CSEC Mathematics flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Standard form

A number written as A × 10^n where 1 ≤ A < 10 and n is an integer. Used to express very large or very small quantities compactly.

Laws of indices

Rules for powers: a^m × a^n = a^(m+n), a^m ÷ a^n = a^(m−n), (a^m)^n = a^(mn), a^0 = 1, and a^(−n) = 1/a^n.

Simple interest

Interest calculated only on the original principal using I = PRT/100, where P is principal, R is the annual rate percent and T is time in years.

Compound interest formula

A = P(1 + r/100)^n gives the total amount after n periods at r percent per period, with interest added to the principal each period.

Depreciation

A decrease in value calculated with A = P(1 − r/100)^n, where r is the annual percentage loss and n is the number of years.

Percentage profit

Profit expressed as a percentage of cost price: (selling price − cost price) ÷ cost price × 100. Loss percent uses the same denominator.

Direct variation

A relationship where one quantity increases as the other increases at a constant ratio, written y = kx, with k found from given values.

Inverse variation

A relationship where one quantity decreases as the other increases, written y = k/x, so the product xy remains constant.

Union and intersection

A ∪ B contains all elements in A or B; A ∩ B contains elements in both. For two sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B).

Complement of a set

The set A′ of all elements in the universal set that are not in A. It satisfies n(A) + n(A′) = n(universal set).

Difference of two squares

The identity a^2 − b^2 = (a + b)(a − b), used to factorise expressions such as x^2 − 25 into (x + 5)(x − 5).

Perfect square expansion

(a + b)^2 = a^2 + 2ab + b^2 and (a − b)^2 = a^2 − 2ab + b^2. The middle term is always twice the product of the two terms.

Quadratic formula

x = [−b ± √(b^2 − 4ac)] ÷ 2a solves ax^2 + bx + c = 0. It is used when factorising is difficult or impossible.

Discriminant

The value b^2 − 4ac in the quadratic formula. Positive gives two real roots, zero gives equal roots, negative gives no real roots.

Simultaneous equations

Two or more equations solved together. Eliminate a variable by matching coefficients and adding or subtracting, or substitute one equation into the other.

Gradient of a line

The slope m = (y2 − y1)/(x2 − x1), measuring vertical change per unit horizontal change. In y = mx + c, m is the gradient.

Perpendicular gradients

Two lines are perpendicular when the product of their gradients equals −1, so one gradient is the negative reciprocal of the other.

Distance between two points

For points (x1, y1) and (x2, y2), distance = √[(x2 − x1)^2 + (y2 − y1)^2], derived from Pythagoras' theorem on the coordinate plane.

Midpoint of a segment

The midpoint of the segment joining (x1, y1) and (x2, y2) is ((x1 + x2)/2, (y1 + y2)/2), the average of the coordinates.

Angle at the centre

The angle subtended by an arc at the centre of a circle is twice the angle that the same arc subtends at the circumference.

Angle in a semicircle

The angle subtended by a diameter at any point on the circumference is a right angle, that is 90 degrees.

Cyclic quadrilateral

A four-sided figure with all vertices on a circle. Its opposite angles are supplementary, adding to 180 degrees.

Tangent-radius theorem

A tangent to a circle is perpendicular to the radius drawn to the point of contact, forming a right angle at that point.

Area of a sector

A sector with angle θ at the centre has area (θ/360) × πr^2 and arc length (θ/360) × 2πr.

Volume of a cone

V = (1/3)πr^2h, one third of the volume of a cylinder with the same base radius and perpendicular height.

Volume of a sphere

V = (4/3)πr^3 for a sphere of radius r. Its surface area is 4πr^2.

Pythagoras' theorem

In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: c^2 = a^2 + b^2.

SOH CAH TOA

In a right-angled triangle: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent, used to find sides or angles.

Sine rule

In any triangle, a/sin A = b/sin B = c/sin C, where each side is opposite its corresponding angle. Used with a matching side-angle pair.

Cosine rule

a^2 = b^2 + c^2 − 2bc cos A relates the three sides of a triangle to one angle; used when two sides and the included angle are known.

Area of any triangle

Area = (1/2)ab sin C, where a and b are two sides and C is the angle between them.

Probability of an event

P(A) = number of favourable outcomes ÷ total number of equally likely outcomes, and P(not A) = 1 − P(A).