Grades: 10th to 12th COMPLETE THE SQUARE of QUADRATIC EXPRESSIONS WORKBOOK to learn and practise: • use integers, square roots of perfect square numbers and surds to complete the square of quadratic expressions. • Factorise monic quadratic expressions by completing the square. The resource includes two style workbooks + Step by step solutions + Students’ folded notes + Teacher notes WORKBOOK STYLE A: Cover + Notes with no solutions for examples + Worksheets WORKBOOK STYLE B: Cover + Completed Notes + Worksheets Total pages for each workbook: 10 Easy classroom preparation: • For the teacher notes: print the notes on transparencies or display them on a whiteboard. • For the workbook: print and staple all pages together to make a book. • For the folded notes: print, fold and glue the pages to make a folded note. Also comply with Australian Curriculum Expand binomial products and factorise monic quadratic expressions using a variety of strategies (ACMNA233) Solve simple quadratic equations using a range of strategies (ACMNA241) Solve quadratic equations using the quadratic formula and by completing the square (ACMMM008) Investigate and use square roots of perfect square numbers (ACMNA150) Algebra

ADVANCED PROBABILITY QUESTION about multi-stage event probability and step by step solution in two different ways (methods). Students think critically to solve the “Probability of Winning Both Games” question. This challenge question requires students to use their knowledge & understanding of probability concepts and to come up with mathematical strategies to solve the problem. Learning Outcomes: • Use arrays or tree diagrams to determine the outcomes and the probabilities for multi-stage events. • Understand events using the language of ‘equally likely’, ‘at least’, etc. • Use complementary event to determine the probabilities associated with simple games. • Use & solve a quadratic equation form that related to the probability of multi-stage events. Also comply with Australian Curriculum Identify complementary events and use the sum of probabilities to solve problems (ACMSP204) Describe events using language of ‘at least’, exclusive ‘or’ (A or B but not both), inclusive ‘or’ (A or B or both) and ‘and’. (ACMSP205) Describe the results of two- and three-step chance experiments, both with and without replacement, assign probabilities to outcomes and determine probabilities of events. Investigate the concept of independence (ACMSP246) Simple probabilities: construct a sample space for an experiment (ACMEM154) Use a sample space to determine the probability of outcomes for an experiment (ACMEM155) Use arrays or tree diagrams to determine the outcomes and the probabilities for experiments. (ACMEM156) Probability applications: determine the probabilities associated with simple games (ACMEM157) Probability

Trigonometry Equations Critical Thinking Problems and step-by-step solutions. Students think critically to demonstrate knowledge • Trigonometry involves the unit circle of cos θ, sin θ and tan θ and periodicity using degrees and radians. • Apply the appropriate formulas and use mathematical strategies to solve equations involving trigonometric functions algebraically. Also comply with Australian Curriculum: Understand the unit circle definition of cos θ, sin θ and tan θ and periodicity using radians (ACMMM034) Recognise the exact values f cos θ, sin θ and tan θ at integer multiples of π/6 and π/4 (ACMMM035) Identify contexts suitable for modelling by trigonometric functions and use them to solve practical problems (ACMMM042) Solve equations involving trigonometric functions using technology, and algebraically in simple cases. (ACMMM043) Other Trigonometry resources: Trigonometry

SIMPLIFYING SURDS WORKSHEETS AND STEP-BY-STEP SOLUTIONS Learning Outcomes: • Perform operations with monomial and binomial surds (Addition, subtraction and multiplication) • Rationalise binomial surds. Also comply with Australian Curriculum Define rational and irrational numbers and perform operations with surds and fractional indices (ACMNA264)

PROBABILITY REVISION 2 WORKSHEETS AND STEP-BY-STEP SOLUTIONS Learning Outcomes: • Venn diagrams and the addition theorem • Multi-stage experiments and the product rule • Mutually Exclusive Events • Probability tree diagrams • Complementary Events Also comply with Australian Curriculum Review the concepts and language of outcomes, sample spaces and events as sets of outcomes (ACMMM049) Use set language and notation for events, including A` for the complement of an event A, A∩B for the intersection of events A and B, and AՍB for the union, and recognise mutually exclusive events (ACMMM050) Use everyday occurrences to illustrate set descriptions and representations of events, and set operations. (ACMMM051) Review probability as a measure of ‘the likelihood of occurrence’ of an event (ACMMM052) Review the probability scale: 0 ≤ P(A) ≤1 for each event A, with P(A) = 0 if A is an impossibility and P(A) = 1 if A is a certain (ACMMM053) Review the rules: P(A`) = 1 − P(A) and P(A∪B) = P(A) + P(B) − P(A∩B) (ACMMM054)

