hsa review. tip 1 always check your calculator to see that it is ready to operate correctly each...

HSA REVIEW

Tip 1

• Always check your calculator to see that it is ready to operate correctly each time you receive it. Press the MODE key and check that the words along the left side of the screen are highlighted. Press Y= and turn off all of the plots at the top of the screen. This is also a good time to clear all equations.

Tip 2

• When evaluating an expression, replace the variables with parentheses. Substitute the given numbers in the parentheses and the calculator will evaluate the expression correctly.

• Complete problems 1-3

Evaluate the expressions

1. x – y2 + 3z if x = 3, y = -2 and z = -4.

zyx 32

4323 2 1243

13

2. 5a + b if a = -2/3 and b = ¼

ba 5

4

1

3

25

4

1

5

10

25.275.1

3. |y + 2| - 9xz2 if x = 4, y = -6 and z = 1/3

292 zxy

2

3

14926

9

1494

44 0

Tip 3

• If you are asked to use a mathematical formula, the formula will be given to you and the variables will be defined in the problem. Read the problem carefully to identify each variable so you will know where to make the correct substitution. The formulas for slope, slope−intercept form, and point−slope form are listed on the formula sheet that is given to you for the test.


4. Sarah bought a new aquarium in the shape of a rectangular prism that measures 22 in x 9 in x 14 in. The volume of a rectangular prism can be found using the formula V = lwh where l is the length, w is the width and h is the height. What is the volume of the tank in cubic inches?

22”

9”

14”

5. The sum of the degree measures of the interior angles of a polygon can be found using the formula S = 180 (n – 2) where n is the number of sides. Find the sum of the degree measures of the interior angles of a hexagon.

6.Simple interest can be calculated using the formula I = prt where I is the amount of interest, p is the principal, r is the rate of interest and t is the time in years. Find the simple interest if Mr. Larson invests $8,000 for 5 years with a bank that offers an interest rate of 3.5%.

7. An inflated basketball has a radius of approximately 4.75 inches. The volume of a sphere can be found using the formula V = (4/3)πr3 where V is the volume and r is the radius. Find the volume in cubic inches to determine how much air the ball holds.

8. Mr. Jones has a metal container in the form of a right circular cylinder. The volume of the cylinder can be found using the formula V = πr2h where V is the volume, r is the radius and h is the height. If the radius of the cylinder is 1.5 feet and the height is 4 feet, find the volume in cubic feet.

9. Find the slope of the line containing the points (-3, 4) and (1, -6)

4’

1.5’

Tip 4

• Given a set of data, you should be able to find the following statistics:

1) Measures of central tendency,2) Quartiles,3) Spread or variability, and4) Interquartile range.

• Frequently, the data is given in order so it is not necessary to use the box−plot feature of the calculator to find the above measures.

• Complete problems 10-11(use the attached tables to answer)

10. a. Which quiz had the greatest variability?

b. Which quiz had the widest spread in the middle 50% of the scores?

c. Which quiz had the greatest median?

11. a. Which shot putter was the most consistent?

b. Which shot putter had the greatest spread?

Tip 5

• Use the Stat menu to enter the values from a table to calculate the mean and median. Use 1−Var Stats to find these measures of central tendency.

• Complete problems 12-13 (use the tables in the provided packet)

12.The table represents the money that Central High School collected for the hurricane relief effort. Find the mean and median amounts of money collected.

13.The table represents the monthly rainfall for the first six months of the year. Find the mean and median amounts of rainfall.

Tip 6

• When dealing with a frequency table, use the Stat menu to enter the values from a table to calculate the mean and median. Use 1−Var Stats L1, L2 to find these measures of central tendency. Type the values in L1 and the frequencies in L2. If you do not type the L1, L2 following the 1−Var Stats command, you will only compute the statistics for the first list.

• Complete problems 14-15 (use the tables in the provided packet)

14. The table represents the salaries of employees at McDougal’s Restaurant. Find the mean and median salaries of McDougal’s employees.

15. The table represents the donations automatically withdrawn from employee paychecks to contribute to the United Fund Charity. Find the mean and median contributions.

Tip 7

• To find a line of best fit use the statement

“SELL Some Cold Lemonade” to help remember the steps.

