Partial Review for Test 2 (over Pie 2)

HINTS (will be included on exams and final)

Units of Measurement

American Units of Length

12 inches (in.) = 1 foot (ft)

                    3 ft = 1 yard (yd)

       36 in. = 1 yd

              5,280 ft = 1 mile (mi)

 

Equivalent Lengths

1 in.  2.54 cm            1 cm  0.3937 in.

1 ft  0.3048 m            1 m  3.2808 ft

1 yd  0.9144 m            1 m  1.0936 yd

1 mi  1.6093 km        1 km  0.6214 mi

 

Metric Units of Length

1 kilometer (km) = 1,000 meters (m)

       I hectometer (hm) = 100m

       I dekameter (dam) = 10m

          1 decimeter (dm) = m

         1 centimeter (cm) = m

         1 millimeter (mm) = m

 

American Units of Capacity

16 ounces (oz) = 1 pound (lb)

2,000 lb = 1 ton

 

 

 

 

 

Equivalent Weights and Masses

1 oz  28.35 g                    1 g  0.035 oz

1 lb  0.454 kg                     1 kg  2.2 lb

 

Metric Units of Capacity

1 kilogram (kg) = 1,000 grams (g)

          I hectogram (hg) = 100g

         I dekagram (dag) = 10g

           1 decigram (dg) = g

          1 centigram (cg) = g

          1 milligram (mg) = g

 

American Units of Capacity

1 cup (c) = 8 fluid ounces (fl oz)

          1 quart (qt) = 2 pints (pt)

                     1 pt = 2 c

       1 gallon (gal) = 4 qts

 

Equivalent Capacities

1 fl oz  0.030 L              1 L  33.8 fl oz

1 pt  0.472 L           1 L  2.1 pt

1 qt  0.946 L             1 L  1.06 qt

1 gal  3.785 L              1 L  0.264gal

 

Metric Units of Capacity

1 kiloliter (kL) = 1,000 liters (L)

       I hectoliter (hL) = 100L

       I dekaliter (daL) = 10L

          1 deciliter (dL) = L

         1 centiliter (cL) = L

         1 milliliter (mL) = L

 

Common Formulas

Distance:  , where d = distance, r = rate,  t = time

Simple Interest:  , where I = interest, P = principal,
                                                       r = annual interest rate,  t = time in years

 

P

E

M

D

A

S

 

Geometric Formulas

Pythagorean Theorem: If the length of the hypotenuse of a right triangle is c and the lengths of the legs are a and b, then

 

Perimeter of a rectangle:

Circumference of  a circle:  or  where

Area Formulas

Square                      

Rectangle                

Parallelogram          

Triangle                 

Trapezoid 

Surface area of a rectangular prism

Volume Formulas

Cube                               

Rectangular solid         

Prism                             

Sphere                 

Cylinder                   

 

 

 

 

I. Whole Number

1.  Express 56 as a product of primes.

2. Jose must choose a number between 67 and 113 that is a multiple of 4, 7, and 14. Write all the numbers that he could choose. If there is more than one number, separate them with commas.

3. What is the average (mean) of 116 and 61?

 

II. Fractions and proportions

4. Solve the following proportion for v:

                       .

    Round your answer to the nearest hundredth.

 

5. Jason drove 212 miles using 10 gallons of gas. At the same rate, how many gallons of gas does he need for a trip of 265 miles?

 

III. Decimals and percent

6. An item regularly priced at $90 is on sale at a discount of 80%. What is the sale price of the item?

7. An item regularly priced at $30 is on sale at a discount of 60%.  What is the sale price of the item?

8. Today only, a sofa is sold at a 34% discount.  The sale price is now $363.  What was the price yesterday?

9. Today only, a desk is sold at a 27% discount.  The sale price is now $292.  What was the price yesterday?

10. Julia deposits $8000 into an account that earns simple interest at a rate of 3% per year. How much interest will Julia's account earn in the first 6 years?

11. The circle graph below shows how the annual budget for the Heavy Equipment Company is divided by department.   Use this graph to answer the questions below.

                             

(a) Which category accounts for approximately one-eighth of the annual budget?

(b) Approximately what percentage of the budget is used for Engineering and Support combined?
Write your answer as a multiple of 10%- that is, 10%, 20%, 30%,…

(c) If 8% of the annual budget is used for Media, approximately what percentage is used for Sales?

