Download Algebra 1 Final Review (Do all work on separate paper)

Algebra 1 Final Review (Do all work on separate paper)
Name____________________________ Date_________Per.___________
1) Evaluate ( x  4) 2 
y
3
when x = -5 and y = -9
2) (Anything)0 = ?
3)
4)
8 4
?
83
64  3 125 = ?
5) Write an equivalent expression to w 7 w 4 .
6) What is the only real number with no reciprocal?
7) What is the multiplicative inverse of
8) Solve the Absolute Value Equation:

4
?
5
3x  2  13 .
9) What is the solution set of the inequality: 9  x  5  2 ?
10) Write an equivalent equation by using distribution: 7 x  5(3x  2)  21x
11) Solve for the variable: 6( x  7)  9  7( x  4) .
12) The total cost (c) in dollars to rent a yacht for n days is given by the equation
c = 1000 + 400n. The total cost was $4200, how many days was the yacht rented?
13) Solve the linear equation: 5(x + 7) = 2x -1.
14) A 210 ft. rope is cut into 3 pieces. The 1st piece is twice as long as the 2nd piece.
The 3rd piece is 4 times as long as the 2nd piece. How long is the longest piece?
15) Solve the inequality: -4x – 2 < 6.
16) The lengths of a quadrilateral are 2x, x + 2, 3x – 4, and 10 cm. If the perimeter is
80cm., what is the value of x?
17) Solve the quadratic equation: x 2  4 x  5  0 .
18) Solve the linear equation: n  2(n  12)  72 .
19) What are the x & y intercepts of: 3x – 4y = 12.
20) Give an example of a linear inequality for each inequality sign: <, >, , and 
21) Graph the linear equation: 3x – 4y = 12.
22) Graph the inequality:  2 x  y  3 .
23) Graph the linear equation:
y
1
x  1.
2
24) What are the x & y intercepts of the line described by: 3x + 5y = 11.
25) Write the equation of the line with slope
2
& that goes through the point (3,5).
3
26) The data in the table shows the cost for renting a limousine by the hour,
including a deposit.
Renting a Limousine
Hours (h)
2
6
10
Cost in dollars (c)
$148
$244
$340
If hours h, were graphed on the horizontal axis and cost c, were graphed on the
vertical axis, what would be the equation of a line that fits the data?
1
h  100
A. c 
B.
c  24h 100
24
1
c
h  100
C.
D.
c  24h 100
24
27) Using y = mx + b form show that the equations represent perpendicular lines:
Eq.1) 5x – 3y = 11 & Eq.2) 3x – 5y = -5.
28) Give an example of an equation that represents a line parallel to 𝑦 =
−3
5
𝑥 − 4.
29) Graph the system of inequalities: Inq.1) 𝑦 − 2𝑥 ≤ 3 & Inq.2) 𝑦 ≤ −𝑥 + 2.
30) Solve the system: Eq.1) 𝑦 = 2𝑥 − 3 & Eq.2) −𝑥 − 2𝑦 = −4.
31) Which ordered pair is the solution to the system of equations below?
5 x  2 y  29
8 x  8 y  80
A. (5, 2)
B. (7, 3)
C. (10, 0)
D. (1,12)
32) Using y = mx + b show that the graphs of the equations are parallel:
Eq.1) 2x – 3y = 9 & Eq.2) -6x + 9y = 9.
33) Simplify:
4𝑥 3
16𝑥 5
34) Subtract: (9𝑥 2 + 7𝑥 − 5) − (5𝑥 2 − 3𝑥 − 9).
35) Simplify: (2𝑥 − 5) + (2𝑥 + 3)(𝑥 − 5).
36) A rectangular garden has a width of 2x meters and a length of 5x meters. What
is the area of the garden?
37) Factor completely: 5𝑚2 + 15𝑚𝑛 − 200.
38) Factor: 𝑥 2 − 13𝑥 + 42.
39) Factor: 9𝑟 2 + 24𝑟 + 16.
40) Factor: 36𝑡 2 − 49𝑢2 .
41) Find the solutions to the quadratic equation: 𝑥 2 − 7𝑥 = 8.
42) Solve the equation by factoring: 9𝑥 2 − 33𝑥 + 30 = 0.
43) Find the zeros of the equation: 𝑦 = 𝑥 2 − 𝑥 + 12.
44) Find, circle, and correct the 2 mistakes in the quadratic formula: 𝑥 =
𝑏±√𝑏 2 +4𝑎𝑐
2𝑎
45) Use the quadratic formula to solve the equation: 2𝑥 2 − 3𝑥 = 20.
46) Use the quadratic formula to find the solution set of the equation: 3𝑥 2 + 6𝑥 = 2
47) Graph: 𝑦 = 𝑥 2 + 3.
48) What are the x-intercepts of the quadratic equation: 𝑦 = (𝑥 − 2)(3𝑥 + 2).
49) Simplify:
6𝑥 2 +21𝑥−45
4𝑥 2 −9
50) Reduce to lowest terms:
51) Multiply:
3𝑦 2 −3𝑦
4𝑦−12
𝑥 2 −7𝑥+10
𝑥 2 +𝑥−6
𝑦 2 −9
× 𝑦 3 −2𝑦 2+𝑦
𝑧−5
3𝑧−4
52) Find the Product of: (2𝑧+5) ( 𝑧+5 ).
53) Divide:
𝑥−3
𝑥 2 −9
3𝑥−3
÷ 𝑥 2 +2𝑥−3
54) Hank’s average driving speed for a 6 hour trip was 60mph. The 1st 5 hours he
drove 55mph. What was his average speed for the last hour of his trip?
55)
2 planes leaving at the same time and travelling toward each other are 2500
miles apart. When do they cross paths if one is going 550mph and the other 450mph?
56) How many liters of 40% salt solution must be added to 40 liters of 23% salt
solution to get 30% salt solution?
A. 28 liters
B. 92 liters
C. 24 liters
D. None of these
57) When is a relation a function?
58) Show a graph of a quadratic with all positive y-values.
59) What is the range of the function: (-4,3), (-2,-4), (3,5), and (6,2)?
60) What is the test to show that a relation is a function?