NEW ZEALAND MATH YEAR 11 – EDmama New Zealand

A. Numbers and Counting

A.01. Identify rational and irrational numbers
A.02. Compare and order rational numbers on a number line
A.03. Convert between decimals, fractions, and percentages
A.04. Evaluate square roots of perfect squares
A.05. Approximate square roots of non-perfect squares
A.06. Evaluate cube roots of perfect cubes
A.07. Explore the properties of real numbers

B. Ratios, Rates, and Proportions

B.01. Understand the concept of a ratio and its different representations
B.02. Identify equivalent ratios using multiplication and division
B.03. Write an equivalent ratio given a ratio and a multiplier
B.04. Calculate unit rates from given ratios
B.05. Determine unit prices for comparing costs
B.06. Solve proportions using cross-multiplication
B.07. Apply proportions to solve word problems involving scaling
B.08. Apply proportions to solve word problems involving scale drawings
B.09. Use proportions to convert between different units of measurement

C. Measurement

D. Consumer Maths

D.01. Calculate simple interest earned on an investment or loan
D.02. Calculate compound interest earned on an investment or loan
D.03. Determine the effective annual rate of compound interest
D.04. Calculate continuously compounded interest
D.05. Calculate the percentage of a number, including GST (Goods and Services Tax) and discounts
D.06. Find the percent discount or mark-up given the original and sale prices
D.07. Solve multi-step problems involving percentages, discounts, and mark-ups
D.08. Compare different financial products using consumer maths skills

E. Coordinate Plane

F. Relations and Functions

F.01. Represent relations using tables, graphs, mappings, and lists of points
F.02. Identify the domain and range of a relation
F.03. Distinguish between independent and dependent variables in a relationship
F.04. Determine whether a relation is a function using the vertical line test
F.05. Find values of a function using its graph
F.06. Evaluate a function for a given input value
F.07. Complete a function table from a graph
F.08. Complete a function table from an equation
F.09. Interpret the graph of a function in the context of word problems
F.10. Use function notation to represent relationships and solve problems

G. Single-Variable Inequalities

G.01. Represent inequalities graphically on a number line
G.02. Write inequalities from given graphs
G.03. Identify solutions to inequalities from a given set of numbers
G.04. Solve one-step linear inequalities using addition and subtraction
G.05. Solve one-step linear inequalities using multiplication and division
G.06. Solve one-step linear inequalities involving negative coefficients
G.07. Graph the solutions to one-step linear inequalities on a number line
G.08. Solve two-step linear inequalities
G.09. Graph the solutions to two-step linear inequalities on a number line
G.10. Solve advanced linear inequalities, including those with distribution
G.11. Graph solutions to advanced linear inequalities on a number line
G.12. Represent real-world situations using linear inequalities

H. Solve Equations

H.01. Model and solve equations using algebra tiles
H.02. Write equations that represent given diagrams or situations
H.03. Solve one-step linear equations using inverse operations
H.04. Solve two-step linear equations
H.05. Solve advanced linear equations, including those with distribution
H.06. Solve equations with variables on both sides
H.07. Solve equations by completing the solution steps
H.08. Determine the number of solutions to a linear equation (none, one, or infinite)
H.09. Create equations with no solutions or infinitely many solutions
H.10. Solve linear equations in the context of word problems
H.11. Solve linear equations using mixed review problems
H.12. Solve absolute value equations

I. Direct and Inverse Variation

I.01. Identify proportional relationships from tables, graphs, and equations
I.02. Find the constant of variation in a direct or inverse variation
I.03. Graph a proportional relationship
I.04. Write direct variation equations from given information
I.05. Write and solve direct variation equations in word problems
I.06. Write inverse variation equations from given information
I.07. Write and solve inverse variation equations in word problems
I.08. Distinguish between direct variation and inverse variation relationships
I.09. Model real-world phenomena using direct and inverse variation

