°.
Alternate angles: Angles on opposite sides of a line that crosses two parallel lines, inside the parallel lines (a Z shape). They are equal.
Area: The amount of flat space a 2-D shape covers. Measured in square units such as cm^{2} or m^{2}.
Arithmetic sequence: A sequence that goes up or down by the same amount each time, for example 3, 7, 11, 15 (add 4).
Bearing: A direction given as an angle measured clockwise from north, written with three figures, such as 045°.
Bisect: To cut exactly in half. An angle bisector cuts an angle into two equal angles.
Circumference: The distance all the way round a circle. C = πd.
Co-interior angles: Angles between two parallel lines on the same side of the crossing line (a C or U shape). They add up to 180°.
Coefficient: The number in front of a letter in a term. In 5x, the coefficient of x is 5.
Compound unit: A unit made from two other units, such as speed in km/h or density in g/cm^{3}.
Congruent: Exactly the same shape and size. One shape could fit exactly on top of the other, even if flipped or turned.
Coordinates: A pair of numbers (x, y) that gives the position of a point: x across first, then y up or down.
Correlation: A relationship between two variables on a scatter graph: positive, negative or none.
Corresponding angles: Angles in the same position at each place where a line crosses two parallel lines (an F shape). They are equal.
Cube number: A number multiplied by itself three times, such as 2^{3} = 8 or 4^{3} = 64.
Cube root: The number that cubes to give a value. The cube root of 27 is 3.
Denominator: The bottom number of a fraction. It shows how many equal parts the whole is split into.
Density: Mass per unit of volume. Density = mass ÷ volume, for example in g/cm^{3}.
Diameter: A straight line across a circle through its centre. It is twice the radius.
Direct proportion: Two quantities where one is always the same multiple of the other: if one doubles, so does the other. y = kx.
Enlargement: A transformation that changes the size of a shape by a scale factor, from a centre of enlargement. The angles stay the same.
Equation: A statement with an equals sign that is true only for some values of the letter, such as 2x + 1 = 9.
Equivalent fractions: Fractions that have the same value, such as 1/2, 2/4 and 5/10.
Error interval: The range of values a rounded number could have come from, written with inequalities, such as 6.5 ≤ x < 7.5.
Estimate: An approximate answer, often found by rounding each number to 1 significant figure first.
Expand: Multiply out brackets. 3(x + 4) expands to 3x + 12.
Expression: A collection of terms with no equals sign, such as 4a + 3b.
Exterior angle: The angle between one side of a polygon and the next side extended outwards. The exterior angles of any polygon add to 360°.
Factor: A whole number that divides exactly into another. The factors of 12 are 1, 2, 3, 4, 6 and 12.
Factorise: Put an expression into brackets by taking out a common factor. 6x + 9 = 3(2x + 3).
Formula: A rule linking two or more variables, such as A = lw for the area of a rectangle.
Frequency: How many times something happens or a value appears in a set of data.
Gradient: The steepness of a line: change in y ÷ change in x. In y = mx + c it is m.
Highest common factor (HCF): The largest number that is a factor of two or more numbers. The HCF of 12 and 18 is 6.
Hypotenuse: The longest side of a right-angled triangle, opposite the right angle.
Identity: A statement that is true for every value of the letter, such as 2(x + 1) ≡ 2x + 2.
Improper fraction: A fraction where the numerator is bigger than the denominator, such as 7/4.
Index (power): The small number that shows how many times a number is multiplied by itself. In 5^{3}, the index is 3.
Inequality: A statement using <, >, ≤ or ≥ that compares two values, such as x > 3.
Integer: A whole number. It can be positive, negative or zero.
Interior angle: An angle inside a polygon, between two sides.
Inverse operation: The operation that undoes another: + and − undo each other, and so do × and ÷.
Inverse proportion: Two quantities where one goes up as the other goes down at the same rate: if one doubles, the other halves. y = k ÷ x.
Like terms: Terms with exactly the same letters and powers, such as 3x and 5x. Only like terms can be collected.
Line of best fit: A straight line drawn through the middle of the points on a scatter graph to show the trend.
