Download Algebra 2 Trig - Parkway C-2

Algebra 2 Trig
Summer Skills Set
This summer skills set represents topics from the first two chapters of the
text. These topics will not be taught in class.
However, please go to www.classzone.com
Select: High School Math, Missouri, Go
Select: Algebra 2 2007
An On-Line Home Tutor, Practice Worksheets and Practice Tests are
available to you to complete problems in this summer skills set!
Vocabulary:
(For help, see the Math Vocabulary Flip Cards for Chapters 1 and 2 of the
text on www.classzone.com)
Opposite
Variable
Equation
Absolute Value
Linear
y Intercept
Reciprocal
Constant
Solution
Relation
Slope
x Intercept
Expression
Coefficient
Solve
Domain
Parallel
Rate of Change
Power
Equivalent
Extraneous
Range
Perpendicular
Scatter Plot
Exponent
Identity
Inequality
Function
Correlation
Slope Intercept Form of a Linear Equation
Standard Form of a Linear Equation
Point Slope Form of a Linear Equation
Function Notation: f(x)
The following link can help you for the following formulas:
http://www.classzone.com/cz/books/algebra_1_2007_na/resources/pdfs/alg1_other_formul
as.pdf
Midpoint Formula
Distance Formula
Slope Formula
Lesson 1.1: Apply Properties of Real Numbers
2
1. Which of the following are integers? -49, 0.2, −5 , 3
7
3
2. Graph − and 8 on a number line. Which is greater?
2
3. Identify the property that the statement illustrates: ( 6 • 1) • 2 = 6 • (1 • 2 )
4. You work 6 hours and earn $37. What is your earning rate?
Lesson 1.2: Evaluate and Simplify Algebraic Expressions
1. Evaluate: a. −53
b.
( −5 )
3
2. Evaluate 4 x 2 − 2 x + 5 when x -2 without a calculator
3. Simplify by combining like terms: −5 ( y + 5) − 5( y − 7)
Lesson 1.3: Solve Linear Equations
1
x+2=5
10
Solve 13x - 5x – 40 = 24
4
Solve ( 6 x + 12 ) = −40
3
Solve 45 – 2x = 9x – 10
2
Solve 14 x − 26 = (20 x + 85)
5
1. Solve
2.
3.
4.
5.
Lesson 1.4: Rewrite Formulas and Equations
1. Solve 3y + xy = -5 for y. Then find the value of y when x = -5.
2. A video store rents new movies for $5 and older movies for $2. The owner wants $10,000 in
revenue per month. How many new movies must be rented if the number of older movies rented
is 700?
3. The perimeter P of a rectangle is given by the formula P = 2l + 2w where l is the length and w
is the width. Solve the formula for the width w. Then use the rewritten formula to find the
width of a rectangle where the perimeter is 20.6 ft and the length is 6.3 ft.
Lesson 1.5: Problem Solving Strategies and Models
1. You are making a leather book cover. You need a rectangular piece of leather to cover a book
that is 10 inches long and 16 inches wide. Find the cost of the piece if leather costs $0.40 per
square inch.
2. Find the 7th number in the sequence: 2, 5, 8, 11, 14 ….
3. A car used 15 gallons of gasoline and traveled a total distance of 445 miles. The car’s fuel
efficiency is 30 miles per gallon on the highway and 25 miles per gallon in the city. How many
gallons of gasoline were used on the highway?
Lesson 1.6: Solve Linear Inequalities
1. Translate a verbal phrase into an inequality. Then graph the inequality. The verbal phrase is:
“All real numbers that are greater than 1 and less than or equal to 4.”
2. Solve −0.4( x − 4) ≤ 4 . Graph your solution.
3. Solve 3 < x + 7 < 10 . Graph your solution.
4. Solve 2x + 14 < 26 or 3x – 9 > 18. Graph your solution.
Lesson 1.7: Solve Absolute Value Equations and Inequalities
1. Solve 3x + 19 = 4 .
2. Solve 3 2 x − 10 − 10 = 8 .
3. Solve x − 9 ≥ 7 . Graph your solution.
4. Solve 6 5m − 8 − 11 ≤ 31 . Graph your solution.
Lesson 2.1: Represent Relations and Functions
1.
2.
3.
4.
5.
Is the following relation a function? {(-2, 1), (1, 0), (2, 4), (3, 2), (4, 3)}
Is the following relation a function? {(-2, 1), (1, 0), (-2, 4), (3, 2), (4, 3)}
What is the domain of {(-2, 1), (1, 0), (2, 4), (3, 2), (4, 3)}?
What is the range of {(-2, 1), (1, 0), (2, 4), (3, 2), (4, 3)}?
Is f ( x) = − x 2 − 2 x + 5 a linear function?
Lesson 2.2: Find Slope and Rate of Change
1. A ramp has a rise of 6 feet and a run of 21 feet. Find its slope.
2. Find the slope of the line through the points (14, 8) and (6, -7)
3. What is the slope of a vertical line? Horizontal line?
4. Tell whether the lines are parallel, perpendicular, or neither.
Line 1: through (6, 1) and (8, -5)
Line 2: through (3, 5) and (-6, 2)
Lesson 2.3: Graph Equations of Lines
1.
2.
3.
4.
Identify the slope, x intercept and y intercept of the line with the equation 6x + y = 5.
Graph -3x + y = -2.
Graph y = 2.
Graph x = -6.
3
5. Graph y = − x − 1
2
6. Determine which lines are parallel: line a through (-7, -6) and (4, 3); line b through (-9, 5)
and (1, 13); line c through (-12, -21) and (3, -9).
Lesson 2.4: Write Equations of Lines
1. Write an equation of the line in slope intercept form given the slope is -3 and the y intercept
is 2.
2. Write an equation of the line that passes through the point (-2, -6) and is parallel to the line
y = 3x -4.
3. Write an equation of the line that passes through the point (24, -9) and is perpendicular to
the line y = 8x +8.
4. Write an equation in point slope form of the line that passes through the points (3, 8) and (9,
10).
Lesson 2.8: Linear Inequalities in 2 Variables
1. Is (2, -5) a solution of 3x -6y < 2?
2. Graph y < 2 on a Cartesian Graph.
3. Graph y ≤ 4 x + 8
4. Graph x + 8 y ≥ −5