J. Linear Functions

J.04. Find a missing coordinate given the gradient and another point
J.05. Determine the gradient and y-intercept of a linear equation
J.06. Graph a linear equation in slope-intercept form (y = mx + c)
J.07. Write an equation in slope-intercept form from a graph
J.08. Write an equation in slope-intercept form given the gradient and y-intercept
J.09. Write an equation in slope-intercept form from a table of values
J.10. Write an equation in slope-intercept form from a word problem
J.11. Use linear functions to solve real-world word problems
J.12. Complete a table of values and graph a linear function
J.13. Compare linear functions represented by graphs, tables, and equations
J.14. Write equations in standard form (Ax + By = C)
J.15. Find the x- and y-intercepts of a line in standard form
J.16. Graph a line in standard form
J.17. Recognize and write equations of horizontal and vertical lines
J.18. Graph horizontal and vertical lines
J.19. Graph an equation in point-slope form
J.20. Write an equation in point-slope form given a point and the gradient
J.21. Write an equation in point-slope form from a graph
J.22. Determine the gradients of parallel and perpendicular lines
J.23. Write an equation for a line parallel or perpendicular to a given line
J.24. Calculate the distance between a point and a line
J.25. Calculate the distance between two parallel lines
J.26. Identify and describe transformations of linear functions (translations, reflections, dilations)
J.01. Identify linear functions from equations, graphs, and tables
J.02. Calculate the gradient (slope) of a line from its graph
J.03. Calculate the gradient from two points on a line

K. Simultaneous Equations

K.01. Determine whether an ordered pair (x, y) is a solution to a system of simultaneous equations
K.02. Solve simultaneous equations by graphing
K.03. Solve simultaneous equations by graphing word problems
K.04. Determine the number of solutions to a system of simultaneous equations by graphing
K.05. Determine the number of solutions to a system of simultaneous equations without graphing
K.06. Solve simultaneous equations using the substitution method
K.07. Solve simultaneous equations using the substitution method word problems
K.08. Solve simultaneous equations using the elimination method
K.09. Solve simultaneous equations using the elimination method word problems
K.10. Solve simultaneous equations using any appropriate method
K.11. Solve simultaneous equations using any appropriate method word problems
K.12. Apply systems of equations to solve real-world mixture problems

L. Monomials

M. Polynomials

M.01. Understand polynomial vocabulary (terms, coefficients, degree)
M.02. Model polynomials using algebra tiles
M.03. Add and subtract polynomials using algebra tiles
M.04. Add and subtract polynomials algebraically
M.05. Add polynomials to find the perimeter of geometric figures
M.06. Multiply a polynomial by a monomial
M.07. Multiply two polynomials using algebra tiles
M.08. Multiply two binomials using the FOIL method
M.09. Multiply two binomials: special cases (difference of squares, perfect square trinomials)
M.10. Multiply polynomials of higher degree
M.11. Apply polynomial operations to solve geometric and algebraic problems

N. Exponents

N.01. Evaluate powers with integer bases
N.02. Evaluate powers with decimal and fractional bases
N.03. Understand and apply negative exponents
N.04. Apply the product of powers property
N.05. Apply the quotient of powers property
N.06. Simplify expressions using both multiplication and division of exponents
N.07. Apply the power of a power rule
N.08. Evaluate expressions using all properties of exponents
N.09. Identify equivalent expressions involving exponents
N.10. Apply scientific notation to represent very large or very small numbers

O. Factorising

O.01. Find the highest common factor (HCF) of monomials
O.02. Factorise out a monomial from a polynomial
O.03. Factorise quadratic expressions with a leading coefficient of 1
O.04. Factorise quadratic expressions with other leading coefficients
O.05. Factorise quadratic expressions: special cases (difference of squares, perfect square trinomials)
O.06. Factorise quadratic expressions using algebra tiles
O.07. Factorise polynomials by grouping
O.08. Factorise polynomials of higher degree
O.09. Verify factorisation by expanding the expression

P. Quadratic Equations

P.01. Identify the key characteristics of quadratic functions (vertex, axis of symmetry, intercepts)
P.02. Complete a function table for quadratic functions
P.03. Solve a quadratic equation using square roots
P.04. Solve a quadratic equation using the zero product property
P.05. Solve a quadratic equation by factorising
P.06. Complete the square in a quadratic expression
P.07. Solve a quadratic equation by completing the square
P.08. Solve a quadratic equation using the quadratic formula
P.09. Use the discriminant to determine the number and nature of the solutions to a quadratic equation
P.10. Apply quadratic equations to model and solve real-world problems

Q. Functions: Linear, Quadratic, Exponential

Q.01. Identify linear, quadratic, and exponential functions from their graphs
Q.02. Identify linear, quadratic, and exponential functions from their tables of values
Q.03. Write equations for linear, quadratic, and exponential functions from given information
Q.04. Analyse linear functions over unit intervals
Q.05. Analyse exponential functions over unit intervals
Q.06. Describe linear and exponential growth and decay
Q.07. Model real-world situations using linear, quadratic, and exponential functions
Q.08. Compare and contrast the properties of linear, quadratic and exponential functions

