Name: _____________________________________ Date: _________ Math Class: ____________
NUMBER SENSE HSPA PREP
‘DO NOW’ A Review With Radicals and Exponents (You should NOT need a calculator here.)
Do not leave any blank answers on the HSPA. While you practice, circle the number of any question where you guessed. After you check your answers with the answer key, you can go back and redo these.
Circle the correct answer: (On this practice sheet you should always ‘showyourwork’).

What is + ?
A. 25 + 100 B. 5 + 10 C. 5^{2} + 10^{2 }D. 50 + 10

Which choice is equivalent to + ?
A. 6 + 50 B. 36 + 25 C. 6^{2} + 5^{2 }D. 11

What is (4)^{2 }+?
A. 16 + 5 B. 8 + 10 C. 16 + 7 D. 8 + 5

Try one more combination. What is 2^{3} +?
A.9+ 7 B. 8 + 7 C. 8 + 7 D. 6 + 7

Which of the following is not equal to 7?
A.+ B. 1^{2} + 2^{2} + 2 C. D. – 1^{2}

All of the following equal 16 except
A. 2^{3} + (4) (2) B. C. 5^{2}  3^{2 }D. 6^{2} – (10) (2)

(2^{8}) (2^{8}) = A. 2^{8} B. 2^{16 } C. 2^{32} D. 26^{4}

(8^{3}) ^{5} = A. 8^{2} B. 8^{15} C. 8^{8} D. 8^{2 }
8a. 6^{5} 6^{3} = A 0 B. 1 C. 6 D. 6^{2}

(x^{4}) (x^{4}) = A. x^{8} B. x^{16} C. X^{0} D x^{8}
9a. (a^{4}b^{3})^{2 }A. (ab)^{9} B. a^{6}b^{5} C. a^{8}b^{6 } D 2a^{4}b^{3}

(x^{2})^{5} = A. x^{3} B.x^{7} C. x^{10} D. x^{25}

(x^{3})^{2} = A. x^{5} B. x^{1} C. x^{5} D. x^{6}

(x^{4}) (x^{4}) = A. x^{8} B. x^{8} C. x^{16} D. x^{16}

(x^{4}) = A. B. C. D. –x^{4 }x^{o} =

x^{o }A. 0 B. 1^{ } C. x D.
Algebraic Order of Operations: PEMDAS (parenthesis, exponents, multiply OR divide from left to right, add OR subtract from left to right)
***** Do NOT use a calculator to practice these examples! *****
15. 27 – 18 6
What do you do first? A. subtract B. divide
Evaluate the expression. A. 9 B. 24 C. 1.5 D. 25
16. 36 +18 2 x 3  8
What do you do first? A. add B. subtract C. divide D. multiply
Evaluate the expression. A. 96 B. 73 C. 32 D. 55
17. Evaluate the expression (72 9 2) + 2 x 3
A. 12 B. 16 C. 24 D. 36
18. Evaluate the expression (20 + 8 4) + (3^{2} x 4)
A.19 B. 43 C. 58 D. 71
19. Evaluate the expression [2(51) + 3(2 x 2)] – 4
A. 7 B. 16 C. 15 D. 20
20. Evaluate the expression (64)^{3}  4
A. 5 B. 2 C. 4 D. 12
21. To evaluate this expression, what should you do first? (9 – 2 x 4) + 2^{3}(6)
A. 2x2x2^{ }B. 92 C. 2(6) D. 2 x 4
22. OpenEnded Question:
Jaime says the evaluation of the following expression is 28, Billy says it is 24.
Who is correct? Explain your answer and show all work.
2(2 + 5 x 2)
When COMPARING numbers, put them in the SAME FORM first!
Example: Put these fractions and decimals in order from lowest to highest:
0.53

One strategy would be to change all numbers to fractions with 100 as the denominator.

