Download Algebra 1 Study Guide

Algebra 1 Study Guide
Chapter 1: Variables, Function Patterns and Graphs
Vocabulary:
absolute value
domain
function
simplify
algebraic expression
range
function rule
order of operations
dependent variable
equation
rational numbers
independent variable
evaluate
irrational numbers
Sets:
1. Please classify the following numbers. List all sets that each is a member of (rational, integers,
whole, and/or natural numbers.
a. –20
b. 0.9
c. 7
d. the square root of 5
e. 0
4
1239
2.
Write an algebraic expression for the following English phrase:
a. the difference of two numbers is one-fourth the sum of two numbers
b plus c plus twice a
3.
Evaluate using the order of operations if a = -3, b = 1, c = 2
a. ac – b
b. a2 + b2 – c
c. abc + bc
4.
Use the table below to answer the questions:
Number of Books
1
2
3
4
Total Cost
$3.50
$7.00
$10.50
$14.00
a. What is the independent variable? ________________
b. What is the dependent variable? _______________
c. What is the function rule? _______________
Chapter 2: Rational Numbers
Vocabulary: Write an equation that matches each of the properties below:
Identity Property of Addition
Identity Property of Multiplication
Inverse Property of Addition
Inverse Property of Multiplication
Multiplication Property of –Zero Multiplication Property of Negative One
Commutative Property
Associative Property
Distributive Property
Operations with Integers
1. (–13) + (–4)
2. –12 – (–7)
3. –12.4 + 22.3
4.
|54.3 – 29.4|
5. 5(4)(–2)
6. –32 + (–3)2
7.
4 – (–2)
3
Simplify each expression: (No like terms, no parentheses)
8.
9m – m + 3
8.
–(3 – 10y)
9.
7 – 16v – 9v
10.
(6 – 3m)(–3)
–2(r – ½)
12.
3/5(15t – 2)
13.
3x2y2 – 6y2 + 4 x – 3y2 – 4x2y2 – x
Probabilities:
Find each probability for one roll of a number cube.
14. P(number  7)
15. P(not 6)
16.
P(2 or 6)
11.
17. You are about to attack a dragon in a role playing game. You will throw two dice, one numbered
one to eight and the other with the letters A through F. What is the probability that you will roll the
values two and C?
18. A face-down deck of cards contains four hearts, three diamonds, six clubs and six spades. What is
the probability that the first two cards drawn will both be clubs?
Chapter 3: Solving Equations
Vocabulary:
ratio
equivalent equations
perfect squares
Solve for x:
1. 5x – 8 = 12
proportion
solution
Solve for y:
2. –3xy + 7xy = 12
Inverse operations
consecutive integers
Solve for c:
3. 8c – 16 + 2(c – 4) = 4c – 18 + 6c – 1
Proportions and Similar Figures
Ian is 3 ft. tall and casts a shadow that is 60 inches. He is standing next to a tree that casts an 8 ft.
shadow. (Draw a picture to help you solve this problem.)
4.
How tall is the tree? ________________
5.
A cat standing on the other side of Ian casts an 18 in. shadow. How tall is the cat? _________
6.
12 =
4____
r 0.5r – 1
7.
d – 2 = __3__
d+9
14
8.
_4_ = _C_
12
6
Equations and Word Problems
9.
A 12-ounce can of green beans is sold for $1.45. What is the price per pound?
10.
The sum of three consecutive integers is 582. Find the three integers.
a. Define a variable for the smallest integer.
b. Write an equation for the situation and solve.
c. Name the three integers.
11. Peter and Paul live 3 miles apart. They both leave their houses at the same time and walk to meet
each other. Peter walks at 2.5 mi/hr and Paul walks at 3.5 mi/hr. How far will Peter walk before he
meets Paul?
Percent of Change
Find the percent of change. Describe the change as an increase or decrease.
12.
A $1500 computer is on sale for $1275.
13.
The value of a stamp collection changes from $160 to $180 in one year.
Use the Pythagorean Theorem to answer this question.
14.
A soccer field is 80 yd. long and 35 yd. wide. What is the diagonal distance across the field?
