Math-Major

Key Contents Detailed Description:

Percent’s
⦁ Convert between percents, fractions and decimals
⦁ Solve percent equations
⦁ Percent word problems
⦁ Percent of change
⦁ Percent of change: word problems
⦁ Simple interest
⦁ Compound interest
⦁ Percent of a number: GST, discount and more
⦁ Find the percent: discount and mark-up
⦁ Multi-step problems with percents

Geometry
⦁   Perimeter
⦁   Area
⦁   Area of compound figures
⦁   Area between two shapes
⦁   Interior angles of polygons
⦁   Transversal of parallel lines
⦁   Volume of cylinders
⦁   Volume
⦁   Surface area
⦁   Congruent figures: side lengths and angle measures
⦁   Similar figures: side lengths and angle measures
⦁   Similar triangles and indirect measurement
⦁   Dilations and scale factors
⦁   Area and perimeter of similar figures
⦁   Similar solids
⦁   Volume and surface area of similar solids
⦁   Perimeter, area and volume: changes in scale
⦁   Pythagoras’ theorem
⦁   Pythagoras’ theorem: word problems
⦁   Converse of Pythagoras’ theorem: is it a right triangle?
⦁   Special right triangles

Trigonometry
⦁ Trigonometric ratios: sin, cos and tan
⦁  Trigonometric ratios: csc, sec and cot
⦁  Find trigonometric functions of special angles
⦁  Find trigonometric functions using a calculator
⦁  Inverses of trigonometric functions
⦁  Trigonometric ratios: find a side length
⦁  Trigonometric ratios: find an angle measure
⦁  Solve a right triangle
⦁  Trigonometric ratios in similar right triangles
Data and graphs
⦁ Interpret bar graphs, line graphs and histograms
⦁ Create bar graphs, line graphs and histograms
⦁ Interpret circle graphs
⦁ Interpret stem-and-leaf plots
⦁ Interpret box-and-whisker plots
⦁ Interpret a scatter plot
⦁ Scatter plots: line of best fit

Matrices
⦁ Matrix vocabulary
⦁ Matrix operation rules
⦁ Add and subtract matrices
⦁ Multiply a matrix by a scalar
⦁ Linear combinations of matrices
⦁ Multiply two matrices
⦁ Simplify matrix expressions
⦁ Properties of matrices
⦁ Solve matrix equations
⦁ Determinant of a matrix
⦁ Is a matrix invertible?
⦁ Inverse of a matrix
⦁ Identify inverse matrices
⦁ Solve matrix equations using inverses

Quadratic functions
⦁ Characteristics of quadratic functions
⦁ Complete a function table: quadratic functions
⦁ Transformations of quadratic functions
⦁ Find a quadratic function
⦁ Graph a quadratic function
⦁ Match quadratic functions and graphs
⦁ Solve a quadratic equation using square roots
⦁ Solve a quadratic equation using the zero product property
⦁ Solve a quadratic equation by factorising
⦁ Complete the square
⦁ Solve a quadratic equation using the quadratic formula
⦁ Using the discriminant

Introduction to derivatives
⦁ Average rate of change I
⦁ Average rate of change II
⦁ Find instantaneous rates of change
⦁ Velocity as a rate of change
⦁ Find values of derivatives using limits
⦁ Find the gradient of a tangent line using limits
⦁ Find equations of tangent lines using limits
⦁ Sum and difference rules
⦁ Power rule I
⦁ Power rule II
⦁ Find derivatives of polynomials

Derivative rules
⦁  Sum and difference rules
⦁  Product rule
⦁  Quotient rule
⦁  Power rule I
⦁  Power rule II
⦁  Chain rule
⦁  Inverse function rule

Functions
⦁ Domain and range
⦁ Identify functions
⦁ Find the gradient of a linear function
⦁ Graph a linear function
⦁ Write the equation of a linear function
⦁ Linear functions over unit intervals
⦁ Complete a function table: absolute value functions
⦁ Graph an absolute value function
⦁ Evaluate functions
⦁ Find values using function graphs
⦁ Complete a table for a function graph
⦁ Add, subtract, multiply and divide functions
⦁ Composition of functions
⦁ Identify inverse functions
⦁ Find values of inverse functions from tables
⦁ Find values of inverse functions from graphs
⦁ Find inverse functions and relations

Probability
⦁  Introduction to probability
⦁  Calculate probabilities of events
⦁  Combinations and permutations
⦁  Find probabilities using combinations and permutations
⦁  Find probabilities using two-way frequency tables
⦁  Identify independent events
⦁  Find conditional probabilities
⦁  Independence and conditional probability
⦁  Find conditional probabilities using two-way frequency tables
⦁  Find probabilities using the addition rule

Statistics
⦁  Identify biased samples
⦁  Variance and standard deviation
⦁  Identify an outlier
⦁  Identify an outlier and describe the effect of removing it
⦁  Outliers in scatter plots
⦁  Match correlation coefficients to scatter plots
⦁  Calculate correlation coefficients
⦁  Find the equation of a regression line
⦁  Interpret regression lines
⦁  Analyse a regression line of a data set
⦁  Analyse a regression line using statistics of a data set
⦁  Find confidence intervals for population means
⦁  Find confidence intervals for population proportions
⦁  Interpret confidence intervals for population means

Two-dimensional vectors
⦁ Find the magnitude of a vector
⦁ Find the direction angle of a vector
⦁ Find the component form of a vector
⦁ Find the component form of a vector from its magnitude and direction angle
⦁ Find a unit vector
⦁ Add and subtract vectors
⦁ Multiply a vector by a scalar
⦁ Find the magnitude or direction of a vector scalar multiple
⦁ Find the magnitude and direction of a vector sum
⦁ Linear combinations of vectors
⦁ Graph a resultant vector using the triangle method
⦁ Graph a resultant vector using the parallelogram method

Three-dimensional vectors
⦁ Find the magnitude of a three-dimensional vector
⦁ Find the component form of a three-dimensional vector
⦁ Find a three-dimensional unit vector
⦁ Add and subtract three-dimensional vectors
⦁ Scalar multiples of three-dimensional vectors
⦁ Linear combinations of three-dimensional vectors