### Topic 1: Numbers and algebra

#### Key concepts to learn:

- The difference between natural numbers, , rational numbers, and real numbers, .
- Making approximations:
- Decimal places
- Significant figures
- Percentage errors

- Scientific notation
- Writing numbers in the form (where k is an integer)

- SI units
- Converting between different currencies
- Being able to use a GDC to solve
- Systems of linear equations with two variables
- Quadratic equations

- Arithemtic sequences and series
- Finding the nth term of an arithmetic sequence:
- Finding the sum of n terms in an arithemtic sequence: either , or

- Geometric sequences and series
- Finding the nth term of an arithmetic sequence:
- Finding the sum of n terms in a geometric sequence:

- Using geometric sequences and series to find:
- Compound interest
- Annual depreciation

#### Helpful learning resources:

Check out the rest of Khan Academy's arithemtic properties playlist here.

Check out the rest of Khan Academy's systems of equations playlist here.

Check out the rest of Khan Academy's quadratic equations playlist here.

Check out the rest of Khan Academy's sequences and series playlist here.

### Topic 2: Descriptive statistics

#### Key concepts to learn:

- Difference between discrete and continuous data
- Using frequency tables and histograms to represent discrete or continuous data
- Cumulative frequency curves
- Difference between mean, median and mode
- A set's mean is the average value of the set
- A set's median is the middle value of the set
- A set's mode is the value that appears the most times in the set

- Measuring dispersion:
- Range
- Interquartile range
- Standard deviation

#### Helpful learning resources:

Check out the rest of Khan Academy's descriptive statistics playlist here.

Check out the rest of Khan Academy's data and statistics playlist here.

### Topic 3: Logic, sets and probability

#### Key concepts to learn:

- Basic concepts of symbolic logic: definition of a proposition; symbolic notation of propositions
- Compound statements:
- Implication,
- Equivalence,
- Negation,
- Conjunction,
- Disjunction,
- Exclusive disjunction,

- Truth tables: concepts of logical contradiction and tautology.
- Converse, inverse, contrapositive.
- Logical equivalence.
- Basic set theory
- Elements (members of a set),
- Subsets,
- Intersection,
- Union,
- Complement, '

- Probability of an event occuring
- Expected value
- Probability of combined, mutually exclusive and independent events
- Using tree diagrams and venn diagrams to find probabilities
- Conditional probability

#### Helpful learning resources:

Check out the rest of Khan Academy's introductory probability playlist here.

Check out the rest of Khan Academy's random variables playlist here.

### Topic 4: Statistical applications

#### Key concepts to learn:

- The normal distribution
- The concept of a random variable; of the parameters µ and σ ; of the bell shape; the symmetry about x = µ
- Diagrammatic representation
- Bivariate data: the concept of correlation
- Scatter diagrams; line of best fit, by eye, passing through the mean point
- Pearson’s product–moment correlation coefficient, r
- The regression line for y on x
- Use of the regression line for prediction purposes
- The χ
^{2}test for independence: formulation of null and alternative hypotheses; significance levels; contingency tables; expected frequencies; degrees of freedom; p-values

#### Helpful learning resources:

Check out the rest of Khan Academy's inferential statistics playlist here.

Check out the rest of Khan Academy's random variables playlist here.

Check out the rest of Khan Academy's regression playlist here.

### Topic 5: Geometry and trigonometry

#### Key concepts to learn:

- Equation of a line in two dimensions: the forms y = mx + c and ax + by + d = 0
- Gradients (slope) and intercepts
- Points of intersection of lines
- Parallel and perpendicular lines
- Parallel lines have the same gradient (slope)
- A line that is perpendicular to another has the negative reciprocal slope of the original line's slope

- Using sine, cosine and tangent to find the lengths and angles of right-angled triangles
- Using the sine and cosine rules to find lengths and angles of triangles that are not right-angled
- The sine rule:
- The cosine rule:

- Finding the area of a triangle using trig. identities
- Geometry of three-dimensional figures
- The distance between two points
- The distance formula:

- The angle between two lines
- Finding the volume and surface area of three-dimensional solids

#### Helpful learning resources:

Check out the rest of Khan Academy's linear equations playlist here.

Check out the rest of Khan Academy's angles playlist here.

Check out the rest of Khan Academy's basic trigonometry playlist here.

Check out the rest of Khan Academy's trig identities playlist here.

Check out the rest of Khan Academy's Pythagorean theorem playlist here.

### Topic 6: Mathematical models

#### Key concepts to learn:

- Concept of a function, domain, range and graph
- Function notation such as and
- Linear functions, and their graphs (lines)
- Quadratic functions, and their graphs (parabolas)
- Properties of a parabola
- Axis of symmetry
- Vertex (found using )
- x- and y-intercepts

- Exponential functions of the form and their graphs
- The concept of a horizontal asymptote
- For example: 0 is not part of the domain of the function , because dividing by zero is illegal

- Drawing sketches of the graphs of functions
- Transferring graphs from a GDC to paper
- Using a GDC to solve equations that involve any of the functions above

#### Helpful learning resources:

Check out the rest of Khan Academy's functions playlist here.

Check out the rest of Khan Academy's quadratic equations playlist here.

Check out the rest of Khan Academy's exponential functions playlist here.

Check out the rest of Khan Academy's rational expressions playlist here.

### Topic 7: Introduction to differential calculus

#### Key concepts to learn:

- The tangent line to a curve
- The concept of the derivative as a rate of change
- Finding derivatives of functions of the form (where n is always an integer)
- Can be found using the power rule: '

- Finding gradients of curves for given values of x
- Finding the equation of the tangent line to a given point in a function
- Finding the equation of the line that is perpendicular to the tangent line at a given point (the normal line)
- Recognizing increasing and decreasing functions
- Finding local maximum and minimum points
- A function will have a maximum or minimum point where '

#### Helpful learning resources:

Check out the rest of Khan Academy's introduction to derivatives playlist here.

Check out the rest of Khan Academy's derivative applications playlist here.