Excel in NZ Year 11 Mathematics

Comparing and ordering rational numbers

Solving problems with rational numbers in decimal form

Solving problems with rational numbers in fraction form

Determine square roots of rational numbers

Ratios

Rates

Proportions

Identifying proportional relationships

Understanding graphs of proportional relationships

Graphing and writing equations of proportional relationships

Applications of proportional relationships

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Midpoint formula: \(M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)\)

Gradient equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Gradient intercept form: y = mx + b

General form: Ax + By + C = 0

Gradient-point form: \(y - y_1 = m (x - x_1)\)

Rate of change

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from gradient-intercept form y=mx+b

Graphing linear functions using a single point and gradient

Word problems of graphing linear functions

Parallel and perpendicular lines in linear functions

Applications of linear relations

Express linear inequalities graphically and algebraically

Solving one-step linear inequalities

Solving multi-step linear inequalities

Compound inequalities

Determining number of solutions to linear equations

Solving simultaneous equations by graphing

Solving simultaneous equations by elimination

Solving simultaneous equations by substitution

Money related questions in linear equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Product rule of exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Negative exponent rule

Combining the exponent rules

Scientific notation

Convert between radicals and rational exponents

Solving for exponents

Exponents: Product rule <i>(a^x)(a^y) = a^(x+y)</i>

Exponents: Division rule (a^x / a^y) = a^(x-y)

Exponents: Power rule <i>(a^x)^y = a^(x * y)</i>

Exponents: Negative exponents

Exponents: Zero exponent: <i>a^0 = 1</i>

Exponents: Rational exponents

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

What is a logarithm?

Converting from logarithmic form to exponential form

Evaluating logarithms without a calculator

Common logarithms

Natural log: ln

Evaluating logarithms using change-of-base formula

Converting from exponential form to logarithmic form

Solving exponential equations with logarithms

Product rule of logarithms

Quotient rule of logarithms

Combining product rule and quotient rule in logarithms

Evaluating logarithms using logarithm rules

Solving logarithmic equations

Graphing logarithmic functions

Finding a logarithmic function given its graph

Characteristics of polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

What is a polynomial?

Polynomial components

Multiplying monomial by monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Applications of polynomials

Common factors of polynomials

Factorising polynomials by grouping

Solving polynomials with the unknown "b" from <i>x^2 + bx + c</i>

Solving polynomials with the unknown "c" from <i>x^2 + bx + c</i>

Factorising polynomials: <i>x^2 + bx + c</i>

Applications of polynomials: <i>x^2 + bx + c</i>

Solving polynomials with the unknown "b" from \(ax^2 + bx + c\)

Factorising polynomials: \(ax^2 + bx + c\)

Factorising perfect square trinomials: <i>(a + b)^2 = a^2 + 2ab + b^2</i> or <i>(a - b)^2 = a^2 - 2ab + b^2</i>

Find the difference of squares: <i>(a - b)(a + b) = (a^2 - b^2)</i>

Evaluating polynomials

Using algebra tiles to factorise polynomials

Solving polynomial equations

Word problems of polynomials

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: <i>y = ax^2 + bx + c</i>

Quadratic function in vertex form: <i>y = a(x-p)^2 + q</i>

Completing the square

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Graphing parabolas for given quadratic functions

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Conics - Parabola

Conics - Ellipse

Conics - Circle

Conics - Hyperbola

Operations with radicals

Conversion between entire radicals and mixed radicals

Adding and subtracting radicals

Multiplying radicals

Solving radical equations

Simplifying algebraic fractions and restrictions

Adding and subtracting algebraic fractions

Multiplying algebraic fractions

Dividing algebraic fractions

Solving equations with algebraic fractions

Applications of equations with algebraic fractions

Simplifying complex fractions

Partial fraction decomposition

What is a rational function?

Point of discontinuity

Vertical asymptote

Horizontal asymptote

Slant asymptote

Graphs of rational functions

Solving rational inequalities

Arithmetic sequences

Arithmetic series

Geometric sequences

Geometric series

Infinite geometric series

Sigma notation

Arithmetic mean vs. Geometric mean

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Line symmetry

Rotational symmetry and transformations

Surface area of 3-dimensional shapes

Classifying Triangles

Isosceles and Equilateral Triangles

Squares and square roots

Pythagorean theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

Angles in a circle

Chord properties

Tangent properties

Circles and circumference

Arcs of a circle

Areas and sectors of circles

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Congruence and Congruent Triangles

Triangles Congruent by SSS Proofs

Triangles Congruent by SAS and HL Proofs

Triangles Congruent by ASA and AAS Proofs

Introduction to volume

Volume of prisms

Volume of cylinders

Word problems relating volume of prisms and cylinders

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Use sine ratio to calculate angles and sides (Sin = \( \frac{o}{h}\) )

Use cosine ratio to calculate angles and sides (Cos = \( \frac{a}{h}\) )

Use tangent ratio to calculate angles and sides (Tan = \( \frac{o}{a}\) )

Combination of SohCahToa questions

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Other word problems relating angles in trigonometry

Standard angle

Coterminal angles

Reference angles

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

Unit circle

Law of sines

Law of cosines

Applications of the sine law and cosine law

Median and mode

Mean

Range and outliers

Application of averages

Determining probabilities using tree diagrams and tables

Probability of independent events

Probability with Venn diagrams

Reading and drawing bar graphs

Reading and drawing histograms

Reading and drawing line graphs

Box-and-whisker plots and scatter plots

Stem-and-leaf plots

Reading and drawing Venn diagrams

Frequency tables and dot plots

Introduction to bearings

Bearings and direction word problems

Angle of elevation and depression

Graphing reciprocals of linear functions

Graphing reciprocals of quadratic functions