• Complete problems 16-19 (for 16 and 17 use the attached tables)

16. Better Homes and Garages Magazine has been keeping track of their new subscriptions for 5 months. The chart shows the number of new subscriptions for each month. Write the equation of the line of best fit.

17. The table represents the population of Perryville for the last six years. Write the equation of the line of best fit.

18. Find the equation of a line that has a x−intercept of −2 and a y−intercept of 4.5.

19. Find the equation of a line that passes through the points (−5, 4) and (−1,−8).

Tip 8

• If you have an equation, you can use the TABLE feature to find a set of values. First, type the equation in Y=. Go to TBL SET (2nd Window) to start your calculator at the proper “x” value. Go to the TABLE (2nd GRAPH) to find multiple values of y.

• Complete problem 20 (use the attached table to assist you)

20. This formula can be used to convert from Fahrenheit to Celsius temperatures. Fill in the table with the equivalent Celsius temperatures.

329

5 FC

Tip 9

• If you multiply or divide both sides of an inequality by a negative number, the sign changes (gets flipped).


21. 22.

27153 x 4010166 xx1515 123 x33 4x

23. 24.183

2 x 20364 x

2

318

3

2

2

3x

27x

25. 26. 1152

x

1045

2 x

Tip 10• To solve a system of equations with your calculator:

1. Go to Y= and type the equations in Y1 and Y2 and graph.2. Re–adjust the WINDOW so that you can see the point of

intersection.3. Go to the CALC (2nd TRACE) menu and pick intersect.4. Follow the instructions on the calculator screen.

Remember, a solution to a system is the ordered pair that makes both equations true.

• You may also use systems of equations and the above technique to solve equations with one variable. Let Y1 = the left side of the equation and let Y2 = the right side of the equation. The x−value of the point of intersection is the solution to the original equation.

• Complete problem 27

a. b.

c. d.

e. f.

g. h.

Solve for xi. j.

y 3x 5

y 3x 7

2x 4y 8

4x 6y 12

x y 7

y 2x 12

y 4x 1

y 2x 5

2x y 4

x y 5

2x 3y 4

x 3y 6

y 3x 4

y 3x 6

y 2x 3

2y 4x 6

2x 4 6x 12 2x 8

3

Tip 11

• Most HSA word problems can be written in two forms:1. Slope−Intercept Form: This type of problem contains a rate of change.

y = mx + b y is total or end point m is rate of change and b is starting point

2. Standard Form: This type of problem usually refers to two items.

Ax + By = C A is item one B is item two and C is total

• Remember to define the variables when writing an equation.


28.Pete’s Plumbers charges a flat fee of $35.00 plus $12.00 per hour for each hour worked. If Mr. Smith received a bill for $107.00, how many hours did the plumbers work?

1071235 x35 35

7212 x12 12

6x

29.Cecil’s CD Club charges $3.50 for each CD you rent plus a monthly fee of $12. If Katrina’s bill for the month is $50.50, how many CD’s did she rent?

5.50125.3 x1212 5.385.3 x

5.3 5.3

11x

30. George rented a truck for a flat fee of $19.00 plus $8.00 per hour. If his final bill is $75.00, how many hours did he rent the truck?

75819 x19 19

568 x8 8

7x

31.Karen purchased paper and pens for school. A pack of paper costs $3.00 and a box of pens costs $2.00. She spent $18.00 on both items. If Karen buys 4 packs of paper, how many boxes of pens can she afford to buy?

1823 yx

182)4(3 y18212 y

12 1262 y

2 2

3y

32.John purchased hot dogs costing $6.00 per pack and hamburgers costing $5.00 per pack for his picnic. He spent a total of $54.00. If John buys 4 packs of hot dogs, how many packs of hamburgers can he afford to buy?

5456 yx545)4(6 y

54524 y24 24

305 y5 5

6y

33.Mrs. Matthews purchased algebra books and geometry books for the Mathematics Department. Algebra books cost $60.00 per book and geometry books cost $72.00 per book. She spent a total of $3,540.00 on both items. If Mrs. Matthews buys 35 algebra books, how many geometry books can she afford to buy?

35407260 yx354072)35(60 y3540722100 y

2100 2100144072 y

72 72

y

20y

Tip 12

• To find the slope from a table of values, you can use the slope formula from your formula sheet.

• To write the equation, use slope−intercept form. The y−intercept, b, can be found when x = 0.