0.53 =

= 1 divided by 4 = 0.25 which =

= 3 divided by 5 = 0.60 which =
The correct order from smallest to largest is
Using the original numbers the correct order is 0.53
or

Another strategy would be to change all numbers to decimals
0.53 = 1 divided by 4 = 0.25 = 3 divided by 5 = 0.60
The correct order is 0.25 0.53 0.60
Using the original numbers the correct order is 0.53

Jeff needs to find a drill bit just a little larger than ½ inch. Which would be the best one to choose? (Remember, you can change all to decimals to compare them easily.)
A. inch B. inch C. inch D. inch
24. Which of the numbers described below is the largest?
A. B. C. D.
25. Which of these numbers has the greatest number of different prime factors?
A. 30 B. 50 C. 99 D. 121
Strategies when doing Multiple Choice Questions:

Read each question carefully and underline or circle the final answer.

Write down your work (even if you use a calculator). Be careful when you press calculator keys; don’t rush!

Check your work (use the calculator)
26. The regular price of a pair of sneakers is $79.00. They are on sale for 15% off. If Jose buys them on sale, how much change will he get from $70?

$ 9.00 B. $ 2.85 C. $ 3.85 D. $ 67.15
OpenEnded Question:
27. Pete takes excellent care of his new car. He takes it to his local service station and rotates the tires every 2,000 miles, and gets the oil changed every 1,500 miles.

If he owned the car since it was new and it now has 20,050 miles on it, how many trips to the service station did he make to rotate the tires and change the oil?

Show your work

Explain how you came to your final answer

Circle your final answer

OpenEnded Question:
The new Office Supply Store is having a grand opening sale. They are giving away a free calculator to every 5^{th} person who enters the store and a packet of blank CDs to every 3^{rd} person.

Show your work

Explain how you came to your final answer

Circle your final answer
RATIO AND PROPORTION
29. The Algebra class of 24 students contains 16 boys. What is the ratio of boys to girls?
A. 1:2 B. 2:1 C. 2:3 D. 3:1
30. In the above class of 24 students, what is the ratio of girls to all the students in the class?
A. 1:2 B. 1:3 C. 1:4 D. 3:1

In a mailing survey 30 out of 750 questionnaires were returned. Write the ratio of questions returned to questions mailed.
A. 1:25 B. 24:25 C. 1:24 D. 1:4
32. Write the ratio of the number of black 3s to the total number of black cards in a regular deck of playing cards.
A. 1:13 B. 1:26 C. 1:52 D. 2:13
33. A summer league softball team won 28 out of the 32 games they played. What is the ratio of games won to games played?
A. 4:5 B. 3:4 C. 7:8 D. 2:3
34. A family has a monthly income of $2,050, but they spend $1,200 a month on rent. What is the ratio of the amount of income to the amount paid for rent?
A. 41:24 B. 8:6 C. 24:41 D. 6:8
35. What fractional part of a week is 98 hours?
A. B. C. D.
36. The Italian class has 12 boys and 18 girls. Boys are what fraction of the class?
A. B. C. D.
37 From 20042005 the number of applicants to a nearby college increase 15% to 5,060 students. How many applicants were there in 2004?
A. 759 B. 4,301 C. 4,400 D. 5,819
38. OpenEnded Question
The population of a town doubled every 10 years from 1960 to 1990. What was the percentage increase in the population during this time? (Show your work!)
Hint: Make a chart or table, label the headings and begin with any number that is easy to work with.
39. In January the value of a particular stock increased by 25%; in February it decreased by 20%. How did the value of the stock at the end of February compare with its value at the beginning of January?
(Hint: Select an easy number for the stock price before January. Use your calculator to avoid a careless mistake. Show your work. Label your work as you write. Do not rush when plugging numbers into the calculator.)
A. It was the same.
B. It was less.
C. It was more.
D. It was 5% greater.
OpenEnded Questions

These questions are scored by hand. The people scoring them work very hard all day reading hundreds of student answers. It is difficult for them to spend extra time trying to figure out what you have written. It is important to be neat and to write clearly. Put a bullet or circle around your answers. In mathematics, using a table or a chart to outline information is often better than writing a long paragraph.

