AM1 - Algebra Booklet

8/10/2019 AM1 - Algebra Booklet

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SPC

PreliminaryGeneral 2

St Patricks College

SPC Preliminary General 2

AM1: Algebraic Manipulation

Name:


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Year 11 GM Algebraic Manipulation Page 1

Table of contentsSection 1: Syllabus Dot Points page 2

Section 2: Terminology page 2

Section 3: Operations with Algebraic Expressions page3

Section 4: Further multiplication and division page 6

Section 5: Expanding and simplifying algebraic expressions

page 7

Section 6: Substitution page 8

Section 7: Solving Linear Equations page 10

Section 8: MIND MAP & REFLECTION page 12


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Section 3: Operations with Algebraic Expressions Date:__/__/__

COEFFICIENT = NUMERAL = number

PRONUMERAL = letter

Watch before class:http://www.youtube.com/watch?v=RPLaKeSBN-Q

In algebra, each pro-numeral used stands in place of a number

Adding & Subtracting Like Terms

Algebraic expressions can be simplified by collecting like terms. Like terms are the only

terms that can be added and subtracted. The coefficient is the number in front of the pro-

numeral.

Examples:

1. Simplify the following by collecting like terms.

a)

b)

c)

d)

e)
http://www.youtube.com/watch?v=RPLaKeSBN-Qhttp://www.youtube.com/watch?v=RPLaKeSBN-Qhttp://www.youtube.com/watch?v=RPLaKeSBN-Qhttp://www.youtube.com/watch?v=RPLaKeSBN-Q


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Index Laws

Example:

1. Write the following iin index form

a)

b)

c)

2. write the following in expanded form

a)

b)


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Multiplication & Division of Algebraic Terms

Algebraic terms can be muliplied and divided to form single expressions.

Exa

mp

les:

Sim

plif

y

eac

h of the following:

1.

2.

3.

4.

5.

6.

7.

8.

9.

Homework

Pace yourself MQ Ex 11A, P371, Q110, a, c, eExtend yourself MQ Ex 11A, P371, Q110, column 3, 1012


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Section 4: Further multiplication and division Date:__/__/__

Examples: Simplify each of the following:

1)

2)

3)

4)

5)

6)

7)

8)

9)

HomeworkPace yourself MQ Ex 11B, P373, Q14, a, c, e

Extend yourself MQ Ex 11B, P373, Q14, column 3, Q5+6, a, c, e


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Section 5: Expanding and simplifying algebraic expressionDate:__/__/__

To expand an algebraic expression means to remove a set of brackets. This is done by

multiplying everything inside the brackets by the term directly outside the brackets.

Examples: Expand and simplify where possible:

1. ( ) 2. ( )

3. ( ) 4. ( )

5. ( ) 6. ( ) ( )

7. ( ) ( ) 8. ( ) ( )

Its important that you master questions 7 and 8 above as they are the typicalHSC

questions.

HomeworkPace yourself MQ Ex 11C, P375, Q15, a, c, e, 6

Extend yourself MQ Ex 11C, P375, Q15, column 3, 6, 7


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Section 6: Substitution Date:__/__/__

Watch before class:http://www.youtube.com/watch?v=nARfQA8Vz6c

When the numerical values of pronumerals are known, we can substitute (replace) them

into an algebraic expression and evaluate it. It can be useful to place any substituted values

in brackets (especially if its a negative number) when evaluating an expression.

Substitutionis an integral part of this course. Its important you follow the following simple

steps when using this technique to evaluate or calculate an expression or a worded

problem accuratly.

STEP 1: Write down the expression

STEP 2: Substitude all pronumerals with the given numerals

STEP 3: Evaluate

All three steps MUST be shown at all times.

NO working out = NO marks in the HSC.

Regardless if the answer is correct.

Examples

1. If , evaluate the following expressions.

a) b) ( ) c)

d)

e) f)

2. Given that , find when .
http://www.youtube.com/watch?v=nARfQA8Vz6chttp://www.youtube.com/watch?v=nARfQA8Vz6chttp://www.youtube.com/watch?v=nARfQA8Vz6chttp://www.youtube.com/watch?v=nARfQA8Vz6c


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3. The cost of hiring a taxi is $3.75 plus $0.50 per kilometre.

a) Write a formula for the codt of a taxi journey, C, in terms of distance travelled , d.

b) Use the formulato calculate the cost of a taxi journey of 35 km.

4. The kinetic energy of an object is found using the formula

, where is the

mass and is the velocity of the object. Find when

HomeworkPace yourself MQ Ex 11D, P377, Q1, 37,

Extend yourself MQ Ex 11D, P377, Q1, 37, 917 odds, column 3, 1823


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Section 7: Solving Linear Equations

Date:__/__/__

Watch before class:

http://www.youtube.com/watch?v=1HLGsKYoUU0

http://www.youtube.com/watch?v=HyUiYeLee3g

When we are given an equation, our task is to SOLVE

IT. That is, to find a value for the pro-numeral which

makes the sentence true.

Examples:

1. Solve the following linear equations.

a) b) c)

d)

e) f)

g) h)

i)

j)

k)

l)
http://www.youtube.com/watch?v=1HLGsKYoUU0http://www.youtube.com/watch?v=1HLGsKYoUU0http://www.youtube.com/watch?v=HyUiYeLee3ghttp://www.youtube.com/watch?v=HyUiYeLee3ghttp://www.youtube.com/watch?v=1HLGsKYoUU0


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Extend yourself MQ Ex 11A, P371, Q110, column 3, 1012

Also complete Chapter Review.

Section 8: MIND MAP & REFLECTION

Please rate the following outcomes:

1still have great difficulty, 2- still having some difficulty, 3ok4can do most questions with ease, 5can do all questions with ease.

OUTCOME- Algebraic Manipulation 1 2 3 4 5

Add and subtract algebraic terms

multiply and divide algebraic terms

simplify fractional algebraic expressions involving

multiplication and division

expand and simplify algebraic expressions

substitute numerical values into algebraic expressions

substitute given values for the other pronumerals in a

mathematical formula from a vocational or other context to

find the value of the subject of the formula

solve linear equations involving two steps

REFLECTION:


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Section 9: Strategies, handy hints and Keywords

AM1 - Algebra Booklet

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