MATSEC SEC 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 for very large or very small values.

Quadratic formula

For ax^2 + bx + c = 0, the solutions are x = [−b ± √(b^2 − 4ac)] / 2a. It solves any quadratic equation.

Difference of two squares

a^2 − b^2 factorises to (a + b)(a − b). This identity is used to simplify expressions and rationalise denominators.

Compound interest formula

A = P(1 + r/100)^n gives the total amount after n years when interest r% is added to the growing balance each year.

Direct proportion

Two quantities are directly proportional if y = kx for a constant k. Doubling one quantity doubles the other; the graph is a straight line through the origin.

Inverse proportion

Two quantities are inversely proportional if y = k/x. As one increases the other decreases, and the product xy stays constant.

Laws of indices

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.

Gradient of a line

m = (y2 − y1)/(x2 − x1), the change in y divided by the change in x between two points on the line.

nth term of arithmetic sequence

For a sequence with first term a and common difference d, the nth term is a + (n − 1)d.

Sine rule

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

Cosine rule

a^2 = b^2 + c^2 − 2bc cos A. It finds a side or angle in a triangle that is not right-angled.

Pythagoras' theorem

In a right-angled triangle, a^2 + b^2 = c^2 where c is the hypotenuse, the side opposite the right angle.

Area of a triangle

Area = (1/2) × base × perpendicular height, or (1/2)ab sin C when two sides and the included angle are known.

Bearings

An angle measured clockwise from north, written with three digits such as 047°. Bearings range from 000° to 360°.

Volume of a cone

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

Volume of a sphere

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

Sector area

Area = (θ/360) × πr^2, where θ is the central angle in degrees. The arc length is (θ/360) × 2πr.

Similar shapes scale factors

If corresponding lengths scale by factor k, areas scale by k^2 and volumes scale by k^3.

Exterior angle of a regular polygon

For a regular polygon with n sides, each exterior angle is 360°/n and each interior angle is 180° − 360°/n.

Angle in a semicircle

An angle subtended by a diameter at any point on the circumference is a right angle, 90°.

Mean from a frequency table

Mean = Σ(f × x) ÷ Σf, where f is the frequency of each value x and Σf is the total frequency.

Median and mode

The median is the middle value of ordered data; the mode is the most frequent value. Both describe a typical value.

Interquartile range

IQR = upper quartile − lower quartile. It measures the spread of the middle 50% of the data and ignores extreme values.

Quartile positions

For n ordered values, the lower quartile is at position (n + 1)/4 and the upper quartile at 3(n + 1)/4.

Probability of complement

P(not A) = 1 − P(A). The probabilities of an event and its complement always add to 1.

Mutually exclusive events

Events that cannot occur at the same time. For such events, P(A or B) = P(A) + P(B).

Independent events

Events where one outcome does not affect the other. For independent events, P(A and B) = P(A) × P(B).

Relative frequency

Number of successful trials divided by total trials. It estimates probability and becomes more reliable as the number of trials increases.

Expected frequency

Expected frequency = probability of an event × number of trials. It predicts how often the event should occur.

Pie chart angle

The sector angle for a category is (frequency ÷ total frequency) × 360°, so all sectors together make a full circle.

Frequency density

Frequency density = frequency ÷ class width. It is plotted on the vertical axis of a histogram with unequal class widths.

Cumulative frequency median

On a cumulative frequency curve, the median is the value at half the total frequency; quartiles are at 25% and 75%.