FPM Exam practice
Advice/Instructions
1 minute = 1 point
Chapter 1 – Logs and Indices
• Rules of Indices
• Surds
• Writing an expression as a Log
• Laws of Logs
• Change of base formula
• The functions y = ax and y = log x
Chapter 1 – Logs and Indices
Chapter 1 – Logs and Indices
Chapter 1 – Logs and Indices
Chapter 1 – Logs and Indices
Chapter 1 – Logs and Indices
Chapter 2 – Quadratic Functions
• Factorizing
• Completing the square
• Solving quadratic equations
• Using the quadratic formula
• Functions of the roots of quadratics
Chapter 2 – Quadratic Functions
Chapter 2 – Quadratic Functions
Chapter 2 – Quadratic Functions
Chapter 3 – Identities and Inequalities
• Dividing a polynomial
• Factorizing a polynomial
• Remainder Theorem
• Substitution method (synthetic division)
• Solving linear inequalities
• Solving quadratic inequalities
• Linear inequalities as graphs/regions
Chapter 3 – Identities and Inequalities
Chapter 3 – Identities and Inequalities
Chapter 3 – Identities and Inequalities
Chapter 4 – Graphs and Functions
• Sketching Cubics
• Sketching reciprocal functions
• Sketching other functions
• Sketching exponential functions
• Using graphs to solve problems
Chapter 4 – Graphs and Functions
Chapter 4 – Graphs and Functions
Chapter 4 – Graphs and Functions
Chapter 5 – Sequences and Series
• Arithmetic sequences
• Adding terms of arithmetic sequence
• Finding the sum of a arithmetic series
• Sigma notation
• Geometric sequences
• Finding the sum of Geometric Series
• Infinite/Convergent series
Chapter 5 – Sequences and Series
Chapter 5 – Sequences and Series
Chapter 5 – Sequences and Series
Chapter 5 – Sequences and Series
Chapter 6 – The Binomial Series
• Binomial expansion
• Pascal's triangle and combinations
• Finding a particular term
• When n is negative
Chapter 6 – The Binomial Series
Chapter 6 – The Binomial Series
nBinomial
(n  1) 2 Series
n(n  1)(n  2) 3
n
Chapter
6
–
The
(1  x)  1  nx 
x 
x  ...
2!
3!
Chapter 7 – Vectors
• Scalars and Vectors
• Vector arithmetic
• Finding positions of points
• Cartesian components of vectors
Chapter 7 – Vectors
Chapter 7 – Vectors
Chapter 7 – Vectors
Chapter 7 – Vectors
Chapter 8 – Coordinate Geometry
• Equation of a straight line
• Gradient using the formula
• Perpendicular and parallel lines
• Distance between two points
• Dividing a line into given ratio
Chapter 8 – Coordinate Geometry
Chapter 8 – Coordinate Geometry
Chapter 8 – Coordinate Geometry
Chapter 9 – Calculus
• Finding gradient function
• Differentiating: xn, eax, sin ax, cos ax
• Product, Quotient and Chain rules
• Finding equation of tangent and normal
• Anti-differentiation (integration)
• Applying Calculus to problems
• Curve sketching (Max, Min, Inflexions)
• Integration to find Areas and Volumes
• Related rates
Chapter 9 – Calculus
Chapter 9 – Calculus
Chapter 9 – Calculus
Chapter 9 – Calculus
Chapter 9 – Calculus
Chapter 10 – Trigonometry
• Radians, arcs, sectors
• Unit circle (defining sine, cosine and tangent)
• Reference angles and using CAST
• Sine and Cosine rules (including ambiguous case – SSA)
• Solving 3D problems
• Trigonometric identities (Pythagorean, compound)
• Solving Trigonometric equations
• Using identities to solve equations
Chapter 10 – Trigonometry
Chapter 10 – Trigonometry
Chapter 10 – Trigonometry
Chapter 10 – Trigonometry
Chapter 10 – Trigonometry