# 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 3x^{2} − 2xy + y^{2} for x = −2 and y = 3

16. Operations with Polynomials:

(x + y)^{2} − (9xy − 6x^{2} ) =

17. Multiply Polynomials :

(2x − 5)(6x + 4) =

18. Divide Polynomials :

19. Factor:

6x^{3} + 27x^{2} −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

x^{2} − 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?

L_{1} 2x + 3y = 6

L_{2} 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 − x^{2}

41. Graph:

x^{2} + y^{2} = 36

42. Functions:

f ( x ) = x^{2} + 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 ) = x^{2} + 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

2log_{a}x - 3log_{a}y =

51. Logarithms:

log_{2} 16 =

52. Sequences:

Find the 10^{th} term of the geometric sequence

2, -6, 18, -54...

53. Factorial:

8! = 5!.____

54. Solve a Quadratic Equation:

solve using quadratic formula

x^{2} + 3x + 6 = 0

55.

A = P_{0}10^{r}

If A = 80, P_{0} = 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

2cos^{2} x + sin^{2} x =

** Math Practice Test
Answers:**

1. 73

2. 5/12

3. 90

4. 4

^{4}= 256

5. 7

6. 3.5 or 7/2

7. 40 coasters

8. 46 ¼ ft.

9. 273

10. 8.1 x 10

^{4}

11. $9.40

12. $3.60

13. $50

14. 240 inches per hour

15. 33

16. 7x

^{2}− 7xy + y

^{2}

17. 12x

^{2}− 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. 2

^{4}a =16a

31. (2.1)

^{2}x 10

^{10}or 4.41 x 10

^{10}

32.

33. 40%

34. $44

35. 65 miles per hour

36.

37. no

38. 3x − y = 7

39. 8.94

40.

41

42. a

^{2}+ 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. a

_{n}= 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 − sin

^{2}x

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