Transcript Exam Review - The Westminster Schools

Exam Review
1st Semester
Algebra I
Topics Covered
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Chapter 2 – Equations and Functions
Chapter 3 – Graphing Linear Equations
Chapter 4 – Solving Equations and Inequalities
Chapter 7 – Systems of Linear Equations and
Inequalities
Chapter 1 –
Using Algebra to Work with Data
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Working with Variables and Data

Order of Operations
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Mean, Median, Mode and Graphs
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Operations with Integers
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Exploring Negative Numbers
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Exploring Variable Expressions
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Applying Variable Expressions
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Working with Data
Chapter 2 –
Equations and Functions
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Solving Equations
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Solving Multi-step Equations
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Applying Functions
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Coordinate Graphs
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Representing Functions
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Using Graphs to Solve Problems
Chapter 3 –
Graphing Linear Equations
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Applying Rates
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Find Slope
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Equations of Lines
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Writing an Equation of a Line
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Modeling Linear Data
Chapter 4 –
Solving Equations and Inequalities
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Solving Problems using Tables and Graphs
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Solving Multi-step Equations
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Equations with Fractions or Decimals
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Writing Inequalities from Graphs
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Solving Inequalities
Chapter 5 –
Connecting Algebra and Geometry
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Ratio and Proportion
Scale Measurements
Similarity
Perimeter and Area
Probability
Geometric Probability
Chapter 6 –
Working with Radicals
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The Pythagorean Theorem
Chapter 7 –
Systems Linear Eqns and Ineqs
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Using Linear Equations in Standard Form
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Solving Systems of Equations
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Graphing
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Substitution
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Elimination (Multiplication)
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Linear Inequalities
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Systems of Linear Inequalities
Chapter Seven
Solving Systems of
Linear Equations
and Linear Inequalities
Standard form
Graph. State the slope,
x- and y-intercepts.
10
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5
-10
-5
5
-5
-10
10
2x + 5y = 20
Standard form
Graph. State the slope,
x- and y-intercepts.
10

5
-10
-5
5
-5
-10
10
3x – 2y = 5
Standard form
Write the following in standard form.
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y = 2x + 5
Standard form
Write the following in standard form.
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2
y  x2
3
Solving Systems of Equations:
By Graphing
Solve the given system by
graphing.
10
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5
-10
-5
5
-5
-10
10
x + y = -3
x – y = 13
Solving Systems of Equations:
By Graphing
Solve the given system by
graphing.
10
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5
-10
-5
5
-5
-10
10
2x + 5y = 10
3x + y = 15
Solving Systems of Equations:
By Substitution
Solve the given system by substitution.
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-x + 4y = 10
3x + y = 9
Solving Systems of Equations:
By Substitution
Solve the given system by substitution.
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x – 3y = 4
3x – 2y = 6
Solving Systems of Equations:
By Elimination
Solve the given system by elimination.
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2x – 3y = 4
3x – 2y = 8
Solving Systems of Equations:
By Elimination
Solve the given system by elimination.
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5x – 2y = -9
3x + 4y = 5
Linear Inequalities
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10
5
-10
-5
5
-5
-10
10
Graph
2x - 3y ≤ 6
Linear Inequalities
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10
5
-10
-5
5
-5
-10
10
Identify the linear
inequality shown.
Systems of Linear Inequalities
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10
5
-10
-5
5
-5
-10
10
Graph
2x + 3y ≤ 6
x – 2y ≥ 5
Systems of Linear Inequalities
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Identify the system of
linear inequalities
shown.
Chapter Six
Working with Radicals
Pythagorean Theorem
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Find the missing leg length.
8
4
Pythagorean Theorem
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Is a triangle with side lengths 4, 5, 6 a right
triangle? Justify your answer.
Chapter Five
Connecting Algebra
and Geometry
Ratio and Proportion
1
2