Chapter 4 –Solving Inequalities
Vocabulary:
inequality
compound inequality
intersection
union
Solving and graphing inequalities
Solve and graph on a number line. Be sure to label each number line.
1.
m  –5
2.
3n + 5  –1
3.
–3  z – 1  3
4.
2t  –4 or 7t  49
Word problems with inequalities
5.
Michael sells computer supplies. Each week he earns $190 plus a commission equal to 4% of his
sales. This week his goal is to earn no less than $500. Write an inequality to find the amount of sales he
must have to reach his goal.
6.
In Sacramento, California, July’s average high temperature is 91F. July’s average low
temperature is 75F. Write a compound inequality to represent Sacramento’s average temperature in
July.
Chapter 5: Graphs and Functions
Graphs of events and situations
For problems 1 – 3, please sketch a graph of the situation or event. You must include the following:
a. Label the x and y axis
b. Sketch each graph and describe each interval.
1.
The amount of milk in your container over one lunch period.
2.
The speed of a bicycle during an afternoon ride.
3.
The height of a lamb from birth to 1 year.
For problems 4 and 5, complete the function table by using the given function rule.
4.
f(x) = 4x – 7
x
f(x)
1
2
3
4
5.
f(w) = 5 – 3z
w
f(w)
1
2
3
4
6.
Determine whether the relation is a function.
w
0
1
2
1
f(w)
1
2
3
4
7.
Clara finds a website to purchase tickets for a Nationals game. They have a surcharge of $18 and
charge $14 per ticket. The function rule for this situation is C(t) = 18 + 14t. Create a function table for
t = 0, 5, 10, 15 and graph the function. Remember to label the x and y axis and use reasonable intervals.
8.
Is each equation a direct variation (DV), and inverse variation (IV) or neither? If it is DV or IV,
please find the constant of variation.
a. y = 2x + 5
b.
f(x) = –3x
c.
y = 2 /5 x
d.
4x + 8y = 0
9.
Write a DV equation that includes the following point.
a. (1, 2)
b. (–2, 6)
10.
Each pair of points is on the graph of an inverse variation. Find the missing value.
a. (9, x) and (3, 12)
b. (4, 2.65) and (y, 4.24)
11.
Find the third, sixth, and fifteenth terms in this sequence.
A(n) = 2 + (n – 1)(–2.5)
12.
Find the second, fifth and twelfth terms in this sequence.
A(n) = –9 + (n – 1)3
Chapter 6: Linear Equations and their Graphs
Vocabulary: slope-intercept form
slope of parallel lines
standard form
point-slope form
slope of perpendicular lines
1.
Find the rate of change: A kitten grows from 5 oz. at birth to 3 lb. 5 oz. at 6 months. (Hint: 1 lb =
16 oz.)
2.
3.
Find the slope of the line that passes through each pair of points.
a. (3, –2) and (–5, –4)
b. (4.5, –1) and (4.5, 2.6)
c. (2, 5) and (–5, –2)
Write an equation for the line in Slope-Intercept form.
a. m= –7, b = 1/2
b.
4.
Write an equation in slope-intercept form for this situation.
A skateboard ramp is ft. high and 12 ft. long from end to end.
5.
Find the x and y intercepts and graph.
a. 6x + y = 12
b.
–2y = 5x – 12
6.
Write an equation in standard form for the following situation:
Caleb can ride his bike at 12 mi/hr and walk at 4 mi/hr. Write the equation that relates the amount
of time Caleb spends riding or walking combined to travel 20 miles.
7.
Use the Point-Slope form to write an equation of a line that passes through the
points (–8, 4), (–4, 2).
8.
A line perpendicular to y = x –3 passes through the point (4, 6). Which other point lies on the
line?
9.
Write an equation for the line in slope-intercept form that is parallel to y = 0.5x – 8 and passes
through the point (8, –5).
10.
Identify the graph of y = 4.
B.
A.
QuickTime™ and a
decompressor
are needed to see this picture.
QuickTime™ and a
decompressor
are needed to see this picture.
A
C.
D.
QuickTime™ and a
decompressor
are needed to see this picture.
QuickTime™ and a
decompressor
are needed to see this picture.
A