R. Logarithms

R.01. Convert between exponential and logarithmic form with rational bases
R.02. Evaluate logarithms
R.03. Apply the change of base formula to evaluate logarithms
R.04. Identify properties of logarithms
R.05. Apply the product property of logarithms
R.06. Apply the quotient property of logarithms
R.07. Apply the power property of logarithms
R.08. Apply properties of logarithms in mixed review problems
R.09. Evaluate logarithms in mixed review problems
R.10. Use logarithms to solve real world exponential growth and decay problems

S. Exponential and Logarithmic Functions

S.01. Determine the domain and range of exponential and logarithmic functions
S.02. Evaluate an exponential function for a given input
S.03. Match exponential functions to their corresponding graphs
S.04. Solve exponential equations by rewriting the base
S.05. Solve exponential equations using common logarithms
S.06. Solve logarithmic equations I
S.07. Solve logarithmic equations II
S.08. Solve exponential growth and decay word problems
S.09. Graph exponential and logarithmic functions
S.10. Apply exponential and logarithmic functions to financial calculations

T. Rational Exponents

U. Radical Expressions

V. Rational Functions and Expressions

V.01. Identify asymptotes and excluded values of rational functions
V.02. Simplify complex fractions
V.03. Simplify rational expressions by factoring and cancelling
V.04. Multiply and divide rational expressions
V.05. Divide polynomials using long division or synthetic division
V.06. Add and subtract rational expressions
V.07. Solve rational equations
V.08. Graph rational functions identifying asymptotes and intercepts
V.09. Apply rational functions to model real-world phenomena

W. Quadratic Equations and Parabolas

W.01. Identify the direction a parabola opens based on the sign of the leading coefficient
W.02. Find the vertex of a parabola
W.03. Find the focus and directrix of a parabola
W.04. Find the axis of symmetry of a parabola
W.05. Write equations of parabolas in vertex form from graphs
W.06. Write equations of parabolas in vertex form using given properties
W.07. Convert equations of parabolas from general to vertex form
W.08. Find properties of a parabola from equations in general form
W.09. Graph parabolas
W.10. Solve real-world optimization problems using quadratic functions

X. Conic Sections: Ellipses and Circles

X.01. Find the centre, vertices, and co-vertices of an ellipse
X.02. Find the length of the major and minor axis of an ellipse
X.03. Find the foci of an ellipse
X.04. Write equations of ellipses in standard form from graphs
X.05. Write equations of ellipses in standard form using given properties
X.06. Convert equations of ellipses from general to standard form
X.07. Find properties of ellipses from equations in general form
X.08. Find the centre of a circle
X.09. Find the radius or diameter of a circle
X.10. Write equations of circles in standard form from graphs
X.11. Write equations of circles in standard form using given properties
X.12. Convert equations of circles from general to standard form
X.13. Find properties of circles from equations in general form
X.14. Graph circles and ellipses

Y. Number Sequences

Y.01. Identify arithmetic and geometric sequences
Y.02. Write the general term (nth term) for arithmetic sequences
Y.03. Write the general term (nth term) for geometric sequences
Y.04. Evaluate variable expressions for number sequences
Y.05. Write variable expressions for arithmetic sequences
Y.06. Write variable expressions for geometric sequences
Y.07. Number sequences: mixed review problems
Y.08. Calculate the sum of finite arithmetic and geometric series
Y.09. Explore infinite geometric series and their convergence

Z. Two-Dimensional Figures

Z.01. Classify triangles based on their sides and angles
Z.02. Understand polygon vocabulary (sides, vertices, angles, diagonals)
Z.03. Apply the Triangle Angle-Sum Theorem to find missing angles
Z.04. Use properties of midsegments of triangles
Z.05. Apply properties of triangles and bisectors
Z.06. Identify medians, altitudes, angle bisectors, and perpendicular bisectors in triangles
Z.07. Calculate the perimeter of various polygons
Z.08. Calculate the area of triangles and quadrilaterals
Z.09. Calculate area and perimeter in the coordinate plane I
Z.10. Calculate area and perimeter in the coordinate plane II
Z.11. Calculate the area and circumference of circles
Z.12. Calculate the area of compound figures
Z.13. Calculate the area between two shapes
Z.14. Calculate the area and perimeter of similar figures
Z.15. Calculate the surface area of two-dimensional objects

