HSPA STUDY GUIDE
MULTIPLE CHOICE
AND
SHORT ANSWER
1)
2)
Which of the following types of numbers would solve
the equation x2 = 45?
A)
Whole numbers
B)
Rational numbers
C)
Integers
D)
Irrational numbers
Which of the following equations represents the
situation: to qualify to be a member of the school’s
math team, a student’s cumulative points on a
qualifying exam must be within 15 points of 275.
A) |x – 15|  275
B) x – 275  15
C) x – 15  275
D) |x – 275|  15
3)
Which of the following represents a commutative
operation?
A) a  b = a2 - b
B) a  b = 4(a + b)
C) a  b = b  a
D) a  b = a  3b
4)
Which of the following is not equal to the other three?
A) 1.5  101
B) 15/10
C) 150%
D) 2.25
5)
Which of the following numbers is between 1/10,000
and 1/100,000 and is correctly expressed in scientific
notation?
A) 4.5  10-3
B) 4.5  103
C) 4.5  10-4
D) 4.5  10-5
6)
A $32 sweater is reduced by 25% for the holiday sale.
By what percent must the sale price of the sweater be
multiplied to restore the price to the original price
before the sale?
A) 133%
B) 125%
C) 25%
D) 8%
7)
The members of the decorating committee for a school
dance have 24 red carnations, 32 white carnations, and
40 pink carnations. They want to form as many
identical centerpieces as possible using all of the
carnations so that each centerpiece has the same
combination of colors as all of the other centerpieces.
How many pink carnations will each centerpiece have?
Why?
A) 4
8)
B) 5
C) 8
D) 10
Which of the following is NOT a way to find 120% of a
number?
A) multiple the number by 1.2
B) divide the number by 5 and add the result to the
number
C) divide the number by 5 and multiple the result by 6
D) multiply the number by 0.20 and multiply the result
by 5
9)
On some days a bakery packages cupcakes 4 to a
package. On other days, cupcakes are in packages of 6
or 8. On a given day, all the cupcakes baked were
packaged and there was once cupcake left over. Which
of the following could NOT be the number of cupcakes
baked on that day? Why not?
A) 22
10)
B) 25
C) 49
D) 97
There are 3 times as many girls as boys in the Spanish
Club of Central HS. If there are 36 members on the
club, how many are boys? How do you know?
A) 9
B) 12
C) 15
D) 27
11)
Light travels at a speed of about 186,281.7 miles per
second. How far would light travel in 365 days?
A) 5.87  1012 miles
B) 6.79  107 miles
C) 7.05  1013 miles
D) 9.7  1010 miles
12)
Mr. Kim, a salesperson, is paid $300 a week plus
commission. His commission is 5% of his weekly sales.
In the month of January, his weekly sales totals were:
Week
Week
Week
Week
1:
2:
3:
4:
$8,576
$9,500
$7,362
$10,567
What is his average weekly commission?
A)
B)
C)
D)
$429
$450
$528
$1,800
13)
Knowing that 23 = 2  2  2 = 8, what number would
make the following true?
86 = 2 ?
A)
B)
C)
D)
14)
9
15
18
24
Mary earns $7.50 an hour for the first 40 hours a
week she works. She earns time and a half for any
hours over 40 she works during the week and double
time for hours worked on the weekend. Her time card
for one week is shown.
Monday: 8.5 hours
Tuesday: 9 hours
Wednesday: 9 hours
Thursday: 8 hours
Friday: 7 hours
Saturday: 3 hours
How much did Mary earn?
A) $341.25
B) $361.88
C) $375.00
D) $382.50
15)
A fraction is equivalent to 3/8. The sum of the
numerator and denominator is 33. What is the
fraction?
16)
Suppose you visited Canada and took $325 to spend.
The rate of currency exchange was $1.1515 Canadian
dollars per U.S. dollar. To the nearest dollar, how
many Canadian dollars would you get for the exchange?
17)
Helen is paid at the rate of $6.50 an hour for the first
40 hours a week that she works. She is paid time-andhalf for any hours over 40. How much will Helen make
working 50 hours compared with working 46 hours?
18)
If 5 students share $450 in the ratio of 1:2:3:4:5, how
much is the largest share?
19)
A baseball player’s batting average is the ratio of the
number of hits to the official number of times at bat.
A player had 150 hits during a season and wound up
with a batting average of .300. What was the total
number of times he was at bat for the season?
20)
A printer charges 4.2 cents per copy of a standard size
original. There is an additional charge of one-half cent
for each copy on colored paper. How much would you
pay for 100 copies of an original on white paper and 100
copies on blue paper?
21)
Ground beef sells for $2.19 per pound. If a package of
ground beef costs $4.25, what is the weight of the
package to the nearest hundredth of a pound?
22)
Because of a printer malfunction, Harry could not read
some of the information on his monthly checking
account statement. From the information given, find
the closing balance of Harry’s account.
Account Summary
Number 00-537-387-5
Beginning Balance 08/01
$875.45
3 deposits/credits
xxxxxxx
3 checks/debits
xxxxxxx
Service Charge
xxxxxxx
Ending Balance 08/31
Date
Amount
Date
08/02
$135.00 + 08/22
08/05
$163.50 - 08/25
08/11
$14.75 08/29 print checks
08/31 interest
Amount
$35.92 $214.35 +
$11.45 $3.45 +
23)
Moe puts $1500 in a bank certificate that pays an
annual rate of 4.5% compounded annually. No
withdrawals or deposits are made. How much will the
certificate be worth (to the nearest dollar) at the end
of 7 years?
24)
If a principal of $1000 is saved at an annual yield of
8% and the interest is kept in the account, in how many
years will the principal double in value?
25)
The cost of a hamburger goes from $2.00 to $2.25.
Determine the percent of increase. Explain.
26)
In York City, the sales-tax rate is increased from 7%
to 7.25%. Under this change, how much additional tax
would you pay in purchasing an item priced at $800?
Show your process in determining this answer.
27)
The scale on a map is ½ inch = 80 miles. How far apart
are two cities that at 4¾ inches apart on the map?
Explain how you determined your answer.
28)
If 4, 5, and 7 are factors of a number, list 4 other
numbers that would also be factors of the number.