Download Algebra 1 FINAL EXAM Semester 2: Short Answer

Algebra 1 FINAL EXAM Preview Semester 2: Short Answer
Name ______________________
Make sure you SHOW YOUR WORK!!!
1. Graph the following lines on the grid
provided and determine the solution.
y  2x  1


y  x  4
Solution: (___, ___)
3. Solve the following system of equations by
the elimination method.
x  y  6

x  y  4
Solution: (___, ___)
2. Solve the following system of equations using
the substitution method.
y  x  3

6x  3y  0
Solution: (___, ___)
4. Solve the following system of equations by
the elimination method. (multiply first)
2x  3y  13


 x y  1
Solution: (___, ___)
5. You have started your own lawn mowing business. Your cost to buy equipment and advertise was
$320. If every lawn costs $8 for gas and oil, and you charge $12 for mowing each lawn, how many
lawns must you mow before you break even? Write the equations and solve. Remember to label
your answer.
6. Solve the equation by showing all work:
2x  4  6 (get rid of
first)
Solution: _____________
Simplify completely.
7.
10x 8 y 2
5x 2 y 5
8.
Solution: _____________
3 a  2 b 7
Solution: _____________
9. Find the degree of the polynomial:
3x3 + 4x5 + y
Degree: _________
10. A researcher studied the number of overnight stays in U.S. National Park Service campgrounds
and in the backcountry of the national park system over a 5 year period. The researcher modeled
the results, in thousands, with the following polynomials.
Campgrounds:
Backcountry:
– 7.1x2
– 180x + 5800
21x2 – 140x + 1900
What polynomial models the total number of overnight stays in both campgrounds and backcountry?
Total = _____________________________
11. On Monday Jill had $80 in her account. On Tuesday she had $40 in her account and on
Wednesday she had $20. If this pattern continues, write a rule for the nth term of the geometric
sequence. an = a1 • r(n − 1)
12. You bought a new computer for $3500 in 2005. The computer depreciates at a rate of 18% per
year. What is the value of the computer 3 years after you bought it? Round to the nearest cent.
Use the formula: y = a(1 – r)t
Solution: _____________
13. Find the product: (x + 5)(x2 – 7x + 12)
(FOIL or box)
Solution: _____________________
14. The arc of a ball that is thrown underhand can
be modeled by the equation y = x2 + 4x + 7.
Complete the T-chart below for the equation.
y = x2 + 4x + 7
X
–1
–2
–3
Y
15. Use the T-chart from problem #16 to
graph the equation.
The given graph shows the downward movement of a
person jumping on a trampoline. Use it to answer the
following questions.
15. Circle One:
Maximum
or
Minimum
16. Vertex: ________
17. y-intercept: ___________
18. In your own words, describe how the graph of y = 6x2 and y = 
1 2
x are different in two separate
2
ways? (up vs. down and narrow vs. wide)
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
19. Find the coordinates for the vertex of y = 2(x – 4)2 + 1.
a) Vertex: _______
20. Factor by special case.
16x2 - 49
( _______)( _______)
21. Solve the equation.
(2x – 3)(x + 2) = 0
x = _____ and x = _____
22. Factor and solve: x2 – 2x – 35
(______)(______) = 0
x = _____ and x = _____
23. Use the quadratic formula to find the solutions to : 4x2 – 4x - 15
 b  (b) 2  4ac
x
2a
24. Find the discriminant of
2x2 – 8x + 10 = 4
25. The data below shows the number of hours per week a group of students spent watching television.
Make a histogram to represent the data.
7
10
1
5
14
22
6
8
0
11
13
3
4
14
5