Nepal SEE Mathematics flashcards

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

Cardinality of a set

The number of distinct elements in a set A, written n(A). Repeated elements are counted once, and the empty set has cardinality zero.

Union of two sets

The set containing every element that belongs to A or B or both, written A ∪ B. Common elements appear only once in the union.

Number of subsets

A set with n distinct elements has 2^n subsets in total. This includes the empty set and the set itself as subsets.

Profit percent formula

Profit percent equals (selling price − cost price) ÷ cost price × 100. It is calculated on cost price, so SP = CP(1 + profit%/100).

Simple interest formula

Simple interest I = P × T × R ÷ 100, where P is principal, T is time in years, and R is annual interest rate percent. Amount A = P + I.

Compound interest amount

Amount A = P(1 + R/100)^T for annual compounding, where P is principal, R annual rate percent, T years. Compound interest = A − P.

VAT amount

VAT amount = taxable value × VAT rate percent ÷ 100. Price including VAT = taxable value × (1 + VAT rate/100).

Currency buying rate

The rate at which a bank buys foreign currency from a customer. To convert foreign currency to local currency, multiply the foreign amount by the buying rate.

Heron's formula for area

Area of a triangle with sides a, b, c is √[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2 is the semi-perimeter.

Cylinder total surface area

Total surface area of a closed cylinder = 2πr(r + h), where r is base radius and h is height. Curved surface area alone is 2πrh.

Cone volume formula

Volume of a cone = (1/3)πr²h, where r is base radius and h is perpendicular height. Slant height l = √(r²+h²).

Sphere surface area

Surface area of a sphere = 4πr², where r is radius. Volume of the same sphere is (4/3)πr³.

Cube diagonal

Length of a space diagonal of a cube with edge a is a√3. Each face diagonal has length a√2.

Quadratic formula

Solutions of ax² + bx + c = 0, a ≠ 0, are x = [−b ± √(b² − 4ac)] ÷ (2a). The expression under the root decides the nature of roots.

Discriminant rule

For ax² + bx + c = 0, discriminant D = b² − 4ac. If D > 0 roots are real and distinct; D = 0 roots equal; D < 0 no real roots.

Index multiplication law

When multiplying powers with the same base, add indices: a^m × a^n = a^(m+n). For division subtract: a^m ÷ a^n = a^(m−n), a ≠ 0.

Inequality sign reversal

Multiplying or dividing both sides of an inequality by a negative number reverses the inequality sign. Adding or subtracting the same number does not reverse it.

Triangle angle sum

The three interior angles of any triangle add to 180°. An exterior angle equals the sum of the two opposite interior angles.

Similar triangle area ratio

If two triangles are similar with corresponding side ratio k, the ratio of their areas is k². Corresponding angles are equal and sides are proportional.

Angle at centre theorem

The angle subtended by an arc at the centre of a circle is twice the angle subtended by the same arc at any point on the remaining circumference.

Tangent perpendicular to radius

A tangent to a circle is perpendicular to the radius drawn to the point of contact. Tangents drawn from an external point to a circle are equal in length.

Sine ratio

In a right triangle, sine of an acute angle = length of opposite side ÷ length of hypotenuse. Its reciprocal is cosecant.

Angle of elevation

The angle between the horizontal line of sight and the line of sight to an object above the horizontal. It is measured upward from the observer's eye.

Trigonometric identity

For any angle θ, sin²θ + cos²θ = 1. Dividing by cos²θ gives 1 + tan²θ = sec²θ; dividing by sin²θ gives 1 + cot²θ = cosec²θ.

Grouped median formula

Median = L + [(N/2 − cf)/f] × h, where L is lower class boundary, N total frequency, cf cumulative frequency before median class, f median-class frequency, h class width.

Probability range

For any event E, 0 ≤ P(E) ≤ 1. Probability 0 means impossible, 1 means certain, and P(not E) = 1 − P(E).

Mutually exclusive events

Events that cannot occur at the same time have P(A and B) = 0. For such events, P(A or B) = P(A) + P(B).

Translation vector

A translation moves every point by the same vector (a, b): (x, y) → (x+a, y+b). Shape, size and orientation remain unchanged.

Rotation 90 degrees clockwise

About the origin, a 90° clockwise rotation maps (x, y) to (y, −x). A 90° anticlockwise rotation maps (x, y) to (−y, x).

Distance formula

Distance between points (x₁, y₁) and (x₂, y₂) is √[(x₂−x₁)² + (y₂−y₁)²]. It follows from Pythagoras' theorem.

Slope of a line

Slope m = (y₂ − y₁)/(x₂ − x₁) for two points on a line. Parallel lines have equal slopes; perpendicular lines have product of slopes −1.

Vector magnitude

Magnitude of vector a = xi + yj is |a| = √(x² + y²). Unit vector in its direction is a/|a|.