• Complete problem 34 on attached sheet

34. Find the slope and determine the equation.

12

12

xx

yym

bmxy

Choose any two points. and

Find the slope.

Find the y-intercept. Or

Write the equation in

slope intercept form.

)5,1( )8,2(

31

3

12

58

b )2(38 b )1(35

b68 b35

66 33 b2b2

23 xy

b. (1, 14) and (4, 2)

43

12

14

142

b )1(414b 414

44 b18

184 xy

41

4

23

106

b )2(410

b 81088 b18

184 xy

Or you can choose (10, 2) and (6,3)

Tip 13

• When dealing with a pattern or sequence, look for a common difference that may be added to continue the pattern. If there is not a common difference, divide two terms to see if there is a common multiplier that will continue the sequence.

• Frequently, you are not asked for the next number in the sequence, but a number further along in the sequence.

• Complete problems 35-40 (see attached sheet for problems 39 and 40)

35.Find the next number in the sequence 12, 7, 2, …

36.Find the 5th number in the sequence 4, 24, 144, …

37.Find the 5th number in the sequence x + 4, x − 2, x − 8, …

38.Find the 5th number in the sequence 15, 45, 135, …

39. How many black dots would be in figure 6 if the pattern continues?

40. If the pattern continues, what will be the total number of prom tickets sold by 3:00?

Tip 14-ELIMINATED FROM HSA

• ECR’s and BCR’s frequently require you to explain or justify.

• Explain: Tell how you arrived at the answer. Show your work. You may show how you solved an equation, list the values from a table, or explain how you interpreted a graph.

• Justify: Tell why this is the correct answer using mathematical principles. Prove it is true. The easiest method for justifying some answers is to write out the check that proves your answer is correct.

Tip 15

• To find a probability you must determine the total number of outcomes and use the formula:

frequency of desired outcomes

probability = ---------------------------------------

total number of outcomes

• Complete problems 42-47 (use the corresponding tables and complete problem 47 on attached sheet)

42. The table shows the number of hits Michael has this season on the baseball team. What is the probability that Michael will hit a homerun?

What is the probability that Michael will not hit a double?

13333333.60

8

8.60

48

43. Samantha has 6 red scarves, 4 blue scarves, and 3 green scarves in her drawer. Without looking, she pulls a green scarf from the drawer. If she does not put the scarf back in the drawer, what is the probability she will pick another green scarf on the second try?

1666666.6

1

12

2

44. There were 200 students on the honor roll at Perryville High School. The matrix shows the number of males and females on the honor roll in each grade level. One student is selected randomly to have breakfast with the principal. If the student chosen is a male, what is the probability that he is in the 11th grade?

372727.110

41

45.Martha is a pilot who flies to different cities each week. She checked the low temperatures for these cities in the newspaper. The stem−and−leaf plot shows the low temperature for each city. What is the probability that she will fly to a city that has a low temperature that is 50 or higher?

3333333.15

5

46.One student who attended the Winter Dance will win a $50 gift certificate to a local restaurant. What is the probability that the winner will be a senior?

341333.750

256

256225141128

256

47. The line plot shows the number of touchdowns the football team has scored in their current season games. What is the probability that the team scored 9 or more touchdowns?

Tip 16

• It is necessary to find the total number of outcomes (denominator) to determine a probability. This may sometimes be found by using the counting principle or a tree diagram.

• Complete 48-49

48. The Soda Shoppe sells soft drinks in small, medium, large, and extra large sizes. They have regular and diet soft drinks. They have coke, cherry, orange, root beer, and vanilla flavors. How many different ways can a customer order a soft drink at the Soda Shoppe? What is the mathematical principle that helped you determine this answer?

40524

49. ACME Motors is manufacturing a new convertible where the customer can pick the color he wants for the car and its convertible top. The cars can be painted white, black, red, or blue. The color choices for the top are white, black, and tan.

• How many different color combinations of convertibles can ACME Motors manufacture?

• Draw a tree diagram that represents all the possible outcomes.

• Janice does not want her convertible to have the same color top and bottom. If she picks a car at random from the lot, what is the probability she will pick a car with a different color top and bottom? Use mathematics to explain your answer. You may use words, symbols, or both in your explanation.

1234

83333333.12

10

Tip 17

• Probabilities are frequently used to make a prediction. First, find the desired probability and then multiply it by the total number of items.

