AUSTRALIA MATH YEAR 10 – EDmama Australia

A. Numbers and Counting

A.05. Approximate square roots and cube roots of non-perfect numbers.
A.06. Express repeating decimals as fractions.
A.07. Understand and apply the properties of real numbers (commutative, associative, distributive, identity, inverse).
A.01. Identify and classify numbers as rational or irrational.
A.02. Compare and order rational numbers on a number line.
A.03. Determine the principal square root of perfect squares.
A.04. Determine the cube root of perfect cubes.

B. Monomials

C. Polynomials

C.01. Define and identify key polynomial vocabulary (terms, coefficients, degree, leading coefficient, constant term).
C.02. Model polynomials using algebra tiles to visually represent addition and subtraction.
C.03. Add and subtract polynomials using algebra tiles.
C.04. Simplify polynomial expressions by adding and subtracting like terms.
C.05. Calculate the perimeter of geometric figures represented by polynomial expressions.
C.06. Multiply a polynomial by a monomial using the distributive property.
C.07. Model the multiplication of two polynomials using algebra tiles.
C.08. Expand the product of two binomials using the FOIL method or distributive property.
C.09. Recognize and expand special product cases, such as the square of a binomial or the difference of squares.
C.10. Multiply polynomials of higher degree.
C.11. Divide polynomials using long division.
C.12. Divide polynomials using synthetic division.
C.13. Determine the roots (zeros) of factorised polynomials by setting each factor to zero.
C.14. Construct a polynomial expression given its roots.
C.15. Understand and apply the conjugate root theorem.
C.16. Analyze the end behavior of polynomial functions to match them with their graphs.
C.17. Use the zeros (x-intercepts) of polynomial functions to match them with their graphs.
C.18. Match polynomial functions with their corresponding graphs by considering end behavior, zeros, and turning points.
C.19. Determine the domain and range of polynomial functions.
C.20. Apply polynomial functions to model real-world phenomena, such as projectile motion or economic trends.

D. Factorising

D.01. Determine the highest common factor (HCF) of monomials.
D.02. Determine the lowest common multiple (LCM) of monomials.
D.03. Factorise a monomial from a polynomial expression.
D.04. Factorise quadratic expressions with a leading coefficient of 1.
D.05. Factorise quadratic expressions with a leading coefficient other than 1.
D.06. Factorise special case quadratic expressions, such as perfect square trinomials and difference of squares.
D.07. Factorise quadratic expressions using algebra tiles.
D.08. Factorise polynomials by grouping terms with common factors.
D.09. Factorise polynomials of higher degree using various techniques.
D.10. Apply factorisation techniques to simplify algebraic fractions.

E. Exponents

E.01. Evaluate powers with integer bases.
E.02. Evaluate powers with decimal and fractional bases.
E.03. Understand and apply negative exponents.
E.04. Multiply exponential expressions with the same base.
E.05. Divide exponential expressions with the same base.
E.06. Simplify expressions by combining multiplication and division of exponents.
E.07. Apply the power rule to simplify expressions with exponents raised to a power.
E.08. Evaluate expressions using multiple properties of exponents.
E.09. Identify equivalent expressions involving exponents.
E.10. Apply the properties of exponents to solve algebraic equations.

F. Rational Exponents

G. Radical Expressions

G.01. Find roots of integer numbers.
G.02. Find roots of rational numbers.
G.03. Determine roots of numbers using a calculator.
G.04. Simplify radical expressions by extracting perfect square factors.
G.05. Simplify radical expressions involving fractions by rationalizing the denominator.
G.06. Multiply radical expressions using the distributive property.
G.07. Add and subtract radical expressions by combining like terms.
G.08. Simplify radical expressions using the distributive property.
G.09. Simplify radical expressions using conjugates to rationalize denominators.
G.10. Simplify radical expressions using a variety of techniques.
G.11. Convert between rational exponents and radical notation.
G.12. Apply radical expressions to solve geometric problems, such as finding lengths or distances.

