Download Math Practice Test 2

Strand: Algebra
Georgia High School Graduation Test
Name:
1. Simplifying Algebraic Expressions
Expanding & Combining Like Terms:
a. 3x  2 y  4 x  8 y  2
b. 4  2 x  3  x  1
c. a  3b  8b  4  2a 
d. 3c  2d  5  c  2d 
Division:
a.
12 x  8 y
4
b.
18 x  27
9
c.
6 x 2  3x
3x
d.
2a  5b
2a
2. Evaluate simple algebraic expressions
a. An auto-repair shop uses the formula 20a + 40b to determine the amount to charge a customer.
The repair shop charges $40 an hour for labor repairing a car and only ½ that amount is charged
for the labor diagnosing the problem. A mechanic spent 1.5 hours diagnosing the vehicle’s
problem and 2 hours repairing the vehicle. Using the given formula how much was the customer
charged for labor?
b. The amount a clothing boutique charges for its clothing is given by the expression 1.5x + 3,
where x represents how much the store paid for the article of clothing. If the store paid $28 for a
skirt, how much would they charge a customer for the skirt?
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3. Substitutes known values in formulas and solves problems with formulas:
a. Janice is going to borrow $7500 from her employer to pay some legal fees. The employer wants
the money paid back to them at the end of 2 years plus 6% simple interest for the 2 years. Using
the formula I  P  R  T how much interest will Janice end up paying to her employer?
8 feet
6 feet
b. The Arnold’s residence has a trapezoid shaped entrance hall. The Arnold’s
wish to have hardwood flooring put down at $4.00 per square foot. Using the
b  b  h
formula for area of a trapezoid, A  1 2 , determine how much it will
2
cost the Arnold’s to put down hardwood flooring in their entrance hall.
12 feet
c. Janiqua is averaging 60 mph on the express way to the beach. If she travels for five and half hours
to get the beach then about how far did she drive to get to the beach (use the formula d = rt)?
4. Identifies and applies mathematics to practical problems requiring direct and inverse
proportions.
a. Mike cut the grass in his yard 7 times with his lawnmower using only 2 gallons of gasoline.
Mike determined that over the course of the year he will have to cut his yard a total of 24
times.
i.
How many gallons of gasoline will Mike need for the entire year to cut the grass in
his yard?
ii.
If gasoline costs $2.90 per gallon, how much will the gas alone cost Mike to cut the
grass in his yard?
b. A homeowner is filling up a 3,500 gallon above ground pool for the first
time. She has measured when the water valve for the hose is completely
open it takes about 1.5 minutes to fill a 14 gallon container. At this rate,
how many minutes will it take to fill the pool? (how many hours does this
suggest?)
c. Speed varies inversely with the amount of time it takes to get to a destination. Gus has an
average speed of 10 mph on his bike ride home which takes an hour, how long will it take
Gus if he increases his speed to 15 mph?
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5. Translates words into simple algebraic expressions and equations.
Rewrite the following as an algebraic expression or equation
a. The sum of twelve and twice a number is twenty.
h. The total of ten, eight, and a number.
b. The product of two and a number minus two is
eighteen.
i. The square of a number increased by two is
eleven.
c. The quotient of twenty-four and a number is eight.
j. The product of 5 and twice a number
increased by six is forty.
d. The difference of three times a number and two is
nineteen.
k. Lori is 2 years older than half Shane’s age.
Shane is 18. How old is Lori?
e. Six less than number doubled is ten.
l. Six plus a number decreased by two is
twenty.
f. Eight subtracted from a number is twelve.
m. One number is 2 greater than twice the other
number. The sum of the two numbers is 26.
Find the numbers.
g. 3 more than a number tripled is fifteen.
6. Algebraic Properties
Match each property to an appropriate example.
a. _____ Commutative property
A. (2 + 4) + 6 = 2 + (4 + 6)
b. _____ Associative property
B. 2(4 + 5) = 8 + 10
c. _____Distributive property
C. 98 + (-98) = 0
d. _____Identity property
D. x + y = y + x
e. _____Inverse property
E. (b)(1) = (b)
7. Solves simple equations, including addition, subtraction, multiplication, division,
proportions, and two step equations.
Describe the next operation that would be used in order to solve the following equations.
a. 6x  12
b.
x
5
10
c. x  4  12
d. x  8  2
Solve the following equations.
a. 6x  2  26
b. 3  2x  25
c.
1
x2 2
3
d.
9 3

2x 4
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8. Identifies ratio and proportion as they appear in applied situations and solves proportions
for missing numbers in applied problems.
a. During the last pay period Jamar worked 18 days and did not work 8 days. What is the ratio
of number of days worked to total number of days in the pay period?
b. Usually home builders estimate the cost to build a house by the number of square
feet in a house. A new home on the market in a particular area is selling for
$98,000 and has 1450 square feet of living space. How much can a new home in
roughly the same area cost if it has 3100 square feet of living space?
c. A case study showed that 2 out of 5 people eat a hot dog while attending a
baseball game. Using the case study ratio, how many people can be expected to
eat a hot dog at a game with 23,000 in attendance?
d. In a cookie jar there are c chocolate cookies and p peanut butter cookies. Write a
fraction to express the ratio of chocolate cookies to total cookies in the cookie jar.
9. Solves linear inequalities in one variable and graphs the solution set on the number line.
a. A particular chemical at a plant is flammable at 150º Celsius and cannot be used effectively
below 5º Celsius. Using set notation AND a graph show the temperature at which the
chemical should always be stored.
b. Describe the following number lines using inequalities.
i.
−4
0
2
ii.
−3
c. Solve and graph the following inequalities:
i. x  5  4
ii. 3x  12
iii. 2x  1  7
10. Graphs a linear equation in two variables & 11.Finds the slope and intercepts of a graphed line.
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Find the equation of each of the lines at the right.
(using the slopes and y-intercept)
e
d
c
a.
b.
b
c.
a
d.
e.
Put the following equations in slope intercept form.
a. 4y = 8x + 12
b. 3x + 3y = 6
c. 2 + x = 6
Graph the problems above
Find the slope of the line that passes through the following 2 points
a. (3, 1) and (6, 4)
b. (2, 6) and (4, -3)
c. (4, –3) and (-2, 9)
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11. Solves problems that involve systems of two linear equations in two variables.
Using the algebraic method suggested solve the following systems.
a. 3x – 2y = 5
– 5x + 7y = – 4
(Elimination)
c. y = 3x - 10 (Substitution)
3x – 5y = – 10
b. x = -3y + 4 (Substitution)
2x – 5y = – 3
d. 4 x  y  3 (Elimination)
5x  2 y  1
Solve the following systems by graphing
e. y = 2x + 3
1
y  x3
2
f. y = –3x + 8
3 y  2 x  9
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