**PROBABILITY REVISION 1 WORKSHEETS AND STEP-BY-STEP SOLUTIONS** Learning Outcomes: • Venn diagrams and the addition theorem • Multi-stage experiments and the product rule • Mutually Exclusive Events • Probability tree diagrams • Conditional Probability • Independent Events Also comply with Australian Curriculum Review the concepts and language of outcomes, sample spaces and events as sets of outcomes (ACMMM049) Use set language and notation for events, including A` for the complement of an event A, A∩B for the intersection of events A and B, and AՍB for the union, and recognise mutually exclusive events (ACMMM050) Use everyday occurrences to illustrate set descriptions and representations of events, and set operations. (ACMMM051) Review probability as a measure of ‘the likelihood of occurrence’ of an event (ACMMM052) Review the probability scale: 0 ≤ P(A) ≤1 for each event A, with P(A) = 0 if A is an impossibility and P(A) = 1 if A is a certain (ACMMM053) Review the rules: P(A`) = 1 − P(A) and P(A∪B) = P(A) + P(B) − P(A∩B) (ACMMM054) Use relative frequencies obtained from data as point estimates of probabilities. (ACMMM055) Understand the notion of a conditional probability and recognise and use language that indicates conditionality (ACMMM056) Use the notation P(A|B) and the formula P(A|B) = P(A∩B)/P(B) (ACMMM057) Understand the notion of independence of an event A from an event B, as defined by P(A|B) = P(A) (ACMMM058) Establish and use the formula P(A∩B) = P(A)P(B) for independent events A and B, and recognise the symmetry of independence (ACMMM059) Use relative frequencies obtained from data as point estimates of conditional probabilities and as indications of possible independence of events. (ACMMM060)

Algebraic Puzzles in Geometric Shapes and Step-by-Step Solutions Algebraic puzzles to keep your learners engaged in algebra and measurement learning. The learners use perimeter and area formulas for 2D shapes and apply algebraic techniques such as the balancing method to complete each puzzle. Puzzle A: find the expression for unknown lengths. The perimeter (P ) of each shape is given and each variable (letter) has a distinct value. Puzzle B: find the expression for unknown lengths. The area (A ) of each shape is given and each variable (letter) has a distinct value. Grades: 7th to 10th Learning Outcomes: Use the formulas for the perimeter and area of two-dimensional shapes in problem-solving Create algebraic expressions and evaluate them by substituting a given value. Solve linear equations using algebraic techniques. Also comply with Australian Curriculum Introduce the concept of variables as a way of representing numbers using letters (ACMNA175). Communicate and connect mathematical ideas using appropriate terminology, diagrams and symbols (MA4-1WM). Solve simple linear equations (ACMNA179). Solve linear equations using algebraic techniques and verify solutions by substitution (ACMNA194). Establish the formulas for areas of rectangles, triangles and parallelograms, and use these in problem-solving (ACMMG159) More Algebra Resources: Algebra

Inequalities on a Number Line Worksheets and Answers Worksheets to keep your learners engaged in math learning and apply mathematical strategies to complete a variety of question styles about inequalities on number lines. Worksheet A: Describing the inequality represented by each number line. Worksheet B: MATCHING ACTIVITY Worksheet C: Graphing inequalities on a number line. Worksheet D: Graphing inequalities on a number line. Grades: 6th to 9th Learning Outcomes: Describe and write inequalities on a number line Graph inequalities on a number line Also comply with for Australian Curriculum Introduce the concept of variables as a way of representing numbers using letters (ACMNA175). Communicate and connect mathematical ideas using appropriate terminology, diagrams and symbols (MA4-1WM).

SQUARE NUMBERS 1 to 16 & SQUARE ROOT Three activities to keep your learners engaged in math learning and apply mathematical strategies to complete all the activities. This activity is to increase their fluency and confidence in number skills involving square numbers and square roots. Answer keys are also included. ACTIVITY 1: FINDING SQUARE ROOTS ACTIVITY 2: COMPLETING PAIRS OF NUMBER & SQUARE ROOT ACTIVITY 3: SQUARE NUMBERS MAZE (SQUARE NUMBERS WITH FOUR OPERATIONS) Grade: 5th to 8th Learning Outcomes: Investigate and use square roots of perfect square numbers 1 to 16. Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with square roots. Also Comply with Australian Curriculum: Investigate and use square roots of perfect square numbers (ACMNA150). Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123).