Even if you cannot answer all parts of the question, answer as much as you can. Every point counts. You must get some points on the openended questions if you are to receive a proficient (passing) score on the HSPA. Openended questions are worth 3 points. You can receive 0, 1, 2 or 3 points; partial credit is given.
40. At the end of week #2 of her new parttime job, Allison earned $110, which is a 25% increase over week #1. How much did she earn her first week?
Use your calculator to avoid a careless mistake. Show your work. Label your work as you write. Do not rush when plugging numbers into the calculator.)
.
41. If a coat is priced at $85 and is reduced by 10% each day, when will Sarah be able to buy the coat if she has $60.00? Remember, most openended GEPA questions can be answered using a chart or table.
Each day

Work shown (computation done with calculator but “work” is still written here)

Price

Original price of coat


$ 85.00

















42. Four local gas stations each advertise that they have the lowest prices in the area. Marco and his dad drove to each station and filled up the tanks of five different cars.
Use the chart below as a guide:

Gas Station  Total cost 
Number of gallons

Alco

$ 18.24

9.5

Bright

$ 18.31

9.2

Custom

$ 17.02

8.3

Dixon

$ 16.80

8

Extra

$18.45

9


Which gas station really has the lowest price? Explain.

If Marco purchases 20gallons at the lowest price, how much would he save instead of going to the most expensive gas station?
43. The Sweater Barn in an upstate NY mall and the Teen Outlet in New Jersey are both having big sweater sales.

TwoPiece Sweater Sets

Sweater Barn (NY)

Sweater
$24 less 15%

Matching cardigan is 50% off of the sweater sale price.

Teen Outlet (NJ)

Sweater
$18 less 10%

Matching cardigan is the same price as the sweater.

Maria wants to purchase three sets as birthday gifts for her nieces. She notices that the New York State store charges 8% sales tax on clothing and New Jersey has no sales tax on clothing.

What will the 3 sets cost at the Sweater Barn in New York?

What will the 3 sets cost at the Teen Outlet in New Jersey?

Which is the better buy? Explain.
ANSWER KEY 1 Number Sense HSPA PREP
1. B 2. D 3. A 4. C 5. D 6. B
7. B 8. B 8a. D 9. A 9a. C 10. C
11. D 12. B 13. A 14. B
15. B divide, B 24
16. C divide, D 55
17. A 12 18. C 58 19. B 16 20. C 4
21. D 2x4 (Work inside parenthesis first.)
22. Billy is correct 2(2 + 5 x 2) = 2(2 + 10) = 2(12) = 24
23. D 9/16 Here, I made fractions with a common denominator and then I compared the numerators ½=16/32 … ¼=8/32 3/8=12/32 5/32 9/16=18/32
24. D 1/10
25. A 30 (5)(3)(2) are the three different prime factors of 30
(11)(3) (3) are the prime factors of 99, but only two are different.
(5) (5) (2) are the prime factors of 50, but only two are different.
121 is a perfect square number; (11) (11) = 121
26. Read the question part of the example twice to be sure you understand what is being asked.

First, determine the sale price.
($79)(0.15) (this is the % off) = $11.85; 79.00 – 11.85 = $67.15 (sale price)
or
(79)(0.85) (this is the % he would pay) = $67.15 (sale price)

Now, determine the change he would receive from $70.00
70.00 – 67.15 = $2.85 (change from $70)
(Watch your computation, a careless error might make you select 3.85)

