Download ASSESSMENT TASK NOTIFICATION Student Name

 ASSESSMENT TASK NOTIFICATION Student Name: …………………………………. Course: Mathematics Assessment Task Title: Assessment task 2 – Year 9 Topic Test Value of Task: 10% Date Task: Term 2 Week 2 Outcomes to be assessed: Algebra and Indices Task description: Formal Written task, 1 hour in class Homework: Start writing your study notes with example questions for each of the points given. Algebra •
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Develop the concept that pronumerals (letters) can be used to represent numerical values. Recognise that pronumerals can represent one or more numerical values (when more than one numerical value, pronumerals may then be referred to as 'variables'). Recognise and use equivalent algebraic expressions. Use algebraic symbols to represent mathematical operations written in words and vice versa. Recognise like terms and add and subtract them to simplify algebraic expressions. Verify whether a simplified expression is correct by substituting numbers for pronumerals. Recognise the role of grouping symbols and the different meanings of expressions. Simplify algebraic expressions that involve multiplication and division. Recognise the equivalence of algebraic expressions involving multiplication. Connect algebra with the commutative and associative properties of arithmetic. Recognise whether particular algebraic expressions involving division are equivalent or not. Translate from everyday language to algebraic language and vice versa. Use algebraic symbols to represent simple situations described in words. Simplify a range of algebraic expressions, including those involving mixed operations. Apply the order of operations to simplify algebraic expressions. Substitute into algebraic expressions and evaluate the result. Calculate and compare the values of x2 for values of x with the same magnitude but opposite sign. Generate a number pattern from an algebraic expression. Connect the processes for simplifying expressions involving algebraic fractions with the corresponding processes involving numerical fractions. Simplify algebraic fractions, including those involving indices. Explain the difference between expressions such as and Simplify algebraic fractions, including those involving indices. . •
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Simplify expressions that involve algebraic fractions, including algebraic fractions that involve pronumerals in the denominator and/or indices. Expand algebraic expressions by removing grouping symbols. Connect algebra with the distributive property of arithmetic. Expand algebraic expressions, including those involving terms with indices and/or negative coefficients. Expand algebraic expressions by removing grouping symbols and collecting like terms where applicable. Add and subtract algebraic fractions, including those with binomial numerators. Recognise and apply the special product . Recognise and name appropriate expressions as the 'difference of two squares' Recognise and apply the special products, and . Recognise and name appropriate expressions as 'perfect squares'. Use algebraic methods to expand a variety of binomial products, including the special products. Simplify a variety of expressions involving binomial products. Indices •
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Describe numbers written in 'index form' using terms such as 'base', 'power', 'index', 'exponent'. Use index notation to express powers of numbers (positive indices only). Investigate and generalise the effect of raising a negative number to an odd or even power on the sign of the result. Apply the order of operations to evaluate expressions involving indices, with and without using a calculator. Use the notations for square root and cube root. Determine through numerical examples , . Apply the order of operations to evaluate expressions involving square roots and cube roots, with and without using a calculator. Develop index laws with positive­integer indices and numerical bases by expressing each term in expanded form. Verify the index laws using a calculator. Explain the incorrect use of index laws. Establish the meaning of the zero index. Verify the zero index law using a calculator. Use index laws to simplify expressions with numerical bases. Use the index laws previously established for numerical bases with positive­integer indices to develop the index laws in algebraic form. Explain why . Simplify expressions that involve the zero index. Simplify expressions that involve the product and quotient of simple algebraic terms containing positive­integer indices. Compare expressions such as 3a 2 × 5a and 3a 2 + 5a by substituting values. Establish the meaning of negative indices for numerical bases. Write given numbers in index form (integer indices only) and vice versa. Evaluate numerical expressions involving a negative index by first rewriting with a positive index. Write expressions involving negative indices as expressions involving positive indices, and vice versa. Apply the index laws to simplify algebraic products and quotients involving negative indices. •
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Verify whether a given expression represents a correct simplification of another algebraic expression by substituting numbers for pronumerals. Write the numerical value of a given numerical fraction raised to the power of –1, leading to
. Define real numbers: a real number is any number that can be represented by a point on the number line. Define rational and irrational numbers. Recognise that all rational and irrational numbers are real. Explain why all integers, terminating decimals and recurring decimals are rational numbers. Explain why rational numbers can be expressed in decimal form use a pair of compasses and a straight edge to construct simple rational numbers and surds on the number line. Distinguish between rational and irrational numbers. Demonstrate that not all real numbers are rational. Use the term 'surd' to refer to irrational expressions of the form such that where x is a rational number and n is an integer . •
Write recurring decimals in fraction form using calculator and non­calculator methods. •
Justify why •
Demonstrate that •
Define •
Use the following results for x > 0 and y > 0 . is undefined for x < 0 and that for x = 0. as the positive square root of x for x > 0, . •
. Apply the four operations of addition, subtraction, multiplication and division to simplify expressions involving surds. •
Expand expressions involving surds. •
Rationalise the denominators of surds of the form .