Lowest common multiple (LCM): The smallest number that is a multiple of two or more numbers. The LCM of 4 and 6 is 12.
Mean: An average: add up all the values and divide by how many values there are.
Median: The middle value when the data is in order. With an even number of values, it is halfway between the middle two.
Mixed number: A whole number and a fraction together, such as 2 3/4.
Mode: The value that appears most often. There can be more than one mode.
Multiple: A number in a times table. The multiples of 6 are 6, 12, 18, 24 and so on.
Mutually exclusive: Events that cannot both happen at the same time, such as getting a 2 and a 5 on one roll of a dice.
Negative number: A number less than zero, such as −4.
nth term: A rule that gives any term of a sequence from its position n. For 5, 8, 11, 14 the nth term is 3n + 2.
Numerator: The top number of a fraction. It shows how many parts you have.
Obtuse angle: An angle more than 90° but less than 180°.
Origin: The point (0, 0) where the x-axis and y-axis cross.
Outlier: A value that is much bigger or smaller than the rest of the data. It can distort the mean and the range.
Parallel: Lines that are always the same distance apart and never meet.
Percentage: A number of parts per hundred. 35% means 35 out of 100.
Perimeter: The total distance around the outside of a 2-D shape.
Perpendicular: At right angles (90°) to another line.
Pi (π): The circumference of any circle divided by its diameter. π = 3.14159... and never ends.
Polygon: A flat shape with straight sides, such as a pentagon (5 sides) or hexagon (6 sides).
Prime factor: A factor that is also a prime number. The prime factors of 12 are 2 and 3.
Prime number: A number with exactly two factors: 1 and itself. 2, 3, 5, 7 and 11 are prime. 1 is not prime.
Prism: A 3-D shape with the same cross-section all the way through, such as a cuboid or a triangular prism.
Probability: How likely something is to happen, from 0 (impossible) to 1 (certain).
Product: The answer when numbers are multiplied together.
Pythagoras' theorem: In a right-angled triangle, a^{2} + b^{2} = c^{2}, where c is the hypotenuse.
Quadratic: An expression or equation where the highest power of x is 2, such as x^{2} + 3x − 4. Its graph is a U shape (or upside-down U).
Radius: The distance from the centre of a circle to its edge. It is half the diameter.
Range: The largest value minus the smallest value. It measures how spread out the data is.
Ratio: A way to compare amounts, written with a colon, such as 3 : 2.
Reciprocal: 1 divided by a number. The reciprocal of 4 is 1/4, and the reciprocal of 2/3 is 3/2.
Reflex angle: An angle more than 180° but less than 360°.
Relative frequency: How often something happened in an experiment ÷ the number of trials. It estimates the probability.
Right angle: An angle of exactly 90°, a quarter turn.
Rotation: A transformation that turns a shape about a centre by an angle, clockwise or anticlockwise.
Sample space: A list or table of every possible outcome of an experiment.
Scale factor: The number every length is multiplied by in an enlargement or on a scale drawing.
Significant figures: The digits of a number counting from the first non-zero digit. 0.0472 to 2 significant figures is 0.047.
Similar: Shapes with the same angles, where every length is multiplied by the same scale factor.
Simple interest: Interest worked out on the original amount only, so you get the same amount each year.
Simplify: Write in the simplest form: collect like terms, or divide a fraction or ratio by a common factor.
Speed: Distance travelled per unit of time. Speed = distance ÷ time, for example in km/h or m/s.
Square number: A whole number multiplied by itself, such as 1, 4, 9, 16 and 25.
Square root: The number that squares to give a value. The square root of 49 is 7 (and −7 also squares to 49).
Standard form: A way to write very big or small numbers as A × 10^{n}, where 1 ≤ A < 10 and n is an integer. 4500 = 4.5 × 10^{3}.
Subject of a formula: The letter on its own on one side. In v = u + at, v is the subject.
Substitute: Replace each letter in an expression or formula with a number, then work it out.
Surface area: The total area of all the faces of a 3-D shape.
Term: One part of an expression or sequence. In 3x + 5, the terms are 3x and 5.