The correct answer is B $2.85 (The change he would receive.)
27. I needed to find the common multiples of 1,500 and 2,000 to see when Pete would be getting his tires rotated and his oil changed on the same trip.
Tires: 2,000miles 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000 2,2000
Oil: 1,500miles 3,000 4,500 6,000 7,500 9,000
10,500 12,000 13,500 15,000 16,500 18,000
19,500 2,100
Pete would make 7 trips for tire rotation only.
10 trips for oil change only
3 trips for tire rotation and oil change on the same day
20 trips in all
Final answer: He would make a total of 20 trips.
28. This is very similar to question #27 above. Here I needed to find common multiples of 3 and 5 from 1 to 120. First I listed the multiples of “5” and then I bolded (or circled) the multiples of 5 that also were multiples of 3.
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120
Or
I could have listed the multiples of 3 first. But, that would have been more timeconsuming and more difficult. Counting by 5’s is much easier.
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120
Final answer: From either set of listed multiples above, I can see that there would be 8 people who would receive the free calculator and the free CDs.
29. = 2:1 answer B
30. = 1:3 answer B
31. = 1:25 answer A
32. Since there are only 2 black 3s, and only 26 black cards in all (13 spades and 13 clubs)
= 1:13 answer A
33. = 7:8 answer C
34. = 41:24 answer A
35. = answer C
36. = answer A
37. The new amount is 115% of the original. (1.15)(x) = 5,060; x = 4,400 answer C
38. I chose to begin with an easy number; I chose 100. 1960 = 100
1970 = (100) (2) = 200
1980 = (200) (2) = 400
1990 = (400) (2) = 800
Answer: There is a 700% increase in population of the town from 1960 to 1990.
Check: ($100) (700%) = ($100) (7.00) = $700; $100 + $700 = $800; check!
39. Here I began with an easy number, $100.
Beginning value: $ 100
January (100) (.25) = $25.00; $100 + 25 = $ 125 or (100)(1.25)=$125
February ($125)(.20)= $25.00; $125 – 25 = $ 100 or (125)(0.80)=$100
Answer: A, They are the same.
40. Second week = $110 $110 is 125% of the first week
110 = (1.25) (week #1)
110 = 1.25x
= x
Answer: She earned $88 the first week.
Check: 125% of 88 = (1.25) (88) = $110. Correct!
41. Check your answers and workshown against this chart. How do you think you would have been scored here? Would you have received full credit (3 points), 2 points, 1 point, or no points?
Each day

Work shown (computation done with calculator but “work” is still written here)

Price

Original price of coat


$85.00

Day #1 of sale
coat is 10% less

100%10% = 90%; She pays 90%
(85) (.90) =

76.50

Day #2 of sale

(76.50) (.90) =

68.85

Day #3 of sale

(68.85) (.90) =

61.965 or 61.97

Day #4 of sale

(61.97) (.90) =

55.768 or 55.77
 
Sarah will be able to buy the coat on day #4 of the sale. On that day it will cost $55.79 (or less than $60.00)

42.

Alco is the least expensive. Gas at Alco costs $1.92 per gallon.
Work shown
Total price number of gallons = price per gallon
18.24 9.5 = $1.92 per gallon Alco
18.31 9.2 = $1.99 per gallon Bright
17.02 8.3 = $ 2.05 per gallon Custom
16.80 8 = $ 2.10 per gallon Dixon
20 gal 2.10 = $42.00 most expensive (at Dixon’s)
20 gal 1.92 = 38.40 least expensive (at Alco’s)
savings: $ 3.60 (I subtracted to find the difference.)
43.
Sweater Barn at the upstate New York mall where there is an 8% sales tax on clothing:
Cost for sweater: $24 less 15% is same as 24 x 0.85 = $20.40 per sweater
Cost for cardigan: $20.40 x 50% is (1/2 of $20.40) = $10.20 per cardigan

Total cost for one sweater and one cardigan before taxes = $30.60 per set
Three sets = (3) (30.60) = $ 91.80

Total for 3 sets w/sales tax = (1.08)(91.80) = $ 99.15 ($99.14 also accepted as correct) total with sales tax
Teen Outlet in New Jersey (where there is no sales tax on clothing):
Cost for sweater: $18 less 10% = $16.20 for each sweater
Cost for cardigan: Each cardigan is the same price = $16.20 per cardigan

Total cost for one sweater and one cardigan = (2) (16.20) = $32.40 per set

Total for 3 sets = (3) (32.40) = $97.20 total
This would be the final price since there is no sales tax on clothing in New Jersey.

The Teen Outlet store in New Jersey would be a slightly better buy. The cost at the New Jersey store would be $1.95 (or $1.94) less than the New York store.
