algebra year 10 ~ maths for further. algebra review

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

https://www.youtube.com/watch?v=5juto2ze8Lg

https://www.youtube.com/watch?v=5juto2ze8Lg

https://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


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


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.


eg1

eg2

X 3

¿4𝑏−34=164𝑏−3𝑏4𝑏

=16−3𝑏4𝑏

X 4 X b


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)


eg1

eg2

¿ 𝑥+42×

6𝑥+4

=6 (𝑥+4 )2(𝑥+4)

=62=3


Simplify


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.


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


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 two step equations:

9)

10)

11)

12)



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


1)

2)

3)

4)

Bracket problems






1)

2)

3)

4)

Bridging problems






Now do:

Worksheet 3 Part 3B – Bracket & Bridging Problems

Then:


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.



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



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.


Now do:


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


This means that is less than or equal to 10

INEQUALITIES

Key Ideas:• We can represent the inequations using a number line


This means that is greater than 5


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


𝑦1 2 3 4 5 6 7 8 9 10 11 12

For the inequation


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

algebra year 10 ~ maths for further. algebra review

Documents

e algebraic fractions

subtracting fractions

multiplying fractions

algebraic fractions

express fractions

lowest common denominator

subtraction problems

difficult problems