AA. Introduction to Congruent Figures

BB. Congruent Triangles

CC. Similarity

CC.01. Identify similar figures based on proportional sides and congruent angles
CC.02. Determine ratios in similar figures
CC.03. Write similarity statements for similar figures
CC.04. Find missing side lengths and angle measures in similar figures
CC.05. Apply similar triangles and indirect measurement techniques
CC.06. Determine the relationship between the perimeters of similar figures
CC.07. Apply similarity rules (AA, SSS, SAS) for triangles
CC.08. Relate similar triangles to similarity transformations (dilations)
CC.09. Determine the relationship between the areas of similar figures
CC.10. Construct similar figures using geometric tools

DD. Right Triangles

EE. Angle Measures

FF. Trigonometry

FF.01. Define and calculate trigonometric ratios: sin, cos, and tan
FF.02. Define and calculate trigonometric ratios: csc, sec, and cot
FF.03. Apply trigonometric ratios in similar right triangles
FF.04. Find trigonometric ratios using the unit circle
FF.05. Understand and apply trigonometric functions of complementary angles
FF.06. Determine sin, cos, and tan of special angles (0, 30, 45, 60, 90 degrees)
FF.07. Determine csc, sec, and cot of special angles (0, 30, 45, 60, 90 degrees)
FF.08. Find trigonometric functions using a calculator
FF.09. Understand and apply the symmetry and periodicity of trigonometric functions
FF.10. Define and evaluate inverses of sin, cos, and tan
FF.11. Define and evaluate inverses of csc, sec, and cot
FF.12. Solve trigonometric equations I
FF.13. Solve trigonometric equations II
FF.14. Apply trigonometric ratios to find a side length in a right triangle
FF.15. Apply trigonometric ratios to find an angle measure in a right triangle
FF.16. Solve a right triangle given sufficient information
FF.17. Apply the Law of Sines to solve non-right triangles
FF.18. Apply the Law of Cosines to solve non-right triangles
FF.19. Solve a triangle given sufficient information using the Law of Sines and Cosines
FF.20. Model periodic phenomena using trigonometric functions

GG. Circles

GG.01. Identify and define parts of a circle (centre, radius, diameter, chord, secant, tangent)
GG.02. Define and measure central angles in a circle
GG.03. Calculate arc measure and arc length
GG.04. Calculate the area of sectors of a circle
GG.05. Solve circle measurement problems: mixed review
GG.06. Apply properties of arcs and chords in a circle
GG.07. Apply properties of tangent lines to a circle
GG.08. Calculate the perimeter of polygons with an inscribed circle
GG.09. Apply properties of inscribed angles in a circle
GG.10. Apply properties of angles in inscribed right triangles
GG.11. Apply properties of angles in inscribed quadrilaterals
GG.12. Use geometric construction techniques to construct circles

HH. Circles in the Coordinate Plane

HH.02. Find the radius or diameter of a circle given its equation or graph
HH.03. Write equations of circles in standard form from graphs
HH.04. Write equations of circles in standard form using given properties (centre and radius)
HH.05. Convert equations of circles from general to standard form
HH.06. Find properties of circles from equations in general form
HH.07. Graph circles from their equations in standard form
HH.08. Solve geometric problems using coordinate geometry techniques
HH.01. Find the centre of a circle given its equation or graph

II. Surface Area and Volume

II.01. Understand the concepts of surface area and volume
II.02. Calculate the surface area of prisms and cylinders
II.03. Calculate the surface area of pyramids and cones
II.04. Calculate the volume of prisms and cylinders
II.05. Calculate the volume of pyramids and cones
II.06. Calculate the surface area and volume of spheres
II.07. Understand the concept of similar solids
II.08. Determine the relationship between the surface area and volume of similar solids
II.09. Solve surface area and volume review problems
II.10. Apply surface area and volume to optimization problems

JJ. Transformations

JJ.01. Perform translations and graph the image of a figure
JJ.02. Find the coordinates of an image after a translation
JJ.03. Write the rule for a given translation
JJ.04. Perform reflections and graph the image of a figure
JJ.05. Find the coordinates of an image after a reflection
JJ.06. Rotate polygons about a point
JJ.07. Perform rotations and graph the image of a figure
JJ.08. Find the coordinates of an image after a rotation
JJ.09. Classify congruence transformations (translations, reflections, rotations)
JJ.10. Perform compositions of congruence transformations and graph the image
JJ.11. Identify transformations that carry a polygon onto itself
JJ.12. Solve congruence transformation problems: mixed review
JJ.13. Perform dilations and graph the image of a figure
JJ.14. Find the coordinates of an image after a dilation
JJ.15. Determine the scale factor and classification (enlargement or reduction) of a dilation
JJ.16. Apply dilations in the context of parallel lines
JJ.17. Use transformations to create geometric designs

