Mathematics for CSEC® 2nd Edition Study Guide

These flashcards cover essential mathematical concepts and formulas for preparing for CSEC® Mathematics.

What is the formula for the area of a triangle?

A = (1/2) × base × height.

What is the Pythagorean theorem?

In a right triangle, a² + b² = c², where c is the hypotenuse.

What is the difference between mean and median?

Mean is the average of all data values, while median is the middle value when data is ordered.

What are the circle theorems about angles?

The angle at the centre is twice the angle at the circumference.

How to find the probability of an event?

Probability = (number of successful outcomes) / (total number of possible outcomes).

What does it mean for two lines to be parallel?

They do not intersect and have the same slope.

What are the properties of similar triangles?

They have equal angles and corresponding sides in proportion.

What is the cosine rule?

In triangle ABC, a² = b² + c² - 2bc cos(A), used to find a side or an angle.

How are vectors represented?

Vectors can be represented by column vectors, arrows, or written as coordinates.

What is the formula for the surface area of a cylinder?

Surface area = 2πr² + 2πrh.

What type of symmetry does a circle have?

Circular symmetry, meaning it looks the same when rotated about its centre.

What is the axis of symmetry in a quadratic function?

The vertical line that passes through the vertex of the parabola.

How to solve simultaneous equations graphically?

By plotting the equations and finding the intersection point of the graphs.

Define the sine rule.

In any triangle, a/sinA = b/sinB = c/sinC, where a, b, and c are side lengths opposite angles A, B, and C.

What is the formula for the area of a circle?

Area = πr².

What does it mean for an operation to be commutative?

The order in which two numbers are added or multiplied does not change the result.

What is the formula for the standard deviation?

Standard deviation = √((Σ(x - μ)²) / N), where μ is the mean and N is the number of data points.

What is a Venn diagram used for?

To show relationships between different sets, including intersections and unions.

What does the gradient of a line represent?

The slope or steepness of the line.

How is the midpoint of a line segment determined?

By averaging the x-coordinates and y-coordinates of the endpoints.