UCS JH Algebra I
SEM 2 REVIEW GUIDE #2
SUGGESTED QUESTIONS
1
Suppose you invest $1500 in an account paying 4.75% annual interest.
Find the account balance after 25 yr with the interest compounded the
following ways.
a. annually b. semiannually c. quarterly d. monthly
2
Mrs. Anderson and her students have been creating patterns and finding rules to
describe those patterns. One pattern that they created using triangles is shown below.
Write an explicit formula that Mrs. Anderson and her students can use to find the
number of triangles in the pattern at the n th stage?
3
The sign below shows the costs for one pizza with toppings.
Number of
Toppings
1
2
3
4
5
Cost
$4.75
$6.00
$7.25
$8.50
$9.75
Write a recursive equation that represents the
relationship between the cost of a pizza p and
the number of toppings t ?
4
A rectangle has sides
what is the coefficient of
2
in
1 and
3
. If
is the perimeter of the rectangle,
?
5
What is the greatest common factor of the terms of 10
6
A rectangular plot of land has an area of 2
dimensions of the plot of land?
7
Write a quadratic function, in both standard and factored form, with x-intercepts at
5 and
.
5
25
40
?
3 square yards. What are the
8
A quarterback throws a football across a field. The equation
16
20
6
models the path of the ball while it is in the air, where is the height of the ball in feet
and is the time in seconds. What is the maximum height reached by the ball?
9
A rectangular flower box measures 7 feet by 5 feet. If each side of this flower box is
extended by
feet, what will be the area of the new box?
10
You are building a rectangular wading pool. You want the area of the bottom to be 90
ft2. You want the length of the pool to be 3 ft longer than twice its width. What will the
dimensions of the pool be?
11
What is the vertex form of the equation of the function graphed below?
12
The volume of wax used in making a cylindrical candle is given by the formula
. What is the height of the candle in terms of the volume and radius?
13
Solve the quadratic by completing the square:
5
8
14
Below is the formula for figuring the time it takes for an object to fall when dropped.
The time in seconds is represented by , and is the height in feet from which the
object is dropped.
16
0
If you drop your least favorite music CD from a height of 40 feet, how long will it be
before it hits the ground?
15
The path of a golf ball can be modeled by the equation
16
, where is
the initial velocity, and is the initial height. When will the ball hit the ground if the
initial velocity is 20 ft/s and the initial height is 6 ft.
16
Solve the following system of equations algebraically and check.
3
4
7
17
Is the following data linear, quadratic, or neither? If linear or
quadratic, find the function rule that models the data.
x
-2
-1
0
1
2
y
-26
-2
6
-2
-26
18
Given
a.
b.
c.
d.
e.
f.
g.
the zeros of –5 and 3, find the following (assume a=1):
Factored Form of the equation
Standard Form of the equation
Coordinates of the Vertex
Vertex Form of the equation
Axis of Symmetry
Is the Vertex a Max or Min
The y-intercept
19
A student launches a rocket into the air. The parabola below shows the height of the rocket in
feet. Write an expression to describe the domain for this situation.
h (height (feet))
250
200
150
100
50
1
2
3
4
5
6
time (seconds)
7
8
20
What is the minimum point of the graph of the equation
21
The graph of
4
2 is shown below. Use the method of completing the
square to re-write in vertex form and identify the vertex and axis of symmetry.
22
What could be a possible equation for the graph given
the graph at the right?
Write the results in factored form and standard form.
2
8
9?
23
Kara translated the parent function,
a.
b.
c.
d.
e.
f.
. Write an equation for each situation below.
up 10 units
down 16 units
wider than the parent function and opens up
more narrow than the parent function and opens down
up 5 units and left 3 units
reflected over the x-axis
24
Write √ 64
25
What is the value of √40
26
What is the sum of the coefficients of the following polynomial:
3
7
8
23
27
Factor
2 as a complex number in the form a + bi.
7
2
18
89
28
Graph these two functions on the
coordinate place and find the solutions.
3
29
State the domain and range for the following function.
2
30
8
19
Suppose a football player kicks a ball and gives it an initial upward velocity of 47 ft/s. The
starting height of the football is 3 ft. Where is the football after 1 second? Where is the
football after 2 seconds? When will the football hit the ground?
16
47
3.
31
32
Solve using the Quadratic Formula:
0
9
1
Match each equation with the correct answers.
1. Crossing zeros: -2
Touching zeros: 6, -4
B
Crossing zeros: 6, -4
Touching zeros: -2
y-intercept: -16
3.
Crossing zeros: -6, 4
Touching zeros: 2
y-intercept: -8
4.
Crossing zeros: -1, 2, 4
Touching zeros: -6, 4
y-intercept: -32
Given the equation
a)
b)
c)
d)
e)
y-intercept: -16
2.
1
36
1
72
A
33
4
6
2
4
6
2
4
4
State the crossing zeros
State the touching zeros
State the end behavior
State the y-intercept
Sketch the graph
C
D
1
3
1
12
1
6
6
2
4
6
2
4
34
Based on her data, Janice expects 20 out of 135 high school centers at a basketball
tournament to be at least 80 inches tall.
Is this a valid inference? Explain your reasoning.
Use words, numbers, and/or pictures to show your work.
35
This table shows the maximum speed, in miles per hour, of six different animals.
Which animal’s speed is closest to the mean
speed?
36
Alicia is training to run in a marathon. The table shows how far she ran each day last
week.
Alicia found the mean, median, and mode of the distances she ran. On Sunday, she did
not run at all. If she includes Sunday’s distance (0 kilometers), what will be the
effect on the mean, median, and mode?
37
A mathematics teacher recorded the gender and hair color of all the students in two of
his classes as shown below.
What percentage of the male students have red hair?