H. Solve Equations

H.01. Determine if a given value of x satisfies a linear equation.
H.02. Model and solve linear equations using algebra tiles.
H.03. Write linear equations to represent diagrams and solve them.
H.04. Solve one-step linear equations using inverse operations.
H.05. Solve two-step linear equations using inverse operations.
H.06. Solve multi-step linear equations using the distributive property and combining like terms.
H.07. Solve linear equations with variables on both sides.
H.08. Complete the steps to solve given linear equations.
H.09. Determine the number of solutions (none, one, or infinite) for a linear equation.
H.10. Create linear equations with no solutions or infinitely many solutions.
H.11. Solve linear equations presented in word problems.
H.12. Solve a variety of linear equations.
H.13. Rearrange multi-variable equations to solve for a specific variable.
H.14. Apply linear equations to solve problems in geometry, such as finding unknown angles or side lengths.

I. Single-Variable Inequalities

I.01. Graph inequalities on a number line.
I.02. Write inequalities from given graphs.
I.03. Write and graph inequalities to represent real-world scenarios.
I.04. Identify solutions to inequalities.
I.05. Solve one-step linear inequalities using addition and subtraction.
I.06. Solve one-step linear inequalities using multiplication and division.
I.07. Solve one-step linear inequalities.
I.08. Graph the solution set to one-step linear inequalities on a number line.
I.09. Solve two-step linear inequalities.
I.10. Graph the solution set to two-step linear inequalities on a number line.
I.11. Solve multi-step linear inequalities.
I.12. Graph the solution set to multi-step linear inequalities on a number line.
I.13. Express the solution set of linear inequalities using interval notation.

J. Coordinate Plane

K. Relations and Functions

K.01. Represent relations using tables, graphs, mappings, and lists of points, and convert between these representations.
K.02. Determine the domain and range of relations.
K.03. Identify independent and dependent variables in a given context.
K.04. Identify whether a relation is a function using the vertical line test or by examining ordered pairs.
K.05. Find values of a function using its graph.
K.06. Evaluate a function given an input value.
K.07. Complete a function table from a graph.
K.08. Complete a function table from an equation.
K.09. Approximate solutions to equations using a table of values.
K.10. Interpret the graph of a function in the context of a word problem.
K.11. Calculate the rate of change from a table of values.
K.12. Calculate the rate of change from a graph.
K.13. Determine the inverse of a given function.

L. Linear Functions

L.10. Write the equation of a line in slope-intercept form from a table of values.
L.11. Write the equation of a line in slope-intercept form from a word problem.
L.12. Write linear functions to solve real-world word problems.
L.13. Complete a table of values and graph a linear function.
L.14. Compare linear functions represented by graphs, tables, and equations.
L.15. Write equations in standard form (Ax + By = C).
L.16. Find the x- and y-intercepts of a line in standard form.
L.17. Graph a linear equation in standard form.
L.18. Recognize and write equations of horizontal and vertical lines.
L.19. Graph horizontal and vertical lines.
L.20. Graph a line using point-slope form.
L.21. Write the equation of a line in point-slope form.
L.22. Write the equation of a line in point-slope form from its graph.
L.23. Determine the gradients of parallel and perpendicular lines.
L.24. Write the equation of a line that is parallel or perpendicular to a given line.
L.25. Calculate the distance between a point and a line.
L.26. Calculate the distance between two parallel lines.
L.27. Describe and perform transformations of linear functions (translations, reflections, dilations).
L.28. Model real-world situations using piecewise linear functions.
L.01. Identify linear functions from equations, graphs, and tables.
L.02. Determine the gradient (slope) of a line from its graph.
L.03. Calculate the gradient of a line given two points on the line.
L.04. Find a missing coordinate given the gradient and another point on the line.
L.05. Determine the gradient and y-intercept of a linear equation.
L.06. Graph a linear equation in slope-intercept form (y = mx + c).
L.07. Write the equation of a line in slope-intercept form from its graph.
L.08. Write the equation of a line in slope-intercept form given the gradient and y-intercept.
L.09. Solve linear equations for y to express them in slope-intercept form.

