ALGEBRA II Sem. 1 Practice Final
2
NAME: _________________________
3
1.) Evaluate (b + y) - 3y if b = 3 and y = -2.
2.) Evaluate −|4𝑐 − 𝑑| if c = -3 and d = 9.
3.) The formula 𝐴 =
180(𝑛−2)
𝑛
relates the measure A of an interior angle of a regular polygon to the number of
sides n. If an interior angle measures 108o, find the number of sides.
4.) Name the sets of numbers to which 0.25 belongs.
1
5.) Simplify 2 (12𝑥 + 8) −
6.) Solve 3 = 7 −
1
(20𝑥
4
− 8)
2
𝑥
5
7.) Solve 4(6x – 5) = 4x + 10
8.) Solve |𝑥 − 2| = 14
9.) Solve -2(x – 10) + 7 > 5
10.) Solve |3𝑥 − 6| ≤ 12
11.) Graph the solution set of -1.3 > 0.3 + 0.4y
12.) A parking garage charges $3 for the first hour and $1 for each additional hour. Carl has $8.75 to spend for
Parking. What is the greatest number of hours Carl can park?
13.) Find f(x+1) if f(x) = x2 – x +3.
14.) Write an equation for a horizontal line.
Write an equation for a vertical line.
Write an equation for a line with a slope of 2.
15.) Find the x-intercept and the y-intercept of the graph of 5x + 2y = 10.
16.) Write 2y – 3x = 15 in standard form.
17.) Find the slope of a line that passes through (3, 1) and (-2, 2).
18.) If a line lowers as it moves to the right, its slope is _________________. (positive, negative, 0, undefined)
If a line rises as it moves to the right, its slope is ___________________. (positive, negative, 0, undefined)
If a line is a horizontal line, its slope is _________________. (positive, negative, 0, undefined)
If a line is a vertical line, its slope is ________________. (positive, negative, 0, undefined)
19.) Write an equation in slope-intercept form for the line that has a slope of 2 and passes through (1, -3).
20.) What is the slope of a line that is parallel to the graph of y = 4x + 7?
21.) Write an equation in slope-intercept form for the line that passes through (0, 2) and is perpendicular to the line
whose equation is y = 3x.
22.) Give an example of each type of function: (examples p. 109 in book).
A. constant
B. identity
C. absolute value
____________
______________
_____________
23.) Identify the domain and range of y = |𝑥 − 2| – 6.
D. quadratic
______________
24.) How many solutions would each system of equations have?
a. two equations that form intersecting lines? _____
b. two equations that parallel lines? _____
c. two equations that form the same line? _____
25.) Look at the two equations below. If you multiply the first equation by 4, what would you multiply the second
equation by if you plan to eliminate the y variable with addition?
3𝑥 − 3𝑦 = 12
4𝑥 + 6𝑦 = 8
26.) Graph the system of equations. (use graph paper)
2x + y = 2
3x – y = 4
27.) Solve the system of equations: 2x + 4y = 4 and 5x – 2y = 1.
28.) Solve the system of equations? (hint calculator and matrices)
3𝑥 + 2𝑦 − 𝑧 = 5 and 𝑥 + 2𝑦 + 𝑧 = 3 and 5𝑥 − 3𝑦 − 2𝑧 = 14
For Questions 32 – 34, use the matrices to find the following.
1 1
𝐴= [
]
−5 0
𝐵= [
0 −0.75
]
2
0.5
1 1
𝐶=[ 3 2 ]
−4
0
3
29.) AB.
30.) 5B – 4C
31.) 𝐵−1
3
5 2
32.) Evaluate |−2 0 3| using diagonals.
1 −2 6
33.) Solve the system of equations 4x - 2y = 20 and x – 3y = -5 by using matrices.
34.) Identify the y-intercept and the axis of symmetry for the graph of f(x) = -2x2 + 8x + 10.
35.) Graph the quadratic function. (use graph paper)
f(x) = x2 – 2x
36.) Determine whether f(x) = -2x2 –8x + 2 has a maximum or a minimum value and find that value.
1
37.) Write a quadratic equation with roots 5 and − 3 ?
38.) Simplify
2 + 3𝑖
1− 5𝑖
39.) The total impedance of a series of circuit is the sum of the impedances of all parts of the circuit. A technician
determined that the impedance of the first part of a particular circuit was 24+ 12j ohms. The impedance of the
remaining part of the circuit was 3 – 4j ohms. What was the total impedance of the circuit?
40.) Solve 4x2 = -160.
41.) Find the exact solutions to 3x2 = 4x + 2 by using the Quadratic Formula.
42.) Use the value of the discriminant to determine the number and types of roots for x2 – 4x + 11 = 0.
1
3
43.) Identify the vertex, axis of symmetry, and direction of opening for 𝑦 = − (𝑥 + 4)2 − 7.
44.) Solve (x – 2)(x + 3) < 0.
0 2
2
4
45.) Simplify (5x y )(3x y) .
46.) Simplify
2𝑎3 𝑏3 𝑐
6𝑎−2 𝑏5 𝑐 4
3
. Assume that no variable equals 0.
2
3
2
47.) Simplify (4a – 6a + 3a) – (a – 3a – 1).
48.) Simplify (4x3 – 10x2 + 10x – 3) ÷ (2x – 6)
49.) Use synthetic division: (x2 – 5x + 6) ÷ (x – 3)?
50.) Factor 125x3 + 1 completely.
51.) Find p(-2) if p(x) = 3x3 – 2x2 + 7x – 8.
52.) State the number of real zeros for the function whose graph is shown at the right.
53.) Determine the values of x between which a real zero is located in the graph at the right.
54.) Solve x4 – x2 –12 = 0
55.) Use synthetic substitution to find f(-3) for f(x) = 2x4 – 2x3 + 3x2 – x + 6.
56.) Find all the rational zeros of f(x) =𝑥 3 − 4𝑥 2 − 3𝑥 + 18.