Algebra I Exam Review 2016
Name ____________________________________
1. Write the prime fact factorization of the following.
a) 112
b) 248
c) 420
2. Evaluate the expressions using the given values.
a) 3a 2 + 2 − 5(a + b) − ab + b3c; a = −3,b = −1,c = 5
b) 8 − 6x + 8xy 2 + y; x = −3, y = −2
3. Find the values that cause each expression to be undefined.
a) x+5
b) 19
9x−12
4. Solve
7x+56
3 10x − 2 = 3 2 − 6x .
7
4
(
)
(
)
5. Solve 7z − 9zy + 2z+ = 4xz − 2 + y for x.
6. Solve 5(3x − 3) = 4zw for x.
7. Translate the words into a mathematical equation. 79 more than the 4 times the
difference of a number and 3 is 16 less than 7 times then number.
8. Solve 4x + 5(6 − x ) > 20 + 3x .
9. A coat cost $57 after a 24% percent decrease in price. How much did it originally
cost?
10. Find the intercepts of 6 y − 8x = 24 and then graph the equation.
11. Determine the slope and the y-intercept of the graph of y = 5x +14 . 12. Determine the slope and the y-intercept. 3x + 7y = 2
13. Determine the slope and the y-intercept of each line a) y = 6 ; b) x = 1 .
14. Calculate the slope of the line connecting the two points (−9, − 3) and (5, − 7) .
15. Write the equation of the line with a slope of -3/4 and a y-intercept of 2. Write the
equation in slope-intercept form.
16. Write the equation of the line with a slope of 9/4 and a y-intercept of -8. Write the
equation in standard form.
17. Write the equation of the line containing the points (6, -1) and (4, -3). Write the
equation in slope – intercept form.
18. Refer to #17. Write the equation in standard form.
19.Write the equation of the line with an x-intercept of -9 and a y-intercept of 16.
20.Write the equation of the line containing the point (-7, 4) which is parallel to the line
represented by 5x + 3y = 10.
21.Determine if the (1, -6) is a solution of 4x – 3(2-y) > -16
22.Sketch a graph of a non-function.
23. f ( x ) = 6x +15
a.)Find f (−11) .
b.) Find f ( z ) .
c.) Find f (8x − 7) .
24. f ( x ) = 7 2x − 6 + 4 Find f (−7) .
25.Graph the inequality. y ≥ 3x + 2
26.Write the equation of the
line given below.
28. Solve by graphing.
27.For the graph below find f(-2) and
f(3).
5x – 2y = 20
2x + 3y = 8
29. Solve using substitution.
5x + 7y = 26
-4x + y = 32
30. Solve using substitution.
9x + 2y = 51
x – 3y = 25
31. Solve using elimination.
3x – 5y = 2
6x + 2y = 64
32. Solve using elimination.
2x + 8y = 26
5x – 3y = -27
33. Solve the system of linear inequalities
y ≤ 2x − 8
2x + y > −4
34. If a boat goes 39 miles in 1.5 hours with the current and 30 miles in three hours
against the current, then what is the speed of the boat in still water and what is the speed
of the current?
35. Tickets for a circus cost $7 for kids and $10.50 for adults. If a total of 220 people
attended and the circus took in $1785, then how many kids and how many adults attended
the circus?
36. If rock candy cost $3.20 per pound and sweet tarts cost $2.60 per pound. Then how
much of each do I need to make 4 pounds of a mix that cost $3 per pound?
37. How much 5% Gatorade solution and how much 15% percent Gatorade solution
should be mixed to create 10 gallons of an 8% Gatorade solution?
38. Solve. 24 ≤ 5x + 9 < 20
39. Solve. 4 − 5 6x + 2 = −6
40. Solve. 5+ 7x − 2 ≥ 26
41. Solve. 3+ 6 7x +1 < 51
42. Consider f ( x ) = 3x − 7 and g ( x ) = −5x + 2
a.) Find ( f + g ) ( x )
b.) Find ( f ⋅ g ) (3)
c.) Find ( f − g ) ( 4)
d.) Find (f / g)(x + 2)
43. State the domain and the range of the following functions. Use interval notation.
a.)
b.)
44. Give an example of a set of ordered pairs that illustrates a function in which there is
an element of the range that corresponds to more than one element of the domain.