M. Simultaneous Equations

M.01. Determine if an ordered pair (x, y) is a solution to a system of simultaneous equations.
M.02. Solve systems of simultaneous equations by graphing.
M.03. Solve word problems involving systems of simultaneous equations by graphing.
M.04. Determine the number of solutions (none, one, or infinite) to a system of simultaneous equations by graphing.
M.05. Determine the number of solutions to a system of simultaneous equations without graphing.
M.06. Solve systems of simultaneous equations using the substitution method.
M.07. Solve word problems involving systems of simultaneous equations using substitution.
M.08. Solve systems of simultaneous equations using the elimination method.
M.09. Solve word problems involving systems of simultaneous equations using elimination.
M.10. Solve systems of simultaneous equations using any appropriate method.
M.11. Solve word problems involving systems of simultaneous equations using any appropriate method.
M.12. Apply systems of equations to solve problems in chemistry, such as balancing chemical equations.

N. Inequalities and Linear Programming

N.01. Determine if an ordered pair (x, y) satisfies a linear inequality.
N.02. Solve linear inequalities for y.
N.03. Graph a linear inequality in the coordinate plane.
N.04. Write and solve linear inequalities to represent real-world constraints.
N.05. Determine if an ordered pair (x, y) is a solution to a system of simultaneous inequalities.
N.06. Solve systems of simultaneous inequalities by graphing.
N.07. Determine the vertices of the feasible region (solution set) of a system of linear inequalities.
N.08. Solve linear programming problems to find the maximum or minimum value of an objective function subject to constraints.
N.09. Apply linear programming to optimize resource allocation in business and industry.

O. Quadratic Equations

O.01. Identify and describe the key characteristics of quadratic functions (vertex, axis of symmetry, intercepts, concavity).
O.02. Complete a function table for a quadratic function.
O.03. Describe transformations of quadratic functions (translations, reflections, dilations).
O.04. Determine the equation of a quadratic function given specific points or properties.
O.05. Graph a quadratic function by hand or using technology.
O.06. Match quadratic functions with their corresponding graphs.
O.07. Solve a quadratic equation using square roots.
O.08. Solve a quadratic equation using the zero product property.
O.09. Solve a quadratic equation with a leading coefficient of 1 by factorising.
O.10. Solve a quadratic equation with a leading coefficient other than 1 by factorising.
O.11. Complete the square to rewrite a quadratic expression in vertex form.
O.12. Solve a quadratic equation with a leading coefficient of 1 by completing the square.
O.13. Solve a quadratic equation with a leading coefficient other than 1 by completing the square.
O.14. Solve a quadratic equation using the quadratic formula.
O.15. Use the discriminant to determine the number and nature of the roots of a quadratic equation.
O.16. Solve systems of simultaneous equations where one is quadratic and the other is linear by graphing.
O.17. Solve real-world problems involving quadratic equations, such as projectile motion or area optimization.

P. Functions: Linear, Quadratic, Exponential

Q. Logarithms

Q.01. Convert between exponential and logarithmic form using rational bases.
Q.02. Evaluate logarithms using the definition of a logarithm.
Q.03. Apply the change of base formula to evaluate logarithms with any base.
Q.04. Identify and apply properties of logarithms (product, quotient, power, etc.).
Q.05. Apply the product property of logarithms to expand or condense logarithmic expressions.
Q.06. Apply the quotient property of logarithms to expand or condense logarithmic expressions.
Q.07. Apply the power property of logarithms to expand or condense logarithmic expressions.
Q.08. Apply properties of logarithms to simplify a variety of logarithmic expressions.
Q.09. Evaluate logarithms using a combination of properties.
Q.10. Use logarithms to solve exponential growth and decay problems.

