Download Chapter 1 Highlights

Chapter 1 Highlights
 Variable:
a letter used to represent one or
more numbers in an expression or equation
Example: 2n + 5
4a
(x – 4)²
 Evaluate:
to ‘plug’ a given number into an
algebraic expression and determine its
‘value’
Example: Evaluate the expression
2n + 5 when n = 7;
Answer: 2*7 + 5 is 19
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Power: an expression that represents
repeated multiplication of the same factor.
A power can be written in a form using two
numbers, a base and an exponent
Example: In the expression 4³, 4 is the
base, 3 is the exponent; it means 4*4*4
which equals 64;
Area of a square is side² (read squared);
Volume of a cube is side³ (read cubed).
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PEMDAS
First evaluate expressions inside grouping
symbols (Parenthesis)
Next evaluate powers (Exponents)
Multiply and/or divide from left to right
(Multiplication, Division)
Last Add and/or subtract from left to right
(Addition/Subtraction)
 [13 –(2 + 3)]²
[13 – 5]²
 [13 – 5] is 8 so *(8)²
 8² is 64
so *64 is 48
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(2 + 3) is 5 so
Evaluate 11 + r³ - 2r when r = 5
11 + 5³ - 2*5 = 11 + 125 - 10 = 126
  of a number n increased by 7:
*n + 7
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4 less than 6 times a number y: 6y – 4
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The sum of 15 and the square of m: 15 + m²
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3 more than twice a number w: 2w + 3
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12
The quotient of 12 and b: b
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The product of 4 and w is at most 12: 4w ≤ 12
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The sum of 9 and twice x is 23: 9 + 2x = 23
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The difference of 9 and the quotient of t and
6 is at least 5: 9  t  5
6
8 less than n is greater than 2: n – 8 > 2
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Read and understand: read each sentence
carefully and separately;
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Make a plan: are you going to +, -, x or 
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Solve the problem: carry out your plan;
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Check your answer: does it make sense? Is it
a reasonable answer?
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D = r*t Distance = rate * time
R = D/t Rate = Distance / time
T = D/r Time = Distance / rate
Distance is how far
Rate is how fast
Time is for how long
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Function: A relation between two
variables
The independent variable is also known
as the Domain or the Input, that is what
is put into a function – the x
The dependent variable is also known as
the Range or the Output, that is what
comes out of the function – the y
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Make a table for the function: y = 3x + 2
Input the numbers: 2, 4, 6, 8
Identify the domain and the range
Input
Output
2
8
4
14
6
20
8
26
Domain: 2, 4, 6, 8
Range: 8, 14, 20, 26
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Each corresponding pair of input and output
values of a function form an ordered pair (x,y)
of numbers that can be plotted as points on a
graph.
The horizontal axis, the x axis is labeled with
the input variable.
The vertical axis, the y axis is labeled with the
output variable.
A relation is NOT a function if an input value
is paired with different outputs (duplication).
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Verbal rule: The output is 1 less than twice
the output
Equation: y = 2x – 1
X
Y
Table:
1
1
2
3
3
5
4
7
Graph the ordered pairs: (1,1) (2,3) (3,5) (4,7)
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Make an input/output table from the graph
Compare each and ask yourself how each
output came from its corresponding input
Example:
X
Y
2
5
3
7
4
9
5
11
Rule: y = 2x + 1