ZIMSEC O-Level Mathematics Paper 1 Review

Comprehensive vocabulary flashcards covering key mathematical concepts, definitions, and theorems derived from ZIMSEC O-Level Mathematics Paper 1 examinations and solutions.

Recurring decimal fraction

A decimal representation of a number whose digits are periodic and repeat indefinitely, such as $\frac{7}{30} = 0.2333...$ or $2.3\dot{3}$.

Significant figures

The digits in a number that carry meaning contributing to its precisison, used to provide approximate values, such as rounding $31.095$ to two figures as $31$.

Standard form

A mathematical notation for writing very large or very small numbers as a product of a number between 1 and 10 and a power of ten, e.g., $1.8 \times 10^7$.

Prime numbers

A set of numbers $A$ whose elements are whole numbers greater than 1 with exactly two factors, 1 and themselves, such as $\{2, 3, 5, 7\}$.

Factorise completely

The process of breaking down an algebraic expression into its simplest constituent factors, such as $3x^3 - 12x = 3x(x - 2)(x + 2)$.

Difference of 2 squares

A mathematical identity where an expression in the form $x^2 - y^2$ is factorised into $(x - y)(x + y)$, as seen in the reduction of $x^2 - \frac{1}{36}$.

Simultaneous equations

A set of equations with multiple variables that are solved together to find a common solution, such as the elimination or substitution methods used for $6y - 3x = 1$ and $3x + y = 13$.

Column vector

A notation for a vector representing translation or position, written in a vertical format, for example $\begin{pmatrix} 4 \\ -3 \end{pmatrix}$.

Percentage increase

A measure of how much a value has grown compared to its original amount, calculated as $\frac{\text{new value} - \text{original value}}{\text{original value}} \times 100\%$, such as a woman's salary increasing by $5\%$.

Logarithms

The inverse operation to exponentiation, where $\log_b M = x$ implies $M = b^x$, used to evaluate expressions like $\log_4 64 = 3$.

Probability

The measure of the likelihood that an event will occur, calculated as the ratio of favorable outcomes to the total possible outcomes, such as getting two heads ($\frac{1}{4}$) when tossing two coins.

Acceleration

The rate of change of velocity with respect to time, calculated as $\text{Acceleration} = \frac{\text{velocity}}{\text{time}}$ and measured in $\text{m/s}^2$.

Tangent

A straight line that touches a circle at exactly one point on its circumference, such as the line $TS$ touching a circle at point $D$, where the angle between the tangent and radius is $90^\circ$.

Modal size

In statistics, the value or category that occurs most frequently in a data set, such as the shoe size with the highest frequency of pupils.

Median

The middle value in a distribution of data when arranged in ascending order; in a class of 42 pupils, it is the average of the 21st and 22nd values.

Gradient

The measure of the steepness of a straight line on a Cartesian plane, calculated as the ratio of the change in $y$ to the change in $x$ ($m = \frac{y_2 - y_1}{x_2 - x_1}$).

Scale of a map

The ratio of a distance on the map to the corresponding actual distance on the ground, such as $1 : 250,000$, where $1\,\text{cm}$ represents $2.5\,\text{km}$.

Octagon

A regular polygon that possesses 8 sides and has an order of rotational symmetry of 8.

Bearing

The direction of one point from another, measured in degrees clockwise from North, often expressed as a three-figure bearing like $325^\circ$.

Determinant

A scalar value derived from a square matrix; for matrix $A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$, it is calculated as $ad - bc$.

Translation

A transformation that moves every point of a figure or space the same distance in a given direction, defined by a translation vector $T = \begin{pmatrix} p \\ q \end{pmatrix}$.

Reflection

A transformation that flips a figure over a line, called the line of reflection, such as the line $x = 2$.

Standard form for population

Representing population data using powers of 10, such as the difference between $4.5 \times 10^4$ and $3.9 \times 10^4$ being $6 \times 10^3$.

Non-singular matrix

A square matrix that possesses an inverse ($A^{-1}$), which occurs only if the determinant of the matrix is not equal to zero.

Modulus of a vector

The magnitude or length of a vector $\mathbf{v} = \begin{pmatrix} x \\ y \end{pmatrix}$, calculated using the formula $|\mathbf{v}| = \sqrt{x^2 + y^2}$.

Cyclic quadrilateral

A quadrilateral whose vertices all lie on a single circle; the opposite angles of such a quadrilateral are supplementary (sum to $180^\circ$).

Similar triangles

Triangles that have the same shape but not necessarily the same size, where corresponding angles are equal and corresponding sides are in the same ratio.

Enlargement

A transformation that changes the size of an object by a scale factor from a specific center of enlargement.

Sector of a circle

A portion of a circle enclosed by two radii and an arc, with an area calculated by $\frac{\theta}{360^\circ} \times \pi r^2$.

Interior angle of a regular polygon

The angle inside a polygon at each vertex; calculated using the formula $\frac{(n-2) \times 180^\circ}{n}$, where $n$ is the number of sides.