Differential Calculus: The Equation of Tangent and Normal to a Curve problems and step-by step solutions. Students think critically, demonstrate knowledge of functions and differential calculus. Apply the appropriate formulas, sketch the graph of y = f(x) with the tangent and normal. Use mathematical strategies to solve all questions. Learning Outcomes: Understand the derivative as the gradient of the tangent to the curve of y = f(x) at a point. Understand that the normal on the curve is perpendicular to the tangent. Find the gradient of the tangent and normal at a point on the curve. Find the equation of the tangent and normal of the curve at a point. Practise sketching a curve with the tangent and normal. Find the angle of inclination. Grades: 11th to 12th Also comply with Australian Curriculum Interpret the derivative as the gradient of the tangent to the graph of y = f(x) at a point (ACMMM085) Estimate numerically the value of the derivative at a point, for simple power functions (ACMMM086) understand the concept of the derivative as a function (ACMMM089) Differential Calculus Resources: Differential Calculus -The Equation of Tangents to a Curve- Critical Thinking

Differential Calculus: The Equation of Tangents to a Curve problems and step-by-step solutions. Students think critically, demonstrate knowledge of functions and differential calculus. Apply the appropriate formulas, sketch the graph of y = f(x) and their tangents. Use mathematical strategies to solve all questions. Learning Outcomes: Use first principles to find the derivative of simple polynomials. Understand the derivative as the gradient of the tangent to the curve of y = f(x) at a point. Find the gradient of the tangents at a point on the curve. Find the equation of the tangent to the curve at a point. Practise sketching a curve and the tangents. Grades: 10th to 12th Also suitable for Australian Curriculum Examine the behaviour of the difference quotient (f(x+h)−f(x))/h as h→0 as an informal introduction to the concept of a limit (ACMMM081) Interpret the derivative as the gradient of the tangent to the graph of y = f(x) at a point (ACMMM085) Estimate numerically the value of the derivative at a point, for simple power functions (ACMMM086) understand the concept of the derivative as a function (ACMMM089)

Right Triangle Trigonometry Workbook - TRUE BEARINGS Scaffolded notes + worksheets + step-by-step solutions + teacher notes + mini folded notes to learn and practise: Identify and write the true bearings of a location. Draw the true bearings of a location. Solve a variety of trigonometry problems involving bearings (critical and creative thinking). There are two styles of workbook. Style 1: Cover, fill in the blank notes and worksheets Style 2: Cover, completed (filled) notes and worksheets Total pages in each workbook: 12 Easy classroom preparation: For the workbook: print and staple all pages together to make a book. For the mini folded notes: print, fold and glue the pages to make a mini notebook. Teacher notes displayed on whiteboards. Grades: 9th to 12th Also comply with Australian Curriculum: Apply trigonometry to solve right-angled triangle problems (ACMMG224). Solve right-angled triangle problems including those involving direction and angles of elevation and depression (ACMMG245). Solve problems involving bearings. (ACMEM120). Solve practical problems involving the trigonometry of right-angled and non-right-angled triangles, including problems involving angles of elevation and depression and the use of bearings in navigation. (ACMGM037). Right Triangle Trigonometry Workbook - Angles of Elevation & Depression

Factors of Numbers Puzzle 3 Activity A fun activity to keep your learners engaged in math learning and apply mathematical strategies to complete the puzzle. In this activity learners practise finding factors of a number and arranging the given factors to fill all boxes. The aims of this activity are: To increase their fluency and confidence in multiplication and division skills. To develop understanding of a variety of problems involving factors of a number. Answer keys are also included. Teaching Ideas: Students cut each factor and glue it to the correct box. Or students write each factor in the correct box. Grades: 4th to 6th Learning Outcomes: • Identify factors of whole numbers in the range 1-100 and use them to solve problems. • Recognize that a whole number is a multiple of each of its factors. Also comply with Australian Curriculum: Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098). Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076) Factors of Numbers: Factors of Number Puzzle 1 Factors of Number Puzzle 2 Factors of Number Puzzle 3

Factors of Numbers Puzzle 2 Activity A fun activity to keep your learners engaged in math learning and apply mathematical strategies to complete the puzzle. In this activity learners practise finding factors of a number and arranging the given factors to fill all boxes. The aims of this activity are: To increase their fluency and confidence in multiplication and division skills. To develop understanding of a variety of problems involving factors of a number. Answer keys are also included. Teaching Ideas: Students cut each factor and glue it to the correct box. Or students write each factor in the correct box. Grades: 4th to 6th Learning Outcomes: • Identify factors of whole numbers in the range 1-100 and use them to solve problems. • Recognize that a whole number is a multiple of each of its factors. Also comply with Australian Curriculum: Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098). Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076) Factors of Numbers: Factors of Number Puzzle 1 Factors of Number Puzzle 2 Factors of Number Puzzle 3

