MSCE Mathematics key terms

A positive whole number (1, 2, 3, ...) used for counting. Some definitions include zero, but in this exam natural numbers are the counting numbers starting from 1.

A whole number that can be positive, negative, or zero, without a fractional part. Examples include -3, 0, and 7.

A number that can be expressed as a fraction a/b where a and b are integers and b is not zero. Its decimal form either terminates or repeats.

A real number that cannot be written as a simple fraction of two integers. Its decimal expansion is infinite and non-repeating, like √2 or π.

An integer greater than 1 that has exactly two positive divisors: 1 and itself. For example, 2, 3, 5, and 7 are prime.

A positive integer greater than 1 that has more than two positive divisors. For example, 4, 6, 8, and 9 are composite.

A number that divides another number exactly, leaving no remainder. For example, 1, 2, 3, and 6 are factors of 6.

The result of multiplying a number by an integer. For example, the multiples of 3 include 3, 6, 9, and 12.

The largest positive integer that divides two or more given numbers exactly. For example, the HCF of 12 and 18 is 6.

The smallest positive integer that is a multiple of two or more given numbers. For example, the LCM of 4 and 6 is 12.

A way of writing very large or very small numbers as A × 10^n, where 1 ≤ A < 10 and n is an integer. For example, 4500 = 4.5 × 10^3.

The digits in a number that carry meaningful information about its precision. Non-zero digits are always significant; zeros between them are significant, but leading zeros are not.

A position of a digit to the right of the decimal point. For example, in 3.146 the digit 4 is in the second decimal place.

A fraction or ratio expressed as a part of 100. For example, 45% means 45 out of 100, or 0.45 as a decimal.

A comparison of two or more quantities of the same kind, often written as a:b. It shows how many times one quantity contains another.

An equation stating that two ratios are equal. For example, 2/3 = 4/6 is a proportion.

A relationship where two quantities increase or decrease together at the same rate. If one doubles, the other doubles; the ratio between them stays constant.

A relationship where one quantity increases as the other decreases, so their product remains constant. For example, speed and time for a fixed journey.

Irrational roots, such as √2 or √5, that cannot be simplified to a rational number. They are often left in exact form in answers.

The process of removing a surd from the denominator of a fraction by multiplying numerator and denominator by a suitable surd or conjugate.

A combination of variables, numbers, and operation signs, without an equals sign. For example, 3x + 2y - 7.

A mathematical statement that two expressions are equal, containing an equals sign. Solving it means finding the value(s) of the variable that make it true.

A statement comparing two expressions using symbols such as <, >, ≤, or ≥. It shows that one side is greater than or less than the other.

An equation in which the highest power of the variable is 1. Its graph is a straight line. For example, 2x + 5 = 11.

An equation of the form ax² + bx + c = 0, where a ≠ 0. It can be solved by factorising, completing the square, or using the quadratic formula.

For a quadratic equation ax² + bx + c = 0, the discriminant is b² - 4ac. It determines the number and type of roots.

Two or more equations that must be solved together so that the same values satisfy all of them at once. Their solution is the point where their graphs intersect.

A technique for solving simultaneous equations by expressing one variable in terms of the other from one equation and substituting it into the other.

A technique for solving simultaneous equations by adding or subtracting the equations to eliminate one variable, after making its coefficients equal.

The process of writing an expression as a product of its factors. For example, x² - 9 factorises to (x - 3)(x + 3).

Multiplying out brackets to remove them and simplify an expression. For example, 2(x + 3) expands to 2x + 6.

A rule that assigns to each input value exactly one output value. It is often written as f(x).

The set of all possible input values for which a function is defined. For example, the domain of f(x) = 1/x is all real numbers except 0.

The set of all possible output values that a function can produce from its domain. For example, the range of f(x) = x² is y ≥ 0.

The steepness of a straight line, calculated as the change in y divided by the change in x between two points. Also called slope.

The point where a graph crosses the y-axis. For the line y = mx + c, the y-intercept is c.

The graph of a linear equation, which is always a straight line. Its equation can be written in the form y = mx + c.

The graph of a quadratic function, which is a U-shaped curve called a parabola. It opens upwards if the coefficient of x² is positive.

The point on a curve where the gradient changes sign, giving a local maximum or minimum. For a parabola, it is the vertex.