R. Exponential and Logarithmic Functions

R.01. Determine the domain and range of exponential functions.
R.02. Determine the domain and range of logarithmic functions.
R.03. Evaluate an exponential function.
R.04. Match exponential functions with their corresponding graphs.
R.05. Match exponential functions with their corresponding graphs, including transformations.
R.06. Solve exponential equations by rewriting the bases.
R.07. Solve exponential equations using common logarithms.
R.08. Solve logarithmic equations.
R.09. Solve more complex logarithmic equations using properties of logarithms.
R.10. Solve exponential growth and decay word problems.
R.11. Apply exponential functions to model compound interest and population growth.

S. Matrices

S.01. Define and use matrix vocabulary (element, row, column, dimension, etc.).
S.02. Understand and apply matrix operation rules (addition, subtraction, scalar multiplication, matrix multiplication).
S.03. Add and subtract matrices of compatible dimensions.
S.04. Multiply a matrix by a scalar.
S.05. Form linear combinations of matrices.
S.06. Multiply two matrices of compatible dimensions.
S.07. Identify transformation matrices for geometric transformations.
S.08. Apply transformation matrices by writing the vertex matrix for a polygon.
S.09. Apply transformation matrices to graph the image of a polygon.
S.10. Use matrices to solve systems of linear equations.

T. Consumer Maths

T.01. Calculate simple interest.
T.02. Solve word problems involving compound interest.
T.03. Solve more complex word problems involving compound interest with varying compounding periods.
T.04. Calculate continuously compounded interest.
T.05. Solve more complex problems involving continuously compounded interest.
T.06. Calculate the percent of a number, including GST, discount, and more.
T.07. Calculate the percent discount or mark-up.
T.08. Solve multi-step problems involving percentages.
T.09. Compare and contrast different investment options based on interest rates and compounding periods.

U. Two-Dimensional Figures

U.01. Classify triangles based on their sides and angles.
U.02. Define and use polygon vocabulary (sides, vertices, angles, diagonals, etc.).
U.03. Apply the Triangle Angle-Sum Theorem to find missing angles in triangles.
U.04. Calculate the perimeter of various two-dimensional figures.
U.05. Calculate the area of triangles and quadrilaterals.
U.06. Calculate the area and perimeter of figures in the coordinate plane.
U.07. Calculate the area and perimeter of more complex figures in the coordinate plane.
U.08. Calculate the area and circumference of circles.
U.09. Calculate the area of compound figures by adding or subtracting areas of simpler shapes.
U.10. Calculate the area between two shapes.
U.11. Calculate the area and perimeter of similar figures using scale factors.
U.12. Apply geometric formulas to solve real-world measurement problems.

V. Surface Area and Volume

V.08. Define similar solids and understand the relationship between their corresponding dimensions.
V.09. Calculate the surface area and volume of similar solids using scale factors.
V.10. Apply a variety of surface area and volume formulas.
V.11. Use geometric nets to visualize and calculate the surface area of three-dimensional figures.
V.01. Define surface area and volume and understand their respective units.
V.02. Calculate the surface area of prisms and cylinders.
V.03. Calculate the surface area of pyramids and cones.
V.04. Calculate the volume of prisms and cylinders.
V.05. Calculate the volume of pyramids and cones.
V.06. Calculate the surface area and volume of spheres.
V.07. Calculate the volume of compound figures by adding or subtracting volumes of simpler shapes.

W. Circles

W.01. Identify and define the different parts of a circle (centre, radius, diameter, chord, secant, tangent).
W.02. Define and measure central angles in degrees and radians.
W.03. Calculate arc measure and arc length.
W.04. Convert between radians and degrees.
W.05. Calculate arc length using radians.
W.06. Calculate the area of sectors of a circle.
W.07. Solve a variety of problems involving circle measurements (arc length, sector area, circumference, area).
W.08. Understand and apply relationships between arcs and chords.
W.09. Understand and apply properties of tangent lines to circles.
W.10. Calculate the perimeter of polygons with an inscribed circle.
W.11. Understand and apply properties of inscribed angles.
W.12. Apply properties of angles in inscribed right triangles.
W.13. Apply properties of angles in inscribed quadrilaterals.
W.14. Use geometric software to explore the properties of circles and their relationships to other geometric figures.

