algebra year 10 ~ maths for further. algebra review
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ALGEBRAYEAR 10 ~ MATHS FOR FURTHER
ALGEBRA REVIEWKey Terms:
Coefficient: Refers to the number in front an unknown.
eg1. eg2. 3 is the coefficient of -6 is the coefficient of
Expression: These are all expressions. 2, 4 + 5,
Equation: Anything including an equals sign, is an equation. = 6, + 2 = 10, - 4 = 2
Pronumeral: Also known as a Variable. This is the unknown in our equation.
ALGEBRA REVIEWKey Terms:
Like Terms have the same pronumeral and can be collected to form a single term.
these are like terms
The expressions can be simplified by grouping like terms together
Factorisation: Many expressions can be factorised by taking out the highest common factor.
eg. can be factorised
eg. can be factorised
these are like terms
(8 𝑎𝑏+9𝑏𝑎 )−2𝑥=17 𝑎𝑏−2𝑥
ALGEBRA REVIEW
Now Do:
Exercise 1A - Questions 1, 2, 3abcd, 4abc
Then Worksheet – Part 1A
Simplifying expressions – collecting like terms
eg1 eg2eg3eg4eg5eg6
ALGEBRA REVIEW
8 𝑥4 𝑦+2𝑥4𝑎𝑏
7𝑏𝑥+6 𝑎𝑏
10 𝑦 𝑥2+7 𝑦2 𝑥2𝑐𝑏+5𝑏𝑐2
ALGEBRA REVIEWSimplifying expressions – multiplying and dividing expressions
eg1
eg2
eg3
eg4
Multiply the numbers and remove the sign
Multiply the numbers and using the basic index
law, add the powers and remove the sign
Simplifying expressions – using the Classpad calculator
ALGEBRA REVIEW
eg.
¿−6 𝑥2 𝑦
ALGEBRA REVIEW
Now Do:
Worksheet – Part 1B
Exercise 1A - Questions 6abcdemnopqr, 7abcdmnopefghqr
ALGEBRA REVIEW
Expanding using the distributive Law
You try:Use the distributive law to expand the following:
7 𝑥+14 4 𝑥−𝑥2
2 𝑥2+8𝑥 𝑔𝑥2−2𝑔2𝑥
ALGEBRA REVIEW
Factorising
You try: Factorise the following
4(𝑥+2) 3 (𝑥2+3)
𝑥 (2𝑥−1) 2𝑔 (2𝑥+h)
ALGEBRA REVIEWUsing the classpad to expand and factorise expressions.
Expand Factorise
eg. eg.
ALGEBRA REVIEW
Now Do:
Worksheet - Part 1C
Exercise 1A - Questions 8abcdemnopqr, 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 fractionshttps://www.youtube.com/watch?v=5juto2ze8Lg
Adding & Subtracting fractions with different denominatorshttps://www.youtube.com/watch?v=RIhwfqULbAE
Now Do:
Worksheet 2 - Part 2A (all problems) - 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
¿21𝑥−7−7
=3 𝑥−1−1
=− (3 𝑥−1 )=−3 𝑥+1
Rewrite to remove fraction format – be careful with the -1 denominator!
¿ 6 𝑥−4 𝑥2
2 𝑥=3 𝑥−2𝑥
2
1 𝑥=3−2𝑥
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
¿3(𝑥−1)6 𝑥
=3 𝑥−36 𝑥
= 𝑥−12𝑥
¿4 (𝑥+3 )9(𝑥+3)
= 49
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
¿4𝑏−34=164𝑏−3𝑏4𝑏
=16−3𝑏4𝑏
X 4 X 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
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
¿ 𝑥+42×
6𝑥+4
=6 (𝑥+4 )2(𝑥+4)
=62=3
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
8 a b c d i j k l4 a b c d e f g h i j5 a b c d j k l6 a b c d e f g h7 a b c d e f9 a b c10 a b c
Now Do:
Homework Sheet #2
Due Monday 16th March
ALGEBRAIC FRACTIONS -WORKING WITH FRACTIONS
A Linear Equation contains a variable (or other pronumeral) with a power of 1 (and no other powers).
