Name: ______________________________________________
2014 Final Exam Review Packet
Algebra I CP
Systems of Equations and Inequalities
1. Name the three methods used in solving systems of equations.
2. Find the ordered pair that is a solution to the system of equations
3. Determine the number of solutions to the system of equations
 x  y  13
3 x  y  19
y  2x  1
2 x  2 y  22
.
4. If lines are perpendicular, how many solutions are there?
If lines are parallel, how many solutions are there?
If lines are the same, how many solutions are there?
5. Name a point that is not a solution to the system of inequalities graphed below.
. Show your work.
6. Solve for x in the following system of equations using the substitution method.
2 x  2 y  38
y  x3
7. You have $3.70 in dimes and quarters. You have 5 more quarters than dimes. How many of each type of
coin do you have? Set up a system of equations and solve.
8. David is responsible for buying the food and drinks for the children and parents at a local carnival. The
food and drinks for each parent costs twice as much as those for a child. He needs to feed 100 parents and
225 kids. His budget is $2, 975. How much can David spend on each child for food and drinks?
Linear Functions
9. Write the equation of a line that has a slope of zero.
10. Write the equation of a line that has an undefined slope.
11. Determine the direction of the line y = -2x + 1. Explain why.
12. Find the x and y intercepts of 3x – 8y = 24.
13. Find the slope of -2x + y = 12.
Find the slope of x = 4.
Find the slope of y = 2.
Exponents
Directions: Simplify completely.
14. x 9  x 2
15. a 10  a 3
a8
17. 3
a (a)
 4m 
18. 

 5n 
16. (3xy7 z 4 )(5x 3 y 5 z )
3
20. Give an example of an exponential function.
19. ( x 4 ) 11
21. Sketch the graph of an exponential growth function and an exponential decay function.
22. Evaluate the exponential function y = 6  3 x if x = 4.
23. What is (-x)-2y if x = 4 and y = 6.
24. Find  y 3 if y  2 .
25. Explain why the two items below are not written in correct scientific notation.
a) 70  10 6
b) 0.06  10 8
Operations on Polynomials
Directions: Simplify completely.
26. (2 x  3) 2

 
27. 4 x 2  7 x  9  3x 3  2 x 2  8x

28. (2a  3)(6a  7)
29. (5a  7)(5a  7)
30.  2 x 4 ( x  8)  3( x 2  6)
31. (a  9) 2
32. A square blue placemat has a yellow square in the center. The side length of the yellow square is
( x  3) inches and the side length of the placemat is ( x  7) .
A. Find the expression that represents the area of the yellow square.
B. Find the expression that represents the area of the entire placemat.
C. Find the expression that represents the area of only the blue area of the placemat.
33. Find the area of a rectangle with a length of 10x 3 and a width of 8x 7 .
Factoring
Directions: Factor completely.
34. x 2  7 x  30
35. 16 x 2  25
36. x 2  14 x  49
37. x 2  4
38. 6 x 2  23x  7
39. x 2  x  56
40. Find the GCF.
a) 63x 5 y 2  14 x 2 y  49 x 4 y 3
b) 4x2y + 8xy
41. Find the GCF and factor: 6x2 + 18x - 24
42. The area of a rectangular deck is given by the trinomial x 2  5d  36 . What are the possible dimensions
of the desk?
Quadratic Functions
43. Solve for x.
a) x 2  36  0
b) x 2  144
44. What are the solutions to (x + 7)(x – 8) = 0?
45. Factor x2 + 3x – 54 = 0 and solve.
46. If f (x) = -x2 +5x−1, find f (1).
47. Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of y = -3x2 +
12x + 1.
48. Based off of the equation of a quadratic function, how can you determine if the parabola has a minimum
or maximum value?