X. Circles in the Coordinate Plane

X.01. Determine the coordinates of the centre of a circle given its equation or graph.
X.02. Determine the radius or diameter of a circle given its equation or graph.
X.03. Write the equation of a circle in standard form from its graph.
X.04. Write the equation of a circle in standard form given its centre and radius or other properties.
X.05. Convert equations of circles from general to standard form by completing the square.
X.06. Determine the centre and radius of a circle from its equation in general form.
X.07. Graph circles given their equations in standard or general form.
X.08. Solve problems involving circles intersecting with lines or other circles.

Y. Angle measures

Z. Trigonometry

Z.01. Define and calculate the six trigonometric ratios (sin, cos, tan, csc, sec, cot) in a right triangle.
Z.02. Define and calculate the reciprocal trigonometric ratios (csc, sec, cot).
Z.03. Understand that trigonometric ratios are constant for similar right triangles.
Z.04. Determine trigonometric ratios using the unit circle.
Z.05. Understand and apply trigonometric functions of complementary angles.
Z.06. Determine the sine, cosine, and tangent of special angles (30°, 45°, 60°).
Z.07. Determine the cosecant, secant, and cotangent of special angles (30°, 45°, 60°).
Z.08. Find trigonometric function values using a calculator.
Z.09. Understand the symmetry and periodicity of trigonometric functions.
Z.10. Define and evaluate the inverses of sine, cosine, and tangent functions.
Z.11. Define and evaluate the inverses of cosecant, secant, and cotangent functions.
Z.12. Solve trigonometric equations.
Z.13. Solve more complex trigonometric equations using identities and algebraic techniques.
Z.14. Calculate a side length in a right triangle using trigonometric ratios.
Z.15. Calculate an angle measure in a right triangle using trigonometric ratios.
Z.16. Solve a right triangle by finding all missing side lengths and angle measures.
Z.17. Apply the Law of Sines to solve triangles.
Z.18. Apply the Law of Cosines to solve triangles.
Z.19. Solve any triangle using appropriate trigonometric laws.
Z.20. Calculate the area of a triangle using the sine formula.
Z.21. Calculate the area of a triangle using the Law of Sines.
Z.22. Apply trigonometric functions to model periodic phenomena, such as sound waves or tides.

AA. Logic

AA.01. Identify the hypothesis and conclusion of a conditional statement.
AA.02. Provide counterexamples to disprove conditional statements.
AA.03. Define and write conditional statements.
AA.04. Construct and interpret truth tables for logical statements.
AA.05. Determine the truth values of logical statements.
AA.06. Write geometric proofs involving angles.
AA.07. Write geometric proofs involving parallel lines.
AA.08. Write more complex geometric proofs involving parallel lines and transversals.
AA.09. Distinguish between inductive and deductive reasoning in mathematical arguments.

BB. Introduction to Congruent Figures

CC. Congruent Triangles

CC.01. Apply the Side-Side-Side (SSS) and Side-Angle-Side (SAS) Theorems to prove triangle congruence.
CC.02. Apply the Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS) Theorems to prove triangle congruence.
CC.03. Apply SSS, SAS, ASA, and AAS Theorems to solve problems involving congruent triangles.
CC.04. Apply the SSS Theorem in the coordinate plane.
CC.05. Apply congruency theorems to isosceles and equilateral triangles.
CC.06. Apply the Hypotenuse-Leg (HL) Theorem to prove the congruence of right triangles.
CC.07. Write formal proofs to demonstrate triangle congruence using SSS and SAS.
CC.08. Write formal proofs to demonstrate triangle congruence using ASA and AAS.
CC.09. Write formal proofs to demonstrate triangle congruence using SSS, SAS, ASA, and AAS.
CC.10. Write geometric proofs involving corresponding parts of congruent triangles.
CC.11. Write geometric proofs involving isosceles triangles.
CC.12. Use congruent triangles to solve real-world problems, such as structural engineering or surveying.