SOLVINGLINEAR EQUATIONS
These are linear
equations
These are not linear equations
Solving one step equations:
1)
2)
3)
4) 5) 6) 7)
8)
SOLVING LINEAR EQUATIONS
Using the calculator:
Solving two step equations:
1)
2)
3)
4) 5) 6) 7)
8)
SOLVING LINEAR EQUATIONS
Solving two step equations:
9)
10)
11)
12)
SOLVING LINEAR EQUATIONS
SOLVING LINEAR EQUATIONS
Now do:
Worksheet 3 Part 3A – One and Two step equations
Then:
Exercise 1C (pg 18 of your text) Questions
4abcde f gh i j5abcde f gh
Solving one and two step problems
SOLVING LINEAR EQUATIONS
1)
2)
3)
4)
Bracket problems
Using the calculator
Using the calculator
Using the calculator
Using the calculator
SOLVING LINEAR EQUATIONS
1)
2)
3)
4)
Bridging problems
Using the calculator
Using the calculator
Using the calculator
Using the calculator
SOLVING LINEAR EQUATIONS
Now do:
Worksheet 3 Part 3B – Bracket & Bridging Problems
Then:
Exercise 1C (pg 18 of your text) Questions
Bracket and Bridging Problems
5 a b c de f gh6 a b c de f gh8 a b c de f
SOLVING LINEAR EQUATIONSConverting worded problems
into linear equations
We can form equations given worded scenarios and solve for unknown values.
Write an equation and solve the unknown. If 7 is added to and the result is 13.
Write an equation and solve the unknown. If 8 is multiplied by and the result is 20.
SOLVING LINEAR EQUATIONSConverting 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 EQUATIONSConverting 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
7 a b c d
1314
15
INEQUALITIES
Key Ideas:• We represent inequalities using 4 different signs, in place of an
equals sign.
less than
greater than
less than or equal to
greater than or equal to
eg1. If we have the inequation
This means that is greater than 5
eg2. If we have the inequation
This means that is less than or equal to 10
INEQUALITIES
Key Ideas:• We can represent the inequations using a number line
eg1. If we have the inequation
This means that is greater than 5
eg2. If we have the inequation
This means that is less than or equal to 10
𝑥1 2 3 4 5 6 7 8 9 10 11 12
𝑦1 2 3 4 5 6 7 8 9 10 11 12
For the inequation
This means that is 7
𝑥1 2 3 4 5 6 7 8 9 10 11 12
For the inequation
This means that is 2
𝑦1 2 3 4 5 6 7 8 9 10 11 12
For the inequation
This means that is 0
For the inequation
This means that is -3
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
𝒙1 2 3 4 5 6 7 8 9 10 11 12
𝒚
-3 -2 -1 0 1 2 3 4 5 6 7 8𝒂-5 -4 -3 -2 -1 0 1 2 3 4 5 6
𝒃
1 2 3 4 5 6 7 8 9 10 11 12
INEQUALITIESFor the following inequations represented on number lines, state the inequation.
𝑥1 2 3 4 5 6 7 8 9 10 11 12
1 2 3 4 5 6 7 8 9 10 11 12
1 2 3 4 5 6 7 8 9 10 11 12
𝑝
𝑦
-5 -4 -3 -2 -1 0 1 2 3 4 5 6
-5 -4 -3 -2 -1 0 1 2 3 4 5 6
1 2 3 4 5 6 7 8 9 10 11 12
𝑥
𝑏
𝑎
𝒙>𝟒
𝒑 ≤𝟏𝟎
𝒚<𝟕
𝒃≥−𝟐
𝒂<𝟒
𝟐<𝒙 ≤𝟏𝟎
INEQUALITIESKey Ideas:• We can solve unknown values in linear inequations in the same way
as normal linear equations.
eg. eg. eg.
1 2 3 4 5 6 7 8 9 10 11 12
1 2 3 4 5 6 7 8 9 10 11 12
1 2 3 4 5 6 7 8 9 10 11 12
𝑥 𝑥 𝑎
INEQUALITIES
Now Do:
Work Record ~ Text Book QuestionsChapter 1D pg24
1 a b c d2 a b c4 a b c d g5 a b c d e f k l