• Complete problems 50-51 (see attached sheet for problem 51)

50.The Super Cola Company had a winner printed in the caps of their soft drinks in 12 out of every 150 bottles during their last contest. If they sold 210,000 bottles of soft drinks during the contest, how many bottles had a prize in the cap?

000,210150

12 x

)(150)000,210(12 x

51. If 800 students attended the first Perry Hall High School football game, use the graph below to determine how many students were seniors. How many more seniors attended the game than freshmen?

Tip 18

• There are two types of sampling problems:1) Simple random samples are chosen so that

each member of the population has the same chance (equally likely) of being selected and the members are chosen independently of each other.

2) Representative samples should reflect the characteristics of the population. Sampling over several time frames and locations will be more representative and less biased. Sample size is also an important factor.


52. Central High School is conducting a survey to determine how many students are involved in after school activities. Which of these methods would provide the Student Council with a simple random sample?

A. Select 50 students from the Band homeroom.

B. Give every student a number and use the school computer to generate 200 random numbers to select students.

C. Choose 5 teachers at random and survey their homerooms.

D. Pick one day of the week randomly and select every tenth student that enters the building on that given day.

53. Zupa Soup is a restaurant chain with 50 locations. Zupa Soup claims to have the best baked potato soup. A local food magazine is planning to evaluate the soup and is considering how to sample Zupa’s soup. Option 1: Send 5 staff members to the local Zupa Soup to have a bowl of baked potato soup every day for

30 days.Option 2: Send 5 staff members to 30 different Zupa

Soup locations to have a bowl of baked potato soup at each location for 10 days.

Which option gives the magazine the most representative sample of the quality of the baked potato soup?

Use mathematics to justify why the other option does not give the magazine a representative sample.

Tip 19

• In designing a simulation, it is important to determine the correct device to model the situation. The total number of outcomes or the denominator of the probability in reduced form helps us determine the best device. Select the device that has the same number of outcomes as the given situation.

• Complete problem 54

54. Match each letter with the tool you could use to conduct a simulation. Use each Roman numeral just once. Describe the rule you would use with each letter.

A. A basketball player makes 90% of his free throws.B. A student will guess correctly on a true or false test.C. A person will pick the correct key from his key ring with 6 keys.D. A baseball player has a .200 batting average.E. A team will win the Super Bowl if it is in the playoffs with 3

other teams.

I. a spinner with 5 equal sections (A, B, C, D, E)II. a calculator with the command randInt (1,10)III. a calculator with the command randInt (1,3)IV. a coinV. a spinner with 4 equal sections (A, B, C, D)VI. a 6−sided number cube

Tip 20

• When using your calculator to find specific values of a graph, the standard window may need to be changed. The table may be helpful in determining the correct values for the window.


55. A rocket is fired from a launch pad 10 feet high and its height is modeled by the function where h is the height of the rocket, in feet, and t is time, in seconds.

• What is the height of the rocket, in feet, 15 seconds after it is launched?

• What is the maximum height of the rocket? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

• Find the zero of the function and describe what it means in the context of this problem.

56. Find the solution of the system.

Tip 21

• The important features of functions or relations that you should be able to determine from a graph or table are: domain, range, maximums, minimums, zeros, values of , and continuity.


57.What are the domain, range, maximum, and minimum of the function below?

58. What are the zeros of the function shown below?

Tip 22

• In problems where you see the words rate of change or average rate of change, you should find the slope.


Tip 23

• When graphing a two−variable inequality, consider the following:

1) Is the line graphed correctly?

2) Is the line dashed or solid?

3) Do the points in the shaded region make the inequality true?


Tip 24

• You may be asked to do the following involving matrices:

1) Add or subtract matrices.

2) Combine corresponding rows or columns.

2) Multiply a matrix by a scalar


Tip 25

• Does your answer make sense? Read it back into the problem to see if the answer you selected is reasonable and answers the question asked in the problem. Make certain that you have answered all parts of the problem.

Tip 26

• Never leave any answer blank. You should know enough mathematics to make an educated guess at the multiple choice questions if you are not certain of the answer. There are thousands of students who fail the test by less than 8 points.

• 1. Evaluate the expression if x = 3, y = −2 and z = −4.

hsa review. tip 1 always check your calculator to see that it is ready to operate correctly each...

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