TERMINOLOGY
1. In the following expression: 𝟐𝒙𝟑 + 𝟑𝒙 − 𝟐
a) What is the coefficient of x? _____________________
b) What is the 𝑥 called? _____________________ ______
c) What is the constant term in the expression? _____________________
d) How many terms are there in the above expression? _______________
e) Write down the coefficient of the following terms:
1.1.1.
2a 3
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1.1.2.
6x 2
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SUBSTITUTION
2. If x = 3 and y = - 2
Find the value of:
a) 3𝑦 ___________________________
b) 𝑥𝑦 ___________________________
c) 𝑥 − 2𝑦 ___________________________
d) 𝑥 − 𝑦 2 ___________________________
1.1.3.
b7
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SIMPLIFYING ALGEBRAIC EXPRESSIONS
Basics
You can only add/subtract like terms (like terms have same variables and same exponents)
When you multiply terms you do the following:
Multiply the signs
Multiply the coefficients
Add the exponents
When you are dividing terms you do the following:
Divide the signs
Divide the coefficients
Subtract the exponents
When a number is right next to a bracket it means you need to distribute. Follow the same
rules for multiplying terms but remember to distribute to all the terms.
DISTRIBUTION
3. Distribute and simplify the following:
a) 4𝑎(2𝑎 – 3)
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b) 3(3𝑥 – 2𝑥) − 2(𝑥 + 3)
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c) −2𝑥(𝑥 2 − 6y)
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SIMPLIFY
4. Simplify the following:
a) 4𝑎 2 𝑏 × −3𝑎𝑏 5
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b) y8 ÷ y2
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c) 13x2y – 2yx2 + 3xy2
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d) 5a + 3a2 + 4a – 5a2
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e) 2𝑎(𝑎 + 1) − 3𝑎(4𝑎 − 1)
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f)
81a3b3
3ab2
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g) 6a4 + 3a3 - 15a2
3a2
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h) Subtract 3𝑥 4 − 2𝑥 2 − 7 from 5𝑥 4 − 2𝑥 2 + 3
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i)
Subtract 5𝑥 2 + 4𝑥 − 9 from 7𝑥 2 − 9𝑥 − 3
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Equations
An equation always has an equal sign. Follow the following steps:
1. Take all variables with their coefficients to the one side and the constants to the other
(remember the sign changes when it is taken over the equal sign)
2. Simplify both sides
3. Divide or multiply by the coefficient to get the variable by itself.
Examples:
1. 𝑥 + 9 = 2
2. 2𝑥 − 3 = 7
3.
4.
3𝑝
5
𝑥
5
=9
+3=2
5. 4𝑚 + 7 = 2𝑚 + 3
6.
5𝑥+4
2
= 12
Transformations
What would the new coordinates of Quadrilateral ABCD be if it were translated:
a) 6 units to the right and 2 units down?
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b) 4 Units to the left and 3 units up?
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