Transformation: A change to a shape: a translation, reflection, rotation or enlargement.
Translation: A transformation that slides a shape without turning it, described by a column vector.
Trigonometry: Using the ratios sin, cos and tan to find missing sides and angles in right-angled triangles.
Venn diagram: Overlapping circles inside a rectangle used to sort items into sets. The overlap shows items in both sets.
Vertex: A corner of a shape, where edges or sides meet. The plural is vertices.
Vertically opposite angles: Angles opposite each other where two straight lines cross. They are equal.
Volume: The amount of space inside a 3-D shape. Measured in cubic units such as cm^{3}.
y-intercept: Where a line crosses the y-axis. In y = mx + c it is c.

Formulas and facts to know 32

Angle facts: Angles on a straight line add to 180°. Angles around a point add to 360°. Vertically opposite angles are equal.
Angles in a triangle and a quadrilateral: The angles in a triangle add to 180°. The angles in a quadrilateral add to 360°.
Angles in polygons: Sum of interior angles = (n − 2) × 180° for n sides. Exterior angles add to 360°, so each exterior angle of a regular polygon = 360° ÷ n.
Area and volume units: 1 m^{2} = 100 × 100 = 10 000 cm^{2}. 1 m^{3} = 100 × 100 × 100 = 1 000 000 cm^{3}.
Area of a circle: A = πr^{2}
Area of a parallelogram: Area = base × perpendicular height
Area of a rectangle: Area = length × width
Area of a trapezium: Area = ½(a + b)h, where a and b are the parallel sides and h is the perpendicular height between them.
Area of a triangle: Area = ½ × base × perpendicular height
Circumference of a circle: C = πd or C = 2πr
Density: Density = mass ÷ volume. Mass = density × volume.
Index laws: a^{m} × a^{n} = a^{m + n}, a^{m} ÷ a^{n} = a^{m − n}, (a^{m})^{n} = a^{mn}, a^{0} = 1.
Mean: Mean = total of the values ÷ number of values. From a frequency table: total of (value × frequency) ÷ total frequency.
Metric length: 10 mm = 1 cm, 100 cm = 1 m, 1000 m = 1 km.
Metric mass and capacity: 1000 g = 1 kg, 1000 kg = 1 tonne, 1000 ml = 1 litre, 1 cm^{3} = 1 ml.
Order of operations: Brackets, then indices (powers and roots), then × and ÷ from left to right, then + and − from left to right (BIDMAS).
Parallel lines: Alternate angles are equal. Corresponding angles are equal. Co-interior angles add to 180°.
Percentage change: Percentage change = change ÷ original × 100
Percentage increase and decrease: Increase by r%: multiply by (1 + r/100). Decrease by r%: multiply by (1 − r/100). Original value = new value ÷ multiplier.
Pie chart angle: Angle = frequency ÷ total frequency × 360°
Prime numbers to learn: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47. 2 is the only even prime; 1 is not prime.
Probability: P(event) = number of favourable outcomes ÷ total number of equally likely outcomes. P(not A) = 1 − P(A).
Pythagoras' theorem: a^{2} + b^{2} = c^{2}, where c is the hypotenuse of a right-angled triangle.
Simple interest: Interest = amount × rate × number of years (rate as a decimal).
Speed: Speed = distance ÷ time. Distance = speed × time. Time = distance ÷ speed.
Square and cube numbers to learn: Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225. Cubes: 1, 8, 27, 64, 125, 1000.
Straight-line graph: y = mx + c, where m is the gradient and c is the y-intercept. Gradient = change in y ÷ change in x.
Time: 60 seconds = 1 minute, 60 minutes = 1 hour. 0.5 hours = 30 minutes, 0.25 hours = 15 minutes.
Trigonometric ratios: sin x = opposite ÷ hypotenuse, cos x = adjacent ÷ hypotenuse, tan x = opposite ÷ adjacent (SOH CAH TOA).
Volume of a cuboid: Volume = length × width × height
Volume of a cylinder: V = πr^{2}h
Volume of a prism: Volume = area of cross-section × length

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