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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 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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