Maths Quest 10 for New South Wales 5.3 Pathway
Work Programs
Chapter 1Rational and irrational numbers
Strands: Number, Patterns and algebra
Substrands and outcomes:
Rational numbersNS5.1.1 Applies index laws to simplify and evaluate arithmetic expressions and uses scientific notation to write large and
small numbers
Rational numbers NS5.2.1 Rounds decimals to a specified number of significant figures, expresses recurring decimals in fraction form and
converts rates from one set of units to another
Real numbersNS5.3.1 Performs operations with surds and indices
Algebraic techniquesPAS5.2.1 Simplifies, expands and factorises algebraic expressions involving fractions and negative and fractional indices
Section / GC tips, Investigations,History of mathematics, Maths Quest challenge,
10 Quick Questions,
Code puzzles,
Career profiles / SkillSHEETS, WorkSHEETS,
Interactive games,
Test yourself, Topic tests
(CD ROM) / Technology applications
(CD ROM) / Learning outcomes
Are you ready? (page 2) / SkillSHEETs (page 2)
1.1: Identifying surds
1.2: Simplifying surds
1.3: Adding and subtracting surds
1.4: Multiplying and dividing surds
1.5: Rationalising denominators
1.9: Evaluating numbers in index form
1.10: Using the index laws / NS5.3.1
- distinguishing between rational and irrational numbers
- using the following results for x, y > 0:
, , - using the operations of addition and subtraction to simplify expressions involving surds
- using the operations of multiplication and division to simplify expressions involving surds
- rationalising the denominators of surds
- evaluating numbers expressed as powers of positive whole numbers
- using index laws to simplify expressions
Classifying numbers (page3)
WE 1a-h
Ex 1A Classifying numbers (page 7) / NS5.3.1
- defining a rational number
- distinguishing between rational and irrational numbers
- using a pair of compasses and a straight edge to construct simple rationals and surds on the number line
- defining real numbers
- explaining why all integers and recurring decimals are rational numbers (Communicating, Reasoning)
- explaining why rational numbers can be expressed in decimal form (Communicating, Reasoning)
- demonstrating that not all real numbers are rational (Communicating, Applying strategies, Reasoning)
Surds (page 8)
WE 2a-f, 3
Ex 1B Surds (page 11) / SkillSHEET 1.1: Identifying surds (page11) / NS5.3.1
- demonstrating that is undefined for x < 0, = 0 for x = 0, and is the positive square root of x when x > 0
- using the following results for x, y > 0:
, ,
Operations with surds (page 12)
WE 4a-d, 5a-c, 6a-d, 7a-b, 8a-d, 9a-c, 10a-b
Ex 1C Operations with surds (page 21) / 10 Quick Questions 1 (page 24) / SkillSHEET 1.2: Simplifying surds (page21)
SkillSHEET 1.3: Adding and subtracting surds (page 22)
SkillSHEET 1.4: Multiplying and dividing surds (page 22)
SkillSHEET 1.5: Rationalising denominators (page 23)
SkillSHEET 1.6: Conjugate pairs (page24)
SkillSHEET 1.7: Applying the difference of two squares rule to surds (page 24)
WorkSHEET 1.1 (page 24) / Mathcad: Simplifying surds (page 21)
Excel: Simplifying surds (page 22)
GC program Casio: Surds (page 22)
GC program TI: Surds (page 22)
Mathcad: Adding and subtracting surds (page22)
Mathcad: Multiplying and dividing surds (page22)
Mathcad: Rationalising denominators (page 23) / NS5.3.1
- using the following results for x, y > 0:
, , - using the four operations of addition, subtraction, multiplication and division to simplify expressions involving surds
- expanding expressions involving surds
- rationalising the denominator of surds of the form
- solving numerical problems involving surds (Applying strategies)
- establishing that
Fractional indices (page25)
WE 11a-b, 12a-b, 13, 14ab, 15a-c
Ex 1D Fractional indices (page 28) / Investigation: Manning’s formula (page 30)
Code puzzle (page 31)
10 Quick Questions 2 (page 32) / SkillSHEET 1.8:Finding square roots, cube roots and other roots (page28)
SkillSHEET 1.9: Evaluating numbers in index form (page 28)
SkillSHEET 1.10:Using the index laws (page28)
Game time 001 (page 30)
WorkSHEET 1.2 (page 30) / Mathcad: Fractional indices (page 28)
Excel: Index laws (page28) / NS5.1.1
- using index laws to define fractional indices for square and cube roots
- writing square roots and cube roots in index form
- using the index laws to demonstrate the reasonableness of the definitions for fractional indices
- translating expressions in surd form to expressions in index form and vice versa
- evaluating numerical expressions involving fractional indices
- using the key on a calculator
- solving numerical problems involving fractional indices (Applying strategies)
- using the index laws previously established for numbers to develop the index laws in algebraic form
- simplifying algebraic expressions that include index notation
- applying the index laws to simplify expressions involving pronumerals
- using index laws to assist with the definition of the fractional index for square root given and then
- using index laws to assist with the definition of the fractional index for cube root
- applying the index laws to simplify algebraic expressions
- explaining why finding the square root of an expression is the same as raising the expression to the power of a half (Communicating, Reasoning)
Negative indices (page 32)
WE 16a-b, 17a-c
Ex 1E Negative indices (page 34) / Game time 002 (page 34)
WorkSHEET 1.3 (page 34) / Mathcad: Negative indices (page 34)
Excel: Negative indices (page 34) / NS5.1.1
- writing reciprocals of powers using negative indices
- solving numerical problems involving indices (Applying strategies)
- evaluating a fraction raised to the power of 1, leading to
- using index notation and the index laws to establish that
Summary (page 35)
Chapter review (page 36) / ‘Test yourself’ multiple choice questions
Topic tests (2)
1