A-LEVEL MATHEMATICS PURE MATH 1 - kumatics education

Standard Form

Standard Form: Completing the square, solving quadratic equations, and using the discriminant (b² – 4ac) to determine the nature of roots. (A)

Standard Form: Completing the square, solving quadratic equations, and using the discriminant (b² – 4ac) to determine the nature of roots. (B)

Standard Form: Completing the square, solving quadratic equations, and using the discriminant (b² – 4ac) to determine the nature of roots. (C)

Functions: Identifying the vertex, axis of symmetry, and range of quadratic functions. (A)

Inequalities: Solving quadratic inequalities graphically and algebraically. (A)

Inequalities: Solving quadratic inequalities graphically and algebraically. (B)

Inequalities: Solving quadratic inequalities graphically and algebraically. (C)

Notation

Notation: Understanding domain, range, and one-to-one functions. (A)

Notation: Understanding domain, range, and one-to-one functions. (B)

Notation: Understanding domain, range, and one-to-one functions. (C)

Composite Functions: Evaluating and finding expressions for fg(x). (A)

Composite Functions: Evaluating and finding expressions for fg(x). (B)

Composite Functions: Evaluating and finding expressions for fg(x). (C)

Inverse Functions: Conditions for existence and finding f⁻¹(x). (A)

Inverse Functions: Conditions for existence and finding f⁻¹(x). (B)

Inverse Functions: Conditions for existence and finding f⁻¹(x). (C)

Transformations: Translations, stretches, and reflections of y = f(x). (A)

Transformations: Translations, stretches, and reflections of y = f(x). (B)

Transformations: Translations, stretches, and reflections of y = f(x). (C)

Lines

Lines: Equation of a straight line (y – y₁ = m(x – x₁)), gradient, and distance between points. (A)

Lines: Equation of a straight line (y – y₁ = m(x – x₁)), gradient, and distance between points. (B)

Lines: Equation of a straight line (y – y₁ = m(x – x₁)), gradient, and distance between points. (C)

Circles: Equation of a circle in the form (x – a)² + (y – b)² = r². (A)

Circles: Equation of a circle in the form (x – a)² + (y – b)² = r². (B)

Circles: Equation of a circle in the form (x – a)² + (y – b)² = r². (C)

Intersections: Solving simultaneous equations to find intersection points of lines and circles. (A)

Intersections: Solving simultaneous equations to find intersection points of lines and circles. (B)

Intersections: Solving simultaneous equations to find intersection points of lines and circles. (C)

Radians

Radians: Conversion between degrees and radians. (A)

Radians: Conversion between degrees and radians. (B)

Radians: Conversion between degrees and radians. (C)

Arc Length & Sector Area: Applying the formulas s = rθ and A = ½r²θ. (A)

Arc Length & Sector Area: Applying the formulas s = rθ and A = ½r²θ. (B)

Arc Length & Sector Area: Applying the formulas s = rθ and A = ½r²θ. (C)

Graphs

Graphs: Properties and sketches of sine, cosine, and tangent functions. (A)

Graphs: Properties and sketches of sine, cosine, and tangent functions. (B)

Graphs: Properties and sketches of sine, cosine, and tangent functions. (C)

Identities: Using sin²θ + cos²θ = 1 and tanθ = sinθ / cosθ. (A)

Identities: Using sin²θ + cos²θ = 1 and tanθ = sinθ / cosθ. (B)

Identities: Using sin²θ + cos²θ = 1 and tanθ = sinθ / cosθ. (C)

Equations: Solving trigonometric equations within a given interval. (A)

Equations: Solving trigonometric equations within a given interval. (B)

Equations: Solving trigonometric equations within a given interval. (C)

Binomial Expansion

Binomial Expansion: Expansion of (a + b)ⁿ for positive integer n (A)

Binomial Expansion: Expansion of (a + b)ⁿ for positive integer n (B)

Binomial Expansion: Expansion of (a + b)ⁿ for positive integer n (C)

Arithmetic Progressions (AP): General term (u□) and sum of the first n terms (S□).(A)

Arithmetic Progressions (AP): General term (u□) and sum of the first n terms (S□). (B)

Arithmetic Progressions (AP): General term (u□) and sum of the first n terms (S□). (C)

Geometric Progressions (GP): General term, sum of n terms, and sum to infinity (|r| <1).(A)

Geometric Progressions (GP): General term, sum of n terms, and sum to infinity (|r| <1). (B)

Geometric Progressions (GP): General term, sum of n terms, and sum to infinity (|r| <1). (C)

Derivatives

Derivatives: Finding dy/dx for xⁿ and composite functions using the chain rule. (A)

Derivatives: Finding dy/dx for xⁿ and composite functions using the chain rule. (B)

Derivatives: Finding dy/dx for xⁿ and composite functions using the chain rule. (C)

Applications: Gradients, tangents, normals, and rates of change. (A)

Applications: Gradients, tangents, normals, and rates of change. (B)

Applications: Gradients, tangents, normals, and rates of change. (C)

Stationary Points: Identifying maximum and minimum points using the second derivative test. (A)

Stationary Points: Identifying maximum and minimum points using the second derivative test. (B)

Stationary Points: Identifying maximum and minimum points using the second derivative test.(C)

Indefinite Integrals

Indefinite Integrals: Integration as the reverse of differentiation for xⁿ (n ≠ -1). (A)

Indefinite Integrals: Integration as the reverse of differentiation for xⁿ (n ≠ -1). (B)

Indefinite Integrals: Integration as the reverse of differentiation for xⁿ (n ≠ -1). (C)

Definite Integrals: Evaluating integrals between limits. (A)

Definite Integrals: Evaluating integrals between limits. (B)

Definite Integrals: Evaluating integrals between limits. (C)

Applications: Finding the area under a curve and the volume of revolution about the x-axis. (A)

Applications: Finding the area under a curve and the volume of revolution about the x-axis. (B)

Applications: Finding the area under a curve and the volume of revolution about the x-axis. (C)

PURE MATH 1

Standard Form

Functions

Inequalities

Notation

Composite Functions

Inverse Functions

Transformations

Lines

Circles

Intersections

Radians

Arc Length & Sector Area

Graphs

Identities

Equations

Binomial Expansion

Arithmetic Progressions (AP)

Geometric Progressions (GP)

Derivatives

Applications

Stationary Points

Indefinite Integrals

DefiniteIntegrals

Applications