Download Math 101 Final practice

Math 101 – Final Problems – Practice
1. 2 + 3(5 – 1) = ?
2. 2(3 – 5) – (2 – 8) = ?
3.
1! 2 ! 3
= ?
1! 2 + 3
4.
5 2 ! 32
= ?
32 ! 2 2
5.
!3 "
6.
1 2
= ?
÷
5 25
7.
3
3
= ?
+
16 20
1 2 5
+ " = ?
7 7 2
8. Solve for x:
5x = 10(x – 1)
9. Solve for x: 3(x – 7) + 5(3 – x) = 0
x
3x
10. Solve for x:
+1=
3
2
11. 1.51 ! .23 = ?
12.
8.26
= ?
41.3
13. Solve for x: .02x – .04(3 – x) = .06
14. Find the slope of the line through the points (1, 3) and (3, 7).
15. Find an equation for the line through the point (–1, –4) with slope –2.
16. Find an equation for the line parallel to 5x – 7y = 7 which goes through the point (–2, 3).
17. Solve for x and y:
2x + 3y = 3
x – 2y = 5
18. Solve for x and y:
4x – 3y = 14
3x + 2y = 2
19. I have 21 coins: quarters and nickels. Their total value is $1.65. How many of each do I
have?
20. Agnes is 17 years older than her cousin Elsie. Seven years ago the sum of their ages was 43.
How old are they now?
21. One number is 2 more than 4 times another number. Their sum is 27. Find the two numbers.
22. Part of $6000 is invested at 3% per year, and the rest is invested at 4% per year. Total
annual interest for the two investments is $230. How much is invested at each rate?
( 3x ) ! ( 2x )
2 3
23.
3 2
( 6x )3 !12x 4
= ?
24. (2x3 + 5x2 – x + 1) – (x3 – 2x2 – 3x + 2) = ?
25. (x + 5)2 – (x – 3)2 = ?
26. What is 36% of 500?
27. 72 is 90% of what number?
28. 15 is what % of 75?
29. At a 15% off sale, what is the sale price of an item that normally sells for $180?
30. At a 20% off sale, what is the regular price of an item on sale for $48?
31. (x + 3)(x – 7) = ?
32. (x + 1)3 = ?
33. (2x + 1)(3x2 – 2x + 3) = ?
34.
x 2 + 4x ! 32
= ?
x+8
35.
x 3 + 2x 2 + 4x + 8
= ?
x+2
36. Factor as completely as possible:
9x2 – 64
37. Factor as completely as possible: 2x2 – 5x – 3
38. Factor as completely as possible: 5x2 – 20
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39. Solve for x:
3x2 = 5x + 2
40. Solve for x:
1
5 9
+ 2 =
2x x
2
41.
1
2
= ?
+
x !1 x +1
42.
x 2 ! 2x ! 3 x 2 + 2x ! 3
÷
= ?
x 2 ! x ! 2 x 2 ! 3x + 2
2
43. Hank can do a job by himself in 4 hours. Frank can do the same job by himself in 5 hours.
How long does it take them to do the job working together?
44. A boat travels 10 miles upstream in the same time it takes for it to travel 20 miles
downstream. If the current of the stream is 2 miles per hour, how fast does the boat travel in
still water?
45. Solve for x:
5x2 – x – 1 = 0
46. Solve for x:
x2 = 5x + 2
47. The sides of a right triangle are x, x + 2, and 4x. If 4x is the hypoteneuse, what is x?
48. The sides of a right triangle are x, x + 2, and x + 4. What is x?
49. Find the vertex of the parabola with equation y = x2 – 4x + 5, and sketch the graph.
50. Sketch the graph of the equation: y = x2 – 2x – 3. Give the coordinates of the vertex and the
points at which the graph crosses the x-axis.
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