NSW Preliminary (Year 11 2 Unit)
- Adding indices when multiplying terms with the same base
- Subtracting indices when dividing terms with the same base
- Multiplying indices when raising a power to a power
- Multiplying indices when raising to more than one term
- Terms raised to the power of zero
- Negative Indices
- Fractional Indices
- Complex fractions as indices
- Scientific notation with larger numbers
- Scientific notation with small numbers
- Changing scientific notation to numerals
- Significant Figures
- Introducing surds
- Some rules for the operations with surds
- Simplifying Surds
- Creating entire surds
- Adding and subtracting like surds
- Expanding surds
- Binomial expansions
- Conjugate binomials with surds
- Rationalising the denominator
- Rationalising binomial denominators
- Algebraic Fractions resulting in Negative Indices
- Factorisation of Algebraic Fractions including Binomials
- Cancelling Binomial Factors in Algebraic Fractions
- Evaluating Absolute Value Expressions
- Solving Absolute Value Equations
- Solving and Graphing Inequalities
- Binomial Products
- Binomial products with negative multiplier
- Binomial Products (nonmonic)
- Squaring a Binomial (monic)
- Squaring a Binomial (nonmonic)
- Expansions Leading to the Difference of Two Squares
- Products in Simplification of Algebraic Expressions
- Larger Expansions
- Highest Common Factor
- Factors by Grouping
- Difference of Two Squares
- Common factor and the difference of two squares
- Quadratic Trinomials (monic): Case 1
- Quadratic Trinomials (monic): Case 2
- Quadratic Trinomials (monic): Case 3
- Quadratic Trinomials (monic): Case 4
- Factorisation of nonmonic quadratic trinomials
- Factorisation of nonmonic quadratic trinomials: Moon method
- Sum and Difference of Two Cubes
- Simplifying Algebraic Fractions
- Simultaneous Equations
- Elimination method
- Elimination method part 2
- Applications of simultaneous equations
- Solving Simultaneous Equations graphically
- Introduction to Quadratic Equations
- Solving Quadratic Equations with Factorisation
- Solving Quadratic Equations
- Completing the square
- Solving Quadratic Equations by Completing the Square
- The Quadratic Formula
-
Problem solving with quadratic equations
- Solving Simultaneous Quadratic Equations Graphically
- Adjacent Angles
- Complementary and Supplementary Angles
- Vertically Opposite Angles
- Angles at a Point
- Additional questions involving parallel lines
- Exterior angle theorem
- Special triangles
- Quadrilaterals
- Points, Lines and Planes
- Angles
- Further difficult exercises involving formal reasoning
- Angle Bisector Construction and its Properties
- Circumcenter and Incenter
- Orthocentre and Centroids
- Midsegments
- Quadrilaterals 1
- Properties of Parallelograms - Opposite Angles Equal
- Properties of Parallelograms - Diagonals, Sides and Angles
- The Parallelogram Umbrella
- Properties of Trapezoids
- Constructions and Loci 1: Transformations
- Constructions and Loci 2
- Angles of regular polygons
- Congruent triangles: Tests 1 and 2
- Congruent triangles: Tests 3 and 4
- Proofs and Congruent Triangles
- Similar Triangles
- Using Similar Triangles to Calculate Lengths
- Examples involving overlapping triangles
- The Triangle Inequality Theorem
- Using Pythagorean Triples to Identify Right Triangles
- Calculating the Hypotenuse of a right-angled Triangle
- Calculating a Leg of a right-angled Triangle
- The Distance Formula
- The Mid-Point Formula
- The Gradient
- The Gradient Formula
- The Straight Line
- Lines Through the Origin
- General Form of a Line and the x and y Intercepts
- Slope Intercept Form of a Line
- Point Slope Form of a Line
- Two Point Formula: equation of a line which joins a pair of points
- Intercept form of a straight line: find the equation when given x and y
- Parallel Lines: identify equation of a line parallel to another
- Perpendicular Lines
- Perpendicular Distance
- Line through the intersection of two given lines
- Inequalities on the Number Plane
-
Trigonometric Ratios
- Using the Calculator
- Using the Trigonometric Ratios to find unknown length [Case 1 Sin]
- Using the Trigonometric Ratios to find unknown length [Case 2 Cosine]
- Using the Trigonometric Ratios to find unknown length [Case 3 Tangent Ratio]
- Unknown in the Denominator [Case 4]
-
Bearings: The Compass
- Angles of Elevation and Depression
- Trigonometric Ratios in Practical Situations
- Using the Calculator to Find an Angle Given a Trigonometric Ratio
- Using the Trigonometric Ratios to Find an Angle in a Right-Angled Triangle
- Trigonometric Ratios of 30, 45 and 60 Degrees: Exact Ratios
- The Cosine Rule to find an unknown side [Case 1 SAS]
- The Sine Rule to find an unknown side: Case 1
- The Sine Rule: Finding a Side
- The Sine Rule: Finding an Angle
- The Sine Area Formula for a Triangle
- Angles of Any Magnitude
- Trigonometric Ratios of 0, 90, 180, 270 and 360 degrees
- Trigonometric Identities
- The Circle: to find radii of circles
- The semicircle: to select the equation given the semicircle and vice versa
- The parabola: to describe properties of a parabola from its equation
- Quadratic Polynomials of the form y = ax^2 + bx + c
- Graphing perfect squares: y=(a-x) squared
- Graphing irrational roots
- Graphing complex polynomials: quadratics with no real roots
- General equation of a circle: determine and graph the equation
- Graphing cubic curves
- Absolute Value Equations
- The Rectangular Hyperbola
- The Parabola
- Circles
- Functions and Relations: domain and range
- Function Notation
- Selecting Appropriate Domain and Range
- Domain and Range from Graphical Representations
- Evaluating and Graphing Piecewise Functions
- Combining Functions
- Limits
- Differentiation from First Principles
- Differentiation of y = x to the power of n
- Meaning of dy over dx - Equations of Tangents and Normals