Download Alg-2-Final-Review-1-2014Name-1

Alg 2 Final Review 1 2014
Name____________________HR__
Solve the equation or formula for the indicated variable.
1.
, for U
Solve the equation.
2.
3.
4. The sides of a triangle are in the ratio 3 : 4 : 5. What is the length of each side if the perimeter of the triangle is 24 cm?
Solve the inequality. Graph the solution set.
5. –2 + 4k  14
6. –k + 6  0
7. 5(4b + 5) < 10 + 20b
8. 21 + 6b  3(2b + 1)
Solve the compound inequality. Graph the solution set.
9. 4x + 12  8 and 8x – 10  30
10. 5x – 3 < –18 or 7x + 4 > 11
11. Graph the equation 4x + y = 12.
Find the slope of the line through the pair of points.
12. (9, 12) and (–9, 8)
13. A cannery processed 605 pounds of strawberries in 3.5 hours. The cannery processed 2100 pounds in 10 hours.
Write a linear equation to model the weight of strawberries S processed in T hours.
14. A balloon takes off from a location that is 176 ft above sea level. It rises 66 ft/min. Write an equation to model the
balloon’s elevation h as a function of time t.
15. Graph the relation. Find the domain and range.
16. The equation
describes a function that is translated from a parent function.
a. Write the equation of the parent function. Then find the number of units and the
direction of translation.
b. Sketch the graphs of the two functions.
Write an equation for the vertical translation.
17.
; 19 units down
18. Write an equation for the horizontal
translation of
y
8
4
–8
–4
O
–4
–8
4
8
x
.
19.
Write the equation that is the translation of
right 12 units and up 4 units.
Solve the system by graphing.
20.
21.
22. A rental car agency charges a flat fee of $26.00 plus $2.75 per day to rent a certain car. Another agency charges a fee of
$17.25 plus $4.00 per day to rent the same car.
a. Write a system of equations to represent the cost c for renting a car at each agency for d
days.
b. Using a graphing calculator, find the number of days for which the costs are the same.
Round your answer to the nearest whole day.
Solve the system by the method of substitution.
23.
Use the elimination method to solve the system.
24.
25.
26.
Solve the system of inequalities by graphing.
27.
28.
29. Your club is baking vanilla and chocolate cakes for a bake sale. They need at most 25 cakes. You cannot have more than
10 chocolate cakes. Write and graph a system of inequalities to model this system.
Alg 2 Semester 1 Final
Answer Section
SHORT ANSWER
1.
2.
1
3
3. 4
4
5
4. 6 cm, 8 cm, and 10 cm
5. k  4
–8 –6 –4 –2
0
2
4
6
8
0
2
4
6
8
0
2
4
6
8
0
2
4
6
8
0
2
4
6
8
0
2
4
6
8
6. k  6
–8 –6 –4 –2
7. no solutions
–8 –6 –4 –2
8. all real numbers
–8 –6 –4 –2
9. x  –1 and x  5
–8 –6 –4 –2
10. x < –3 or x > 1
–8 –6 –4 –2
11.
y
12
8
4
–12
–8
–4 O
–4
4
8
12 x
–8
–12
12.
2
9
13. S = 230T – 200; 2560 lb
14. h = 66t + 176
15.
y
2
–2
2
–2
domain:
range:
16.
; 1 unit up;
x
y
6
4
2
–6
–4
–2
O
2
4
6
x
–2
–4
–6
17.
18.
19.
20.
y
4
2
–4
–2
O
–2
–4
(–2, –1)
2
4
x
21.
y
4
2
–4
–2
O
2
4
x
2
4
x
–2
–4
no solutions
22.
a.
b. 7
23. (–2, –5)
24. (0, –3)
25. no solutions
26. infinite solutions
27.
y
4
2
–4
–2
O
–2
–4
28.
y
4
2
–4
–2
O
2
4
x
–2
–4
29. Let x = the number of vanilla cakes.
Let y = the number of chocolate cakes.
y
25
20
15
10
5
0
0
5
10
15
20
25
x