Many lost marks come from a single word: a student knows the method but answers a slightly different question. This glossary gives each term a plain meaning, a small example and the word it is most often mixed up with.
Sixteen terms are grouped by topic, and each links to the topic page that teaches it. The English, Malay and Chinese concept bridge shows the same terms in three languages.
Functions and algebra
Domain and range. The domain is the set of inputs allowed, and the range is the set of outputs produced. For f(x) = √x, the domain is x ≥ 0 and the range is f(x) ≥ 0. Confused with each other, because both are sets of numbers. See functions and restrictions.
Inverse and reciprocal. The inverse function undoes f: if f(x) = 2x + 1 then f⁻¹(x) = (x − 1)/2. The reciprocal is 1/f(x). Confused with each other because of the superscript −1. See functions and restrictions.
Root, zero and factor. For f(x) = x² − 5x + 6, the roots of f(x) = 0 are 2 and 3, these are also the zeros of f, and (x − 2) and (x − 3) are the factors. Confused with each other because they describe one fact from three angles. See polynomial factors and remainders.
Discriminant. The quantity b² − 4ac, which tells you how many real roots a quadratic has. Example: x² + 2x + 5 gives 4 − 20 = −16, so there are no real roots. Confused with the quadratic formula itself, which uses the discriminant. See quadratic structure and discriminants.
Equation and identity. An equation is true for certain values: 2x = 6. An identity is true for all values: 2(x + 3) = 2x + 6. Confused with each other when you solve something that is already an identity. See trigonometric identities.
Logarithms, lines and angles
Exponential and logarithm. An exponential such as 2ˣ grows by repeated multiplying, and a logarithm asks which power gives a value: log₂ 8 = 3 because 2³ = 8. Confused with each other, because they are inverse operations. See exponential and logarithmic reasoning.
Gradient and intercept (in linearisation). When a curve such as y = axⁿ is turned into a straight line by taking logs, the gradient gives one constant and the intercept another. Example: lg y = n lg x + lg a has gradient n. Confused with the original variables. See straight lines and linearisation.
Radian and degree. Two units for angle: 180° equals π radians. Example: an arc of a circle of radius 5 with angle 2 radians has length 10. Confused with each other when a calculator is in the wrong mode. See radians, arcs and sectors.
Principal value and general solution. A calculator returns one principal value, such as sin⁻¹(0.5) = 30°, but an interval may hold more solutions, such as 150°. Confused with the complete answer. See trigonometric equations and graphs.
Counting and sequences
Permutation and combination. A permutation counts ordered selections, a combination counts unordered ones. From 5 people choosing 2: 20 ordered pairs but only 10 groups. Confused with each other when order is not stated clearly. See permutations and combinations.
Arithmetic and geometric sequence. Arithmetic adds the same amount each time (3, 7, 11), and geometric multiplies by the same ratio (3, 6, 12). Confused with each other when a question gives only three terms. See arithmetic and geometric series.
Binomial coefficient and term. The coefficient is the number in front, and the term includes the power of x. In (1 + x)⁴ the x² term is 6x², and its coefficient is 6. Confused with each other in “find the coefficient” questions. See binomial expansion.
Vectors and calculus
Position vector and displacement. A position vector starts at the origin. A displacement from A to B is b − a. Confused with each other when the start point is not the origin. See vector proofs.
Gradient function and gradient at a point. The derivative dy/dx is a function, and substituting an x-value gives one number. For y = x², dy/dx = 2x, and at x = 3 the gradient is 6. Confused with the tangent line itself. See differentiation.
Stationary point and turning point. A stationary point has dy/dx = 0, a turning point changes direction. On y = x³ the point (0, 0) is stationary but not a turning point. Confused with each other, because most stationary points are turning points. See stationary points and optimisation.
Signed integral and area. A definite integral can be negative where the curve is below the axis, while area is always positive. ∫ from −1 to 1 of x dx is 0, but the area between the line and the axis is 1. Confused with each other. See areas and motion.
Using the list
Pick two terms you mix up, write one example of each, and check them against your study route. Words that stop you belong in your mistake log.
For an overview of how the topics connect, see the Additional Mathematics learning guide. If a pair still blurs when you explain it aloud, online one-to-one Additional Mathematics tuition gives you a teacher who can ask the follow-up question and hear where the idea breaks.