DD. Similarity

DD.01. Identify similar figures by visually comparing their shapes and proportions.
DD.02. Calculate ratios of corresponding side lengths in similar figures.
DD.03. Write similarity statements for similar figures.
DD.04. Determine side lengths and angle measures in similar figures.
DD.05. Apply similar triangles and indirect measurement to solve real-world problems.
DD.06. Compare the perimeters of similar figures.
DD.07. Apply similarity rules for triangles (AA, SSS, SAS).
DD.08. Relate similar triangles to similarity transformations (dilations).
DD.09. Understand and apply the concept of similarity of circles.
DD.10. Compare the areas of similar figures.
DD.11. Write geometric proofs involving similar triangles.
DD.12. Write more complex geometric proofs involving similar triangles.
DD.13. Use similarity to construct geometric figures, such as creating scaled drawings or models.

EE. Right Triangles

FF. Parabolas

FF.01. Determine the direction a parabola opens from its equation.
FF.02. Find the vertex of a parabola.
FF.03. Find the focus and directrix of a parabola.
FF.04. Find the axis of symmetry of a parabola.
FF.05. Write the equation of a parabola from its vertex and another point.
FF.06. Write the equation of a parabola from its vertex, focus, and directrix.
FF.07. Convert equations of parabolas from general to vertex form.
FF.08. Find properties of a parabola from equations in general form.
FF.09. Graph parabolas.
FF.10. Solve real-world problems involving parabolas, such as the trajectory of a projectile.

GG. Hyperbolas

GG.01. Find the centre of a hyperbola.
GG.02. Find the vertices of a hyperbola.
GG.03. Find the length of the transverse and conjugate axes of a hyperbola.
GG.04. Find the equations for the asymptotes of a hyperbola.
GG.05. Find the foci of a hyperbola.
GG.06. Write equations of hyperbolas in standard form from graphs.
GG.07. Write equations of hyperbolas in standard form using properties.
GG.08. Convert equations of hyperbolas from general to standard form.
GG.09. Find properties of hyperbolas from equations in general form.
GG.10. Apply hyperbolas to model real-world phenomena, such as the path of a comet or the design of cooling towers.

HH. Problem solving

II. Probability

II.02. Calculate experimental probabilities based on data.
II.03. Find probabilities using two-way frequency tables.
II.04. Find conditional probabilities using two-way frequency tables.
II.05. Calculate the number of outcomes for compound events.
II.06. Identify independent and dependent events.
II.07. Calculate probabilities of independent and dependent events.
II.08. Calculate geometric probabilities.
II.09. Use probability to make predictions and informed decisions in real-world scenarios.
II.01. Calculate theoretical probabilities of simple events.

JJ. Statistics

KK. Data and graphs

KK.01. Interpret histograms to understand data distribution.
KK.02. Create histograms to represent data.
KK.03. Interpret dot plots to understand data distribution.
KK.04. Create dot plots to represent data.
KK.05. Create frequency charts to organize data.
KK.06. Interpret stem-and-leaf plots to understand data distribution.
KK.07. Interpret box plots to understand data distribution.
KK.08. Create scatter plots to visualize relationships between two variables.
KK.09. Identify trends (positive, negative, no correlation) using scatter plots.
KK.10. Make predictions using scatter plots.
KK.11. Identify outliers in scatter plots.
KK.12. Determine a line of best fit for a scatter plot.
KK.13. Analyze and interpret data presented in various graphical formats.

Course Content

A. Numbers and Counting

A.05. Approximate square roots and cube roots of non-perfect numbers.

A.06. Express repeating decimals as fractions.

A.07. Understand and apply the properties of real numbers (commutative, associative, distributive, identity, inverse).

A.01. Identify and classify numbers as rational or irrational.

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

A.03. Determine the principal square root of perfect squares.

A.04. Determine the cube root of perfect cubes.

B. Monomials

B.01. Recognize and identify monomials in algebraic expressions.

B.02. Multiply monomials using the product of powers rule.

B.03. Divide monomials using the quotient of powers rule.

