# ALGEBRA YEAR 10 ~ MATHS FOR FURTHER. ALGEBRA REVIEW.

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ALGEBRA YEAR 10 ~ MATHS FOR FURTHER

ALGEBRA REVIEW

Now Do: Exercise 1A - Questions 1, 2, 3abcd, 4abc Then Worksheet – Part 1A

ALGEBRA REVIEW

Simplifying expressions – using the Classpad calculator ALGEBRA REVIEW

Now Do: Worksheet – Part 1B Exercise 1A - Questions 6abcdemnopqr, 7abcdmnopefghqr 7abcdmnopefghqr

ALGEBRA REVIEW Expanding using the distributive Law

ALGEBRA REVIEW

Now Do: Worksheet - Part 1C Exercise 1A - Questions 8abcdemnopqr, 9abcdef, 10abcdeijklmn 9abcdef, 10abcdeijklmn

ALGEBRAIC FRACTIONS - REVIEW OF WORKING WITH FRACTIONS Key Ideas: For addition and subtraction problems, express fractions in terms of their lowest common denominator and then add/subtract the numerators keeping the new denominator. For multiplication problems, cancel common factors and then multiply the numerators and the denominators. Videos: Multiplying Fractions / Adding & Subtracting basic fractions https://www.youtube.com/watch?v=5juto2ze8Lg Adding & Subtracting fractions with different denominators https://www.youtube.com/watch?v=RIhwfqULbAE

Now Do: Worksheet 2 - Part 2A (all problems) - Part 2B (a,b,d,e) - Part 2B (a,b,d,e) ALGEBRAIC FRACTIONS - REVIEW OF WORKING WITH FRACTIONS

Simplifying by cancelling common factors SOLVING ALGEBRAIC FRACTIONS eg1 eg2 5 goes into 20 4 times 4 goes into 36 9 times Cancel ‘a’s Cancel 1 ‘b’

Simplifying by cancelling common factors SOLVING ALGEBRAIC FRACTIONS eg1 eg2 Lowest common factor of 21 and 7 is 7, so divide all numbers by 7 Rewrite to remove fraction format – be careful with the -1 denominator! Lowest common factor of 6, 4 & 2 is 2, so divide all numbers by 2 Cancel ‘x’s and rewrite to remove fraction format

Simplifying multiplication problems SOLVING ALGEBRAIC FRACTIONS eg1 eg2 Multiply the numerators and multiply the denominators and then simplify

Simplifying addition and subtraction problems with an unknown Step 1. We want the denominators to be the same, so we need to find the lowest common denominator (LCD) – Remember what you do to the bottom you need to do to the top! Step 2. We then add the numerators and divide by the LCD. SOLVING ALGEBRAIC FRACTIONS eg1 eg2 X 3 X 4X b

SOLVING ALGEBRAIC FRACTIONS Step 1. We want the denominators to be the same, so we need to find the lowest common denominator (LCD) – Remember what you do to the bottom you need to do to the top! Step 2. We then add the numerators and divide by the LCD. Simplifying addition and subtraction problems with an unknown X 4 X 3 Using the calculator

Simplifying division problems Simplifying division problems Step 1. Invert the second expression Step 2. Multiply the first expression by the inverted second expression. For more difficult problems please use the simplify function on your calculator (like in eg2) SOLVING ALGEBRAIC FRACTIONS eg1 eg2 Using the calculator

Simplify SOLVING ALGEBRAIC FRACTIONS Using the calculator:

Summary – How to…. Multiplication: * Multiply denominators together. * Multiply numerators together. * Simplify the equation by grouping any like terms/cancelling. Addition/ Subtraction: * Make denominators the same by multiplying each by LCD. * Add/subtract the numerators and keep the new denominator. * Simplify the equation by grouping any like terms/cancelling. Division: * Flip the second fraction. * Apply the multiplication rules to the new expression. ALGEBRAIC FRACTIONS - WORKING WITH FRACTIONS

Now Do: Exercise 1B (pg13) – all problems from this section on your work record. ALGEBRAIC FRACTIONS - WORKING WITH FRACTIONS 8abcdijkl 4abcdefghij 5abcdjkl 6abcdefgh 7abcdef 9abc 10abc

Now Do: Homework Sheet #2 Due Monday 16 th March ALGEBRAIC FRACTIONS - WORKING WITH FRACTIONS

SOLVING LINEAR EQUATIONS These are linear equations These are not linear equations

SOLVING LINEAR EQUATIONS Using the calculator:

SOLVING LINEAR EQUATIONS

Now do: Worksheet 3 Part 3A – One and Two step equationsThen: Exercise 1C (pg 18 of your text) Questions 4abcdefghij 5abcdefgh Solving one and two step problems

SOLVING LINEAR EQUATIONS Bracket problems Using the calculator

SOLVING LINEAR EQUATIONS Bridging problems Using the calculator

SOLVING LINEAR EQUATIONS Now do: Worksheet 3 Part 3B – Bracket & Bridging ProblemsThen: Exercise 1C (pg 18 of your text) Questions Bracket and Bridging Problems 5abcdefgh 6abcdefgh 8abcdef

SOLVING LINEAR EQUATIONS Converting worded problems into linear equations

SOLVING LINEAR EQUATIONS Converting worded problems into linear equations The cost (C) to hire a hall is \$200 for cleaning costs plus an additional \$100 per hour (h). Write an equation to model this scenario. How much does it cost to hire the hall for 5 hours? It costs \$700 to hire the hall for 5 hours

SOLVING LINEAR EQUATIONS Converting worded problems into linear equations The total time taken (T) to detail a car is 90 minutes plus an additional 20 minutes per wheel polished (w). Write an equation to model this scenario for total time taken to detail the car. How long does it take to detail the car and polish 3 wheels? It takes 150 minutes to detail the car and polish 3 wheels.

SOLVING LINEAR EQUATIONS Now do: Exercise 1C (pg 18 of your text) Questions Converting worded problems into linear equations 7abcd 131415

INEQUALITIESINEQUALITIESINEQUALITIESINEQUALITIES

INEQUALITIESINEQUALITIESINEQUALITIESINEQUALITIES Key Ideas: We can represent the inequations using a number line 1 2 3 4 5 6 7 8 9 10 11 12

greater than greater than or equal to less than less than or equal to 1 2 3 4 5 6 7 8 9 10 11 12 -3 -2 -1 0 1 2 3 4 5 6 7 8 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

1 2 3 4 5 6 7 8 9 10 11 12 INEQUALITIESINEQUALITIESINEQUALITIESINEQUALITIES For the following inequations represented on number lines, state the inequation. 1 2 3 4 5 6 7 8 9 10 11 12 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10 11 12

INEQUALITIESINEQUALITIESINEQUALITIESINEQUALITIES

INEQUALITIESINEQUALITIESINEQUALITIESINEQUALITIES Now Do: Work Record ~ Text Book Questions Chapter 1D pg24 1abcd 2abc 4abcdg 5abcdefkl