College Math Preparation semester review questions
Solve the following equations. If the equation is an inequality or absolute value inequality then write the answer in
interval notation and do a line graph for the solution.
1.
5x + 8 = 3x – 7
2. 2(3x – 4) = 5x + 4
3. 2/3 x + 5 = 3/5 x – 2
4. 2x + 7 = 5x + 4
5. 4/5 x – 2/5 = 4/3 x + ½
6. 3(2x – 7)= 8 + 6x
7. 4x + 8 > 12
8. 2x + 5 ≤ 5𝑥 + 9
9. ¾ x + 3 > 2/3 x + 5
10. 8 < 2x – 6 < 14
11. 4≥ 5 − 2𝑥 ≥ −7
12. -5 < 2/3 x + 2 < 8
13. | x + 5 | = 8
14. 8 + | 2x = 5| = 20
15. | 2x – 4| ≥ 4
16. | 8 – x| < 5
17. 5 + |3x – 4| > 12
18. |6x| + 5 < 2
19. x2 – 8 = 12
20. Y2 -9 = 0
21. (x – 6)2 =81
22. 4 + ( x + 3)2 = 20
23. x2 + 8x = 0
24. X3 = 5x2
25. X2 + x – 12 = 0
26. x2 + 7x + 6 = 0
27. X2 – 3x – 18 = 0
28. X2 + 8x + 12 = 0
29. 3x2 – 8x + 5 = 0
30. 6x2 + x – 15 = 0
31. 4x2 + 8x + 4 = 0
32. x2 + x + 5 = 0
33. X2 – 8x + 2 = 0
34. 3x2 + x + 5 = 0
35. x2 + 4x + 2 = 0
36. 5x2 + 4x – 1 = 0
36. 7x2 + 9x + 2 = 0
Given the following information determine the equation of the line
a.
Slope of 2/3 point (0,5)
e. slope of 2 point (4,6)
b. Slope of -3 point ( 3,-2)
f. points ( 2,5) and (3,6)
c. Points (4,7) and (4,12)
g. parallel to Y = 4x + 6 and contains point (4,2)
d. Perpendicular to 2x + 5y = 8 can contains point (-2,8)
H
I
J
H.
J.
I.
k.
Look at each set of lines and tell me whether they are parallel, perpendicular, or intersecting
1.
Y = 4x – 8 and y = -1/4 x + 5
3. Y = 3x + 2 and y = -3x -4
2.
2x + 5y = 8 and -4x – 10y = 4
4. 2x + 3y = 2 and 3x – 2y = 5
Find the solution to the following systems of equations
X + 2y = 7
2x – y = 5
4x + 3y = 1
2x – y = -1
4x + y = 13
x=y+2
4x + y = -12
2x – 3y = 1
2x – y = 6
2x + 2y = -6
4x – 6y = 2
x=4+y
The following are parabolas, circles, ellipses, or hyperbolas. Look at each equation and determine what it is. Determine
the information at the right.
1. X2 + y2 = 25
center________ radius _______ vertices ______,______,_____,_____
2. X2 + y2/9 = 1
center________ radius _______ vertices ______,______,_____,_____
3. (x-4)2 + ( y – 3)2 = 8
center________ radius _______ vertices ______,______,_____,_____
4. (x+6)2/9 + (y-1)2/16 = 1
center________ radius _______ vertices ______,______,_____,_____
5. X2 + 8x + y2 – 2y = 12
center________ radius _______ vertices ______,______,_____,_____
6. 4x2 + 9y2 = 36
center________ radius _______ vertices ______,______,_____,_____
7. 9(x-3)2 + 25(y+2)2 = 225
center________ radius _______ vertices ______,______,_____,_____
8. Y = x2 + 4x – 3
Opens _____ vertex __________ axis of symmetry ______________
9. Y = -2x2 + 4x + 5
Opens _____ vertex __________ axis of symmetry ______________
10. X = 4y – 2y2 + 1
Opens _____ vertex __________ axis of symmetry ______________
11. X = y2 + 6y – 4
Opens _____ vertex __________ axis of symmetry ______________
12. Y = 2(x+3)2 – 4
Opens _____ vertex __________ axis of symmetry _____________
13. X = (y -4)2 =3
Opens _____ vertex __________ axis of symmetry ______________
14. X = (y -4)2 =3
Opens _____ vertex __________ axis of symmetry ______________
15. Y = 5x – 2x2 + 6
16. X2/9 – y2 = 1
Opens _____ vertex __________ axis of symmetry ______________
opens_____center________vertices_________________________
Asymptotes____________________________________________
17. - (x+6)2/4 + y2/49 = 1
opens_____center________vertices_________________________
Asymptotes____________________________________________
18. 4(x-4)2 – 9y2 = 36
opens_____center________vertices_________________________
Asymptotes____________________________________________
19. - 5(x+3)2 + (y-2)2 = 225
opens_____center________vertices_________________________
Asymptotes____________________________________________
20. – (x+7)2/16 + (y+3)2/4 = 1
opens_____center________vertices_________________________
Asymptotes____________________________________________
Equation ___________________________
Equation ____________________________
Equation ____________________________
Equation _______________________________
Equation ____________________________
Equation ____________________________