 

VI. Measurement, Data and Probability

12. A container holds 44 cups of water. How much is this in gallons?  Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.

13. A rectangular board is 1.5 meters long by 1.2 meters wide. What is the area of the board in square millimeters? Do not round your answer. Be sure to include the correct unit in your answer.

14. A boy weighs 88 pounds. How much does he weigh in kilograms?

15.  The data for this problem are gas mileages for 17 cars: 27 mpg, 29 mpg, 33 mpg, 21 mpg, 21 mpg, 12 mpg, 16 mpg, 25 mpg, 8 mpg, 17 mpg, 24 mpg, 34 mpg, 38 mpg, 15 mpg, 19 mpg, 19 mpg, and 41 mpg.  Complete the histogram.

 

       

 

16. The graph below represents the number of games won by a basketball franchise in the regular season during a five-season period.

a) What was the highest number of games won by the franchise during the five-season period?

 

b) In which season did the franchise have the greatest decrease in the number of games won compared to the previous season?

 

17. The following list contains the number of hours that a sample of 10 middle-school students spent watching television last week: 11, 4, 12, 13, 4, 16, 16, 20, 11, 18.  
a) Find the mean number of hours for that sample.
b) Find the median number of hours for that sample.

 

18. The following list gives the number of pets for each of 11 students:

                      4, 1, 2, 3, 2, 3, 3, 2, 2, 1, 3.

Find the mode of this data set. (If there is more than one mode, write them separated by commas.)

 

V. Variable expressions and polynomials

19.  Evaluate the following: .

 

20.  Evaluate the following.

 

(a)   – 42 – 30 = [      ]

 

(b)   (–6)(1)(–15) = [      ]

 

(c)   – 59 + 29 =  [      ]

 

(d)    = [      ]

 

(e)   6 – 9(6 – 11) = [     ]

 

 

21. Evaluate the following: .   Leave your answer as a fraction in simplest form. 

 

22. Evaluate the following: .  Leave your answer as a fraction in simplest form.

 

23. Evaluate the following: .  Leave your answer as a fraction in simplest form. 

 

24. Evaluate the following: .  Leave your answer as a fraction in simplest form. 

 

25. Add. 

 

26.  Evaluate the expression

 

27. Evaluate the expression

 

28. Evaluate the expression

 

29. Evaluate the expression

 

30. Use the Distributive Property to remove parentheses from the following expression: 

 

31. Use the Distributive Property to remove parentheses from the following expression: 

 

32. Simplify the following expression: 

 

33. Simplify the following expression: 

 

34. Simplify the following expression: .

35. Multiply and simplify. 

 

36. Multiply and simplify. 

 

37. Evaluate:

 

38. Evaluate:

 

39.  Evaluate the following.

 

(a)    = [      ]

 

(b)    = [      ]

 

(c)    = [      ]

 

 

V. Linear equations

40. Solve for x:

41. Solve for x. 

 

42 Solve for x. 

 

43. Solve for x: 

 

44. Solve for x: 

 

45. Solve for x: 

 

46. Betty needs to memorize words on a vocabulary list for Korean class. She has 24 words to memorize, and she is three-fourths done. How many words has Betty memorized so far?

47. The first three terms of a geometric sequence are as follows. 64, 32, 16.  Find the next two terms of this sequence.

 

VII. Geometry

 

48. a) An angle measures 390.  What is the measure of its complement?

      b) An angle measures 790.  What is the measure of its supplement?

 

49.  For the figure below, give one pair of vertical angles and one pair of supplementary angles.

 

         

 

50. Find the missing value x0.

        

51. A bike wheel has a radius of 13 in.  What is the circumference of the wheel?  (Use the value 3.14 for , and do not round your answer.)  Be sure to include the correct unit in your answer.

 

52. Find the area of this triangle:

            

 

53. Find the area of this triangle:

           

 

54. Find the area of this trapezoid.  Be sure to include the correct unit in your answer.

 

 

55. A semicircle is cut out of a rectangular paperboard 25 in long and 17 in wide, as shown below.  What is the perimeter of the paperboard that remains after the semicircle is removed?  (Use the value 3.14 for , and do not round your answer.  Be sure to include the correct unit in your answer.)

         

56. Find the volume of the solid below.