Factors of Numbers Puzzle 1 Activity A fun activity to keep your learners engaged in math learning and apply mathematical strategies to complete the puzzle. In this activity learners practise finding factors of a number and arranging the given factors to fill all boxes. The aims of this activity are: To increase their fluency and confidence in multiplication and division skills. To develop understanding of a variety of problems involving factors of a number. Answer keys are also included. Teaching Ideas: Students cut each factor and glue it to the correct box. Or students write each factor in the correct box. Grades: 4th to 6th Learning Outcomes: • Identify factors of whole numbers in the range 1-100 and use them to solve problems. • Recognize that a whole number is a multiple of each of its factors. Also comply with Australian Curriculum: Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098). Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076) Factors of Numbers: Factors of Number Puzzle 1 Factors of Number Puzzle 2 Factors of Number Puzzle 3

NUMBERS IN INDEX FORM WORKSHEETS & ANSWERS Students practise: Identify the base number and index (power or exponent) of numbers written in index form. Write numbers in index form. Use BODMAS (PEMDAS) to calculate mathematics operations involving indices. Use scientific notation to write large and small numbers. Grade: 6th to 8th Learning Outcomes: Describe numbers written in index form. Write numbers in index form. Calculate mathematics operations involving indices. Use scientific notation to write large and small numbers. Also Comply with Australian Curriculum: Investigate index notation and represent whole numbers as products of powers of prime numbers (ACMNA149). Use index notation with numbers to establish the index laws with positive integral indices and the zero index (ACMNA182). Express numbers in scientific notation (ACMNA210) Indices (Exponents) Resources: INTRODUCTION TO INDICES Numbers in Index Form Worksheets

INTRODUCTION TO INDICES (EXPONENTS) NOTES, WORKSHEETS & ANSWERS. Students learn to Understand numbers written in index form and write numbers in index form. Use BODMAS (PEMDAS) to calculate mathematics operations involving indices. Use scientific notation to write large and small numbers. Grade: 6th to 8th Learning Outcomes: Describe numbers written in index form. Write numbers in index form. Calculate mathematics operations involving indices. Use scientific notation to write large and small numbers. Also Comply with Australian Curriculum: Investigate index notation and represent whole numbers as products of powers of prime numbers (ACMNA149). Express numbers in scientific notation (ACMNA210). Indices (Exponents) Resources: INTRODUCTION TO INDICES Numbers in Index Form Worksheets

AREA OF 2D SHAPES ACTIVITY Math Challenge Activity- to keep your learners engaged, thinking critically and making connections to 2D shapes. This activity requires learners to Determine which shape has complete dimensions to calculate its area Calculate the area of the other shapes including their type. Find the exact value of each pronumeral. The activity encourages them to think creatively and come up with mathematical strategies to solve unknown lengths. The aims of this activity are to: Increase their fluency and confidence in geometry and measurements Develop understanding of a variety of problems with 2D shapes. Step-by-step solutions are also included. Grades: 6th to 9th Learning Outcomes: Solve problems involving the area of 2D Shapes. Find the unknown lengths (Critical Thinking) Also comply with Australian Curriculum: Establish the formulas for areas of rectangles, triangles and parallelograms, and use these in problem-solving (ACMMG159) Critical Thinking Problems: Area of Composite Shape-Critical thinking Activity-Math Challenge 1 Area of Composite Shape-Critical thinking Activity-Math Challenge 2 Area of 2D Shapes-Critical thinking Activity-Math Challenge 3

AREA OF COMPOSITE SHAPES ACTIVITY Math Challenge Activity- to keep your learners engaged, thinking critically and making connections to 2D shapes. This activity requires learners to determine the area of circles and squares based on the given dimensions. It also encourages them to think creatively and come up with mathematical strategies to solve unknown lengths and compare the areas of circles and squares and shaded parts. The aim of this activity is to: Increase their fluency and confidence in geometry and measurements Develop understanding of a variety of problems with 2D shapes. Step-by-step solutions are also included. Grades: 6th to 9th Learning Outcomes: Solve problems involving the area of circles and squares. Calculate the area of composite shapes. Determine the ratio of square area to circle area. Determine the ratio of shaded areas. Also comply with Australian Curriculum: Calculate areas of composite shapes (ACMMG216) Critical Thinking Problems: Area of Composite Shape-Critical thinking Activity-Math Challenge 1 Area of Composite Shape-Critical thinking Activity-Math Challenge 2 Area of 2D Shapes-Critical thinking Activity-Math Challenge 3