Course Content

A. Numbers and Counting

A.01. Identify rational and irrational numbers

A.02. Compare and order rational numbers on a number line

A.03. Convert between decimals, fractions, and percentages

A.04. Evaluate square roots of perfect squares

A.05. Approximate square roots of non-perfect squares

A.06. Evaluate cube roots of perfect cubes

A.07. Explore the properties of real numbers

B. Ratios, Rates, and Proportions

B.01. Understand the concept of a ratio and its different representations

B.02. Identify equivalent ratios using multiplication and division

B.03. Write an equivalent ratio given a ratio and a multiplier

B.04. Calculate unit rates from given ratios

B.05. Determine unit prices for comparing costs

B.06. Solve proportions using cross-multiplication

B.07. Apply proportions to solve word problems involving scaling

B.08. Apply proportions to solve word problems involving scale drawings

B.09. Use proportions to convert between different units of measurement

C. Measurement

C.01. Convert between different units of measurement within the same system (e.g., metric or imperial)

C.02. Apply precision to measurements and calculations

C.03. Calculate the greatest possible error in a measurement

C.04. Determine the minimum and maximum possible area and volume based on measurement error

C.05. Calculate percent error in measurements

C.06. Determine the effects of measurement errors on area and volume calculations

C.07. Apply unit analysis to convert rates and measurements effectively

D. Consumer Maths

D.01. Calculate simple interest earned on an investment or loan

D.02. Calculate compound interest earned on an investment or loan

D.03. Determine the effective annual rate of compound interest

D.04. Calculate continuously compounded interest

D.05. Calculate the percentage of a number, including GST (Goods and Services Tax) and discounts

D.06. Find the percent discount or mark-up given the original and sale prices

D.07. Solve multi-step problems involving percentages, discounts, and mark-ups

D.08. Compare different financial products using consumer maths skills

E. Coordinate Plane

E.01. Review the basics of the coordinate plane, including axes, quadrants, and ordered pairs

E.02. Determine the coordinates of the midpoint of a line segment

E.03. Calculate the distance between two points in the coordinate plane

E.04. Use the coordinate plane to represent and solve geometric problems

E.05. Apply the Pythagorean theorem in the coordinate plane

F. Relations and Functions

F.01. Represent relations using tables, graphs, mappings, and lists of points

F.02. Identify the domain and range of a relation

F.03. Distinguish between independent and dependent variables in a relationship

F.04. Determine whether a relation is a function using the vertical line test

F.05. Find values of a function using its graph

F.06. Evaluate a function for a given input value

F.07. Complete a function table from a graph

F.08. Complete a function table from an equation

F.09. Interpret the graph of a function in the context of word problems

F.10. Use function notation to represent relationships and solve problems

G. Single-Variable Inequalities

G.01. Represent inequalities graphically on a number line

G.02. Write inequalities from given graphs

G.03. Identify solutions to inequalities from a given set of numbers

G.04. Solve one-step linear inequalities using addition and subtraction

G.05. Solve one-step linear inequalities using multiplication and division

G.06. Solve one-step linear inequalities involving negative coefficients

G.07. Graph the solutions to one-step linear inequalities on a number line

G.08. Solve two-step linear inequalities

G.09. Graph the solutions to two-step linear inequalities on a number line

G.10. Solve advanced linear inequalities, including those with distribution

G.11. Graph solutions to advanced linear inequalities on a number line

G.12. Represent real-world situations using linear inequalities

H. Solve Equations

H.01. Model and solve equations using algebra tiles

H.02. Write equations that represent given diagrams or situations

H.03. Solve one-step linear equations using inverse operations

H.04. Solve two-step linear equations

H.05. Solve advanced linear equations, including those with distribution

H.06. Solve equations with variables on both sides

H.07. Solve equations by completing the solution steps

H.08. Determine the number of solutions to a linear equation (none, one, or infinite)

H.09. Create equations with no solutions or infinitely many solutions

H.10. Solve linear equations in the context of word problems

H.11. Solve linear equations using mixed review problems

H.12. Solve absolute value equations

I. Direct and Inverse Variation