x x 1
Ratio and Proportion
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800 children a day ride on the roller coaster,
but another 200 are turned away because
they're not tall enough. What proportion of
the total number of children are turned away?
Ratio and Proportion
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At Washington High School, two out of
every three students usually buys a
yearbook. How many yearbooks should the
school plan for if there are 1460 students at
the school?
Ratio and Proportion
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Methane is a compound consisting of a
1 : 4 ratio of carbon and hydrogen atoms. If a
sample of methane contains 1565 atoms,
how many carbon and hydrogen atoms are
present?
Scale Factor
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Nathan plans to include a map in his report
on Africa. The map he has is 6 in. wide and
8 in. long. He wants to use a photocopier to
enlarge the map so that it fills the width of the
page.
What scale factor should he use to make the
map 7.5 in. wide?
How long will the enlarged map be?
Similarity
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A tree 48 feet high casts a shadow 36 feet
long. If a flag pole casts a shadow 12 feet
long, the height of the flag pole is
Perimeter and Area
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The perimeters of ABC is 2 ft. The
perimeter of DEF is 15 in. These two
figures are similar.
Find the ratio of the corresponding side
lengths.
Find the ratio of the areas.
Probability
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A six sided die was rolled 60 times.
1 came up 10 times, 2 came up 9 times,
3 came up 15 times, 4 came up 8 times,
5 came up 7 times. What is the theoretical
and the experimental probability of getting
an even roll?
Geometric Probability
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Find the area of the
shaded region.
Geometric Probability
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Find the area of the
shaded region.
Chapter Four
Solving Equations
and Inequalities
Solving Problems using
Tables and Graphs
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At Homecoming, 2000 tickets were sold at the
football game. Adult tickets sold for $7.50 and
student tickets solve for $5.00. The total
revenue was $11,625.00. How many student
tickets were sold? How many adult tickets
were sold?
Solving Multi-step Equations
3( x  4)  2 x  4 x  6
Solving Multi-step Equations
4( x  3)  x  11 3x
Equations with
Fractions or Decimals
2
3 1
x  x
3
4 2
Equations with
Fractions or Decimals
6.5n  3.9  2.9n
Writing Inequalities from Graphs
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y>0
Writing Inequalities from Graphs
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x≤3
Solving Inequalities
1  3 x  8  x
Solving Inequalities
2x x
 5
3 4
Chapter Three
Graphing Linear Equations
Applying Rates
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How many miles per hour is 44 ft/s?
Applying Rates
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How many feet per second is 100 mph?
Find Slope
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Find the slope of a line that passes through
(-6, -1) and (-1, 4).
Find Slope
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Find the slope of a line that passes through
(1, -3) and (-2, 8).
Equations of Lines
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10
5
-10
-5
5
-5
-10
10
Find an equation of the
graphed line.
Equations of Lines
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10
5
-10
-5
5
-5
-10
10
Find an equation of the
graphed line.
Writing an Equation of a Line
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Find the equation of a line that passes
through (-6, 2) and has a slope of -2/3.
Writing an Equation of a Line
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Find the equation of a line that passes
through (-4, 1) and (-6, 2) .
Chapter Two
Equations and Functions
Solving Equations
1
x 1  4
5
Solving Equations
4 x  3x  5 x  16
Solving Multi-step Equations
5( x  30)  10  175
Solving Multi-step Equations
3
( x  96)  7
4
Applying Functions
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The cost of making T-shirts is $5 per shirt plus
$150 for printing supplies. What is the cost of
making 100 T-shirts?
Applying Functions
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You have moved to a new city and plan to join
the Racquet Club. The membership fee is $250
and you must pay $ 7 every time you use a
court. If your bill from the Racquet Club was
$630, how many times did you play racquetball?
Coordinate Graphs
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In the figure, is a rectangle with center at the
origin. If the coordinates of A are (3, 4), the
coordinates of C are
Representing Functions
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If the x-coordinate of a function is three times
that of the y-coordinate, the function would be
represented by
Using Graphs to Solve
Problems
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It took Myron 90 minutes, at an average rate
of 50 miles per hour, to drive home from a
business trip. Which of these graphs best
represents Myron’s drive home?
Chapter One
Using Algebra to Work with Data
Working with Variables and Data
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Write an algebraic expression to represent the
following expression:
the difference in six times a number and nine
Working with Variables and Data
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Write an algebraic expression to represent the
following expression:
the sum of twice a number and three
Order of Operations
3
2
2
 2(3)  9  3  (3  4)
3
3
Order of Operations
7  6(8  3)
Mean, Median, Mode, Graphs
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Find the mean, median, and mode:
26, 26, 27, 27, 42, 42, 44, 44, 44, 60
Mean, Median, Mode, Graphs
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What is the mean
points scored by
the starting players?
Operations with Integers
2   2  6   2  1
2
Exploring Negative Numbers
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Simplify the following expression if
a = -2 and b = -3.
a  2ab  b
2
2
Operations with Variable
Expressions
3x  2x  4  2( x  2 x  3)
2
2
Operations with Variable
Expressions
3( x  4)  2( x  2)
Applying Variable Expressions
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The cost of making T-shirts is $3.50 per shirt plus
$150 for printing supplies. What is the cost of
making 250 T-shirts?
Working with Data