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Math Practice Test

1. Basic Operations with Integers :
36 + (−20) + 50 − (−17) −10 =

2. Basic Operations with Fractions :
What number added to 1/3 plus 1/4 will
equal the number 1?

3. Basic Operations with Decimals :
36 ÷ 0.4 =

4. Basic Operations with Exponents:

5. Order of Operations :
8 − 5 × 2 + 9 = 7

6. Ratio and Proportion :
solve for w

7. Jan is making clay coasters for an art fair. Each coaster costs $2.25 to make. If she sells
the coasters for $4.00 each, how many will she have to sell to make a profit of exactly
$70.00?

8. Four pieces of ribbon are cut from a length of ribbon that is 80 ft long. One of the pieces is
15 feet long. Two of the pieces are 7 ½ feet long. One of the pieces is 3 ¾ feet long. How
many feet of ribbon are left from the original length?

9. Percentages:
What number is 65% of 420?

10. Scientific Notation:
Write answer in scientific notation
(2,700,000,000)(0.00003) =

11. Amy charged $500 worth of merchandise on her credit card. When she got her bill, which
did not include any interest, she paid $100. During the next month she charged another
$70 worth of goods. When she got her next bill she was charged 2% interest on her entire
unpaid balance. How much interest was she charged?

12. A taxi cab charges $0.80 for the first 1/5 of a mile and $0.10 for each additional 1/10 of a mile.
What is the cost of a 3 mile trip?

13. Averages:
John works a variety of different jobs . On Monday he earned $50. Tuesday he earned $40.
On Wednesday and Thursday he earned $30 each day, and on Friday he earned $100.
What was John’s average daily pay for the 5 days?

14. Rates:
2½ inches per minute, 240 inches per hour, 1/4 foot per minute; which is fastest?

15. Evaluate an Expression :
Evaluate 3x2 − 2xy + y2 for x = −2 and y = 3

16. Operations with Polynomials:
(x + y)2 − (9xy − 6x2 ) =

17. Multiply Polynomials :
(2x − 5)(6x + 4) =

18. Divide Polynomials:

19. Factor :
6x3 + 27x2 −105x =

20. Simplify a Rational Expression:

21. Simplify a Radical Expression :

22. Evaluate an Expression:
A = P(1 + r)
If P = $450 and r =12%, find A

23. Simplify a Radical Expression:

24. Rationalize the Denominator:

25. Solve a Linear Equation:
3x + 7 = 2(x −1)

26. Solve a Quadratic Equation :
Find the sum of the solutions
x2 − 6x = 7

27. Solve an Equation w/Rational Expressions:

28. Solve a Linear Inequality :
 −2x + 3 < 5

29. Solve a System of 2 Linear Equations:
2x + 3y = -11
6x + y = 7

30. Use Laws of Exponents:

31. Use Laws of Exponents:

32. Radicals and Rational Exponents:

33. In selling stock an investor made a profit of $160 plus 20% of the amount originally paid for
the stock. If the cost of the stock was originally $800 what percent of the cost was the total
profit?

34. Altogether Mark, John, and Alan earned $ 104. John earned twice as much as Mark and
Alan earned $4 more that John. How much did Alan earn?
 

35. A train travels 4 hrs at 60 miles per hour and 2 hours at 75 miles per hour. What is the
train’s average rate for 6 hours?
 

36. Graph a Linear Equation:
Graph 2x + y = 5

37. Slope:
Are these 2 lines parallel?
L1  2x + 3y = 6
L2  line through (3, 10) (5, 7)

38. Write the Equation of the Line:
A line goes thru (2,−1) and has
slope m = 3 , what is the equation
in general form?

39. Distance Formula :
 What is the distance between
A(2,−5) and B(6,3)?
(Round answer to nearest hundredth)

40. Graph:
y = 4 − x2

 41. Graph:
x2 + y2 = 36

42. Functions:
f ( x ) = x2 + 2x + 3
find f ( a + 1)

43. Domain of a Function:
What is the domain of

44. Domain of a Function:
What is the domain?

45. Range of a Function:
 What is the range?

46. Composite Functions:
f ( x ) = 3x - 2, g ( x ) = x2 + 1
find f ( g(3) )
* other notation ( ( f o g)(3)

47. Inverse Functions:

If h(x) contains the point (4, -1) then
h-1 must contain the point ( , ),

48. Complex Numbers :
Leave your answer in a+bi form

49. Solve an Exponential Equation:

50. Logarithms:
Express as a single log
2logax - 3logay =

51. Logarithms:
log2 16 =

52. Sequences:
Find the 10th term of the geometric sequence
2, -6, 18, -54...

53. Factorial:
8! = 5!.____

54. Solve a Quadratic Equation:
solve using quadratic formula
x2 + 3x + 6 = 0

55.
A = P010r
If A = 80, P0 = 90, find r

56. A saline solution is 20% salt. How many gallons of water must be added to dilute the
mixture to 8 gals of a 15% saline solution?

57. Trigonometry:
Find x

58. Trigonometry:
If sin (x + y ) = sinx cosy + cosx siny
Find sin

59. Trigonometry:
If sinθ = 5/13 and tanθ < 0.
then secθ =

60. Trigonometry:
Rewrite using only the sine function
2cos2 x + sin2 x =

Math Practice Test
Answers:

1. 73
2. 5/12
3. 90
4. 44 = 256
5. 7
6. 3.5 or 7/2
7. 40 coasters
8. 46 ¼ ft.
9. 273
10. 8.1 x 104
11. $9.40
12. $3.60
13. $50
14. 240 inches per hour
15. 33
16. 7x2 − 7xy + y2
17. 12x2 − 22x − 20
18.
19. 3x (2x − 5)(x + 7)
20. x − 4
21.
22. 504
23. 7
24.
25. x = −9
26. 6
27.x = 3/10
28. x > −1
29. x = 2, y = −5
30. 24a =16a
31. (2.1)2 x 1010 or 4.41 x 1010
32.
33. 40%
34. $44
35. 65 miles per hour
36.

37. no
38. 3x − y = 7
39. 8.94
40.

41

42. a2 + 4a + 6
43. x ≠ − 3
44. x ≥ 7
45. y ≠ 0
46. 28
47. (- 1, 4)
48.

49. x = -5/2
50.
 
51. 4
52. an = 2·( -3)9 or -39,366
53. 6·7·8
54.

55. or - .051153
56. 2 gallons of water
57.
58 cosα
59.-13/12
60. 2 − sin2 x

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