Final Exam Review MAT 1033 1. Evaluate the expression for the values given. 5ab + 3c; a = 5, b = -3, c = 7 A) B) C) D)
78 -54 -72 96
2. Solve. 8y + 4(4 + y) = 3(y - 7) + 10y A) B) C) D)
y = -11 y = 11 y = -37 y = 37
3. Solve for x. x5 1 x6 4 14 7
A) x 3 B) x 3 61 C) x 3 13 D) x 11
4. Given the function, find the indicated value. Find f(4) when f(x) = x2 + 2x + 7. A) B) C) D)
1 31 17 15
5. Graph the equation by plotting the intercepts. 2x - 4y = 4 A)
B)
C)
D)
6. Find an equation of the line. Write the equation in standard form. Through (1, -1) and (4, -10) A) x + 3y = 2 B) -3x + y = 2 C) 3x + y = 2 D) x - 3y = 2 7. Find the equation of the line that has the given slope and passes through the given point. Write the equation in the slope-intercept form. m = -4, (-5, 7) A) y = -4x + 7 B) y = -4x – 13 C) y = -4x + 13 D) y = -4x - 5 8. Find the solution to the system by addition (elimination) method. 7x + 18y = 18 9x - 3y = -3 A) (0, 0) B) (1, 0) C) (0, 1) D) (1, 1)
9. Solve the system by graphing. 3x + y = -1 2x + 4y = 16
A) x = 1, y = -4 B) x = 2, y = 5 C) x = -2, y = -3 D) x = -2, y = 5 10. Solve. The manager of a bulk foods establishment sells a trail mix for $5 per pound and premium cashews for $15 per pound. The manager wishes to make a 200-pound mixture that will sell for $9 per pound. How many pounds of each should be used? A) 100 pounds of trail mix 100 pounds of cashews B) 80 pounds of trail mix 120 pounds of cashews C) 120 pounds of trail mix 80 pounds of cashews D) 140 pounds of trail mix 60 pounds of cashews
11. Graph the system of inequalities. y>5 x≥4 A)
B)
C)
D)
12. Factor the polynomial. t3 + 27 A) B) C) D)
(t + 3)(t2 + 9) (t - 27)(t2 - 1) (t - 3)(t2 + 3t + 9) (t + 3)(t2 - 3t + 9)
13. Factor the polynomial completely. x2 - x – 45 A) B) C) D)
prime polynomial (x + 5)(x - 9) (x - 45)(x + 1) (x - 5)(x + 9)
14. Solve the quadratic equation by factoring. 55n2 + 35n = 0 7 ,0 11 7 B) , 35 11 7 C) 11 D) 0
A)
15. Multiply. 2
k 11k 24 2
k 17k 72
2
k 9k 2
k 12k 27
2
A) B) C)
k 9k k 9 1 k 9 k k 9
k
D) k
2
17k 72
16. Divide.
y
4
2
12
A)
B)
C)
y
12y 48 144
4
3
144
12 y 4
2
12y 48
1 y 4
D) y 4
17. Perform the indicated operation and simplify.
A)
B)
2 6 x4 x4
4 x 32 x 4 x 4 4
x 4 x 4
C)
4 x 32 x 4 x 4
D)
4 x 16 x 4 x 4
18. Solve the equation and check your solution. If there is no solution, say so. m7 2
m 2m 8
A) m = 56 B) m = -8 C) m = 8 D) m = -56
7 2
m 4m 4
m7 2
m 2m 8
19. Solve the equation for the specified variable. A
1 h B b for b 2
A) b
2A Bh h
B) b 2A Bh C) b
A Bh h
D) b
2A Bh h
20. Simplify.
y-1/5 ∙ y5/10
A) y3/10 B) y-5/50 C) y2/10 D) y2/15 21. Evaluate the numerical expression. 644/3 A) B) C) D)
256 1024 4096 16,384
22. Simplify. Assume that all variables represent positive real numbers.
A) B) p7 C) p D) p9
23. Add or subtract. Assume all variables represent positive real numbers. 3
8y
3
54y
A) 2 3 3 2 B) 5 3 y C) 3 3 2y 2 3 y D) 2 3 y 3 3 2y
24. Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
13 3
13 3
A) 22 B) 13 2 3 C) 4 D) 26 9
25. Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
5 27x
A)
15 x 9x
B)
5 x 3x
C)
5 27 27x
D)
5 3x 9x
26. Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
7 8 56 7 62 56 7 B) 62 56 7 C) 6 56 7 D) 6
A)
