Video Lesson Flashcards: Geometry, Algebra, Trigonometry, and Probability

Vocabulary flashcards covering circle theorems, trigonometry, algebra, geometry, probability, and standard form as presented in the video.

Angle in a semicircle theorem

The angle subtended by a diameter at the circumference is a right angle (90°).

Central angle vs circumference angle

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

Angles in the same segment

Angles in the same segment are equal.

Alternate segment theorem

The angle between a tangent and a chord equals the angle in the alternate segment.

Cyclic quadrilateral theorem

Opposite angles in a cyclic quadrilateral sum to 180°.

Pythagoras’ theorem

In a right-angled triangle, a² + b² = c² (c is the hypotenuse).

Sine (SOH)

Sine = Opposite ÷ Hypotenuse.

Cosine (CAH)

Cosine = Adjacent ÷ Hypotenuse.

Tangent (TOA)

Tangent = Opposite ÷ Adjacent.

Quadratic formula

x = (-b ± √(b² - 4ac)) / (2a).

Difference of two squares

a² - b² = (a - b)(a + b).

Binomial expansion of (a + b)²

a² + 2ab + b².

Law of indices (multiplication)

a^m × a^n = a^(m+n).

Law of indices (division)

a^m ÷ a^n = a^(m-n).

Law of indices (powers)

(a^m)^n = a^(mn).

√a × √b

√(ab).

√a ÷ √b

√(a/b).

Sum of angles in a triangle

180°.

Sum of angles in a quadrilateral

360°.

Angles on a straight line

180°.

Angles at a point

360°.

Alternate angles

Alternate interior angles are equal (Z-shape rule).

Corresponding angles

Corresponding angles are equal (F-shape rule).

Co-interior angles

Co-interior angles sum to 180° (C-shape rule).

Sum of exterior angles

360°.

Interior angle of a regular n-sided polygon

Interior angle = ((n − 2) × 180°) ÷ n.

Area of a triangle

Area = ½ × base × height.

Area of a parallelogram

Area = base × height.

Area of a trapezium

Area = ½ × (a + b) × height.

Area of a circle

Area = πr².

Circumference of a circle

Circumference = 2πr.

Volume of a cuboid

Volume = length × width × height.

Volume of a prism

Volume = area of cross-section × length.

Volume of a sphere

Volume = (4/3) π r³.

Surface area of a sphere

Surface area = 4π r².

Volume of a cone

Volume = (1/3) π r² h.

Surface area of a cone

Surface area = π r² + π r l (l = slant height).

Volume of a cylinder

Volume = π r² h.

Surface area of a cylinder

Surface area = 2π r² + 2π r h.

Surface area of a cylinder

(Duplicate term kept for completeness) 2π r² + 2π r h.

Volume of a pyramid

Volume = (1/3) × base area × height.

Probability of all outcomes added together

1.

Probability of something impossible

0.

Probability of something certain

1.

Addition rule of probability

P(A or B) = P(A) + P(B) − P(A and B).

Multiplication rule of probability

P(A and B) = P(A) × P(B) (if independent).

Mutually exclusive

Events that cannot happen together (P(A and B) = 0).

Exhaustive

Events that cover all outcomes (probabilities add to 1).

A′ (A-prime)

The complement of A (everything not in A).

A ∩ B

The intersection: outcomes in both A and B.

A ∪ B

The union: outcomes in A or B or both.

Reflection

A flip in a mirror line (line of symmetry).

Rotation

A turn around a point (given centre and angle).

Translation

A slide, described by a vector.

Enlargement

A stretch from a centre with a scale factor.

Standard form

a × 10^n where 1 ≤ a < 10 and n is an integer.

Multiplying in standard form

Multiply the a’s, add the powers of 10.

Dividing in standard form

Divide the a’s, subtract the powers of 10.

Adding/subtracting in standard form

Convert to the same power of 10, then add/subtract the a's.