B.04. Simplify expressions by multiplying and dividing monomials.

B.05. Apply the power rule to simplify powers of monomials.

B.06. Combine multiple rules of exponents to simplify complex monomial expressions.

B.07. Use monomials to model real-world scenarios, such as area or volume calculations.

C. Polynomials

C.01. Define and identify key polynomial vocabulary (terms, coefficients, degree, leading coefficient, constant term).

C.02. Model polynomials using algebra tiles to visually represent addition and subtraction.

C.03. Add and subtract polynomials using algebra tiles.

C.04. Simplify polynomial expressions by adding and subtracting like terms.

C.05. Calculate the perimeter of geometric figures represented by polynomial expressions.

C.06. Multiply a polynomial by a monomial using the distributive property.

C.07. Model the multiplication of two polynomials using algebra tiles.

C.08. Expand the product of two binomials using the FOIL method or distributive property.

C.09. Recognize and expand special product cases, such as the square of a binomial or the difference of squares.

C.10. Multiply polynomials of higher degree.

C.11. Divide polynomials using long division.

C.12. Divide polynomials using synthetic division.

C.13. Determine the roots (zeros) of factorised polynomials by setting each factor to zero.

C.14. Construct a polynomial expression given its roots.

C.15. Understand and apply the conjugate root theorem.

C.16. Analyze the end behavior of polynomial functions to match them with their graphs.

C.17. Use the zeros (x-intercepts) of polynomial functions to match them with their graphs.

C.18. Match polynomial functions with their corresponding graphs by considering end behavior, zeros, and turning points.

C.19. Determine the domain and range of polynomial functions.

C.20. Apply polynomial functions to model real-world phenomena, such as projectile motion or economic trends.

D. Factorising

D.01. Determine the highest common factor (HCF) of monomials.

D.02. Determine the lowest common multiple (LCM) of monomials.

D.03. Factorise a monomial from a polynomial expression.

D.04. Factorise quadratic expressions with a leading coefficient of 1.

D.05. Factorise quadratic expressions with a leading coefficient other than 1.

D.06. Factorise special case quadratic expressions, such as perfect square trinomials and difference of squares.

D.07. Factorise quadratic expressions using algebra tiles.

D.08. Factorise polynomials by grouping terms with common factors.

D.09. Factorise polynomials of higher degree using various techniques.

D.10. Apply factorisation techniques to simplify algebraic fractions.

E. Exponents

E.01. Evaluate powers with integer bases.

E.02. Evaluate powers with decimal and fractional bases.

E.03. Understand and apply negative exponents.

E.04. Multiply exponential expressions with the same base.

E.05. Divide exponential expressions with the same base.

E.06. Simplify expressions by combining multiplication and division of exponents.

E.07. Apply the power rule to simplify expressions with exponents raised to a power.

E.08. Evaluate expressions using multiple properties of exponents.

E.09. Identify equivalent expressions involving exponents.

E.10. Apply the properties of exponents to solve algebraic equations.

F. Rational Exponents

F.01. Evaluate expressions with rational exponents.

F.02. Multiply expressions with rational exponents using exponent rules.

F.03. Divide expressions with rational exponents using exponent rules.

F.04. Apply the power rule to expressions with rational exponents.

F.05. Simplify expressions involving rational exponents.

F.06. Simplify complex expressions involving rational exponents.

F.07. Use rational exponents to solve equations involving radicals.

G. Radical Expressions

G.01. Find roots of integer numbers.

G.02. Find roots of rational numbers.

G.03. Determine roots of numbers using a calculator.

G.04. Simplify radical expressions by extracting perfect square factors.

G.05. Simplify radical expressions involving fractions by rationalizing the denominator.

G.06. Multiply radical expressions using the distributive property.

G.07. Add and subtract radical expressions by combining like terms.

G.08. Simplify radical expressions using the distributive property.

G.09. Simplify radical expressions using conjugates to rationalize denominators.

G.10. Simplify radical expressions using a variety of techniques.

G.11. Convert between rational exponents and radical notation.