2 2
2 2 2
27. Solve.
2x 9 x 3 A) B) C) D)
-4, -3 -4 -4, 0 0
28. Perform the indicated operation. Write the result in the form a + bi. (6 – 2i) - (3 – 5i) A) B) C) D)
3 – 7i 9 + 3i 3 + 3i -18 - 12i
29. Perform the indicated operation. Write the result in the form a + bi. 6i(2 - 8i) A) 48 + 12i B) -48 + 12i C) 14 + 12i D) -14 +12i
30. Perform the indicated operation. 5 2i 3 2i
A)
11 16 i 13 13
B)
11 19 i 13 13
C)
11 16 i 9 9
D)
11 19 i 9 9
31. Solve the equation by completing the square. Express any complex numbers using i notation. x2 + 8x = 3 A) 1
19
B) 1 2 19 C) 4 2 19 D) 4
19
32. Solve by the quadratic formula. Simplify answers. Use i notation for nonreal complex numbers. x2 = -2x – 11 A) 1 i 10 B) 1 i 10 C) 1
10
D) 1 i 10
33. Solve. The area of a rectangular wall in a classroom is 171 square feet. Its length is 8 feet shorter than three times its width. Find the length of the wall of the classroom. A) length = 33 ft B) length = 35 ft C) length = 17 ft D) length = 19 ft
34. Find the coordinates of the vertex and the intercepts of the quadratic function. When necessary, approximate the x-intercepts to the nearest tenth. f(x) = x2 - 14x – 72 A) V(7, 11); I(0, 72); (4, 0); (-18, 0) B) V(7, -11); I(0, 18); (-72, 0); (72, 0) C) V(7, -121); I(0, -72); (18, 0); (-4, 0) D) V(-7, -121); I(0, -72); no x-intercepts
35. Find the vertex, the y-intercept, and the x-intercepts (if any exist), and graph the function. f(x) = -x2 - 2x + 8 A)
B)
C)
D)
ANSWER KEY 1. B http://youtu.be/xrHgzmwL4XY 2. D http://youtu.be/ihHc1cTQoJM 3. A http://youtu.be/D-DN1o_RiLU 4. B http://youtu.be/Kf4npSNQ4y0 5. C http://youtu.be/Q3t4dL4SLhQ 6. C http://youtu.be/0Gv0DVaCFPc 7. B http://youtu.be/haRKNmHeHz8 8. C http://youtu.be/sC_wmcHuBT0 9. D http://youtu.be/cDI_Vyqn6oo 10. C http://youtu.be/NG8Y-4d22mg 11. D http://youtu.be/1sQIvcWp2EA 12. D http://youtu.be/h-f8VEboQsI 13. A http://youtu.be/l_R3ZVmk-aE 14. A http://youtu.be/usf-_C8E8pM 15. C http://youtu.be/lO3DHLRREMY 16. D http://youtu.be/UUjBzXMSFrQ 17. C http://youtu.be/Q8H9uO2oRJY 18. C http://youtu.be/SZJ-Z10onJQ 19. D http://youtu.be/mjkzGoAqav4 20. A http://youtu.be/Lf5XfIz7bmk 21. A http://youtu.be/_a7gTqAGya0 22. B http://youtu.be/vuL6isqdcvs 23. D http://youtu.be/w3g4KsfahJw 24. C http://youtu.be/aZKrFVIqsHA 25. D http://youtu.be/r96xaCDTd4g 26. B http://youtu.be/rq4yav0F6N8 27. D http://youtu.be/J2rcEpzzoks 28. C http://youtu.be/chDHRY54Dfo 29. A http://youtu.be/NTjn4Q8pVYI 30. A http://youtu.be/jGDGhvyiWHA 31. D http://youtu.be/VrVwi24MHho 32. B http://youtu.be/Wa4boUXiVe0 33. D http://youtu.be/vYctojHrMoc 34. C http://youtu.be/2zhJ-qPHGmw 35. B http://youtu.be/0DQnkV3dVuc
