Name: __________________________ Date: ______________
1. A pair of jeans is priced at $50.00, but is on sale for 25% off. What is the sale price of the pair of jeans?
a. $37.50
b. $40.00
c. $66.66
d. $12.50
2. If a television costs $311 after a 35% discount, what was the original cost?
a. $276.00
b. $419.85
c. $888.57
d. $478.46
3. If a DVD player costs $306 after a 30% increase in price, what was the original cost?
a. $91.80
b. $214.20
c. $437.14
d. $235.39
4. Find the amount of money now necessary to be invested at 5% simple interest to yield $200 interest in 8 years.
a. $125.00
b. $500.00
c. $320.00
d. $2500.00
5. The length of a rectangular garden is 8 more meters than its width. Its perimeter is 76 meters. Find the length of the garden.
a. 23 meters
b. 76 meters
c. 345 meters
d. 15 meters
6. The perimeter of a triangle is 30 inches. The length of the middle side is 2 inches more than the length of the smaller side and the largest side is 4 inches more than twice the length of the smallest side. Find the length of the smallest side.
a. 6 inches
b. 8 inches
c. 4 inches
d. 2 inches
7. If 8 times a number is increased by 20, the result is 26 less than the square of the number. Choose the equation that could be used to find this number, x.
a.
b.
c.
d.
8. Identify the proportion listed below that solves the problem: A car can travel 603 miles on 11 gallons of gasoline. How far can the car travel on 36 gallons?
a.
c.
b.
d.
9. Two cars start from the same point and travel in opposite directions. The rate of the slower car is 15 miles per hour less than the rate of the faster car. After 8 hours they are 840 miles apart. Find the speed of the cars.
a. 90 mph and 75 mph
b. 105 mph and 90 mph
c. 60 mph and 45 mph
d. 100 mph and 85
10. If a student completed this worksheet that covers word problems that are on the state competency exam to pass this class and had some difficulty. Should the student make sure that they ask questions, always go to class, take good notes, complete their homework, and seek extra help when needed?
a. Yes
b. Yes
c. Yes
d. Yes
1. A
To find the discount you multiply the original price by the percent of the discount.
So, the discount is $50.00(0.25) = $12.50.
To find the sale price you subtract the original price from the discount.
So, to find the sale price you take 50.00 – 12.50 = 37.50. The sale price is $37.50.
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2. D Check
Original Cost – Discount = Sale Price 478.46 - .35(478.46) = 311
X - .35X = 311 478.46 – 167.46 = 311
1X - .35X = 311 311 = 311
.65X = 311
.65 .65
X = 478.46
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3. D
Original Cost + Increase = New Price Check: 235.39 + .30(235.39) = 306
X + .30X = 306 235.39 + 70.61 = 306
1X + .30X = 306
306 = 306
1.30X = 306
1.30 1.30
X = $235.39
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4. B
The formula to find simple interest is: Interest = Principal x Rate x Time (I = P*R*T)
The information gives would lead to: 200 = X (0.05) (8)
Then simplify: 200 = X(0.4)
Then solve for x by dividing both sides by 0.4: 200/0.04 = X(0.04)/0.04
X = $500.00, the principal (amount to be invested) is $500.00.
Check: 200 = 500(0.05)(8)
200 = 200
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5. A
Width: W
W + 8 Length: W + 8
Perimeter: 76
W W
W + 8
Equation: W + W + 8 + W + W + 8 = 76 Width: W = 15
Combine Like Terms: 4W + 16 = 76 Length: 15 + 8 = 23
- 16 - 16
4W = 60 Check: 15 + 23 + 15 + 23 = 76
4 4 76 = 76
Solve: W = 15
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6. A
Small:
X
Middle: X + 2
Large: 2X + 4 X X + 2
Perimeter: 30
2X + 4
The equation will be: X + X + 2 + 2X + 4 = 30
Combine like terms: 4X + 6 = 30
Solve: - 6 - 6
4X = 24 Check: 6 + 6 + 2 + 2(6) + 4 = 30
4 4 6 + 8 + 16 = 30
14 + 16 = 30
X = 6 30 = 30
Small: X = 6
Middle: 6 + 2 = 8
Large: 2(6) + 4 = 16
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7. B
Translate the problem to:
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8. A
Note: If your proportion does not match the
proportion on the test, multiply the
diagonals to see which matches.
Matches:
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9. C
|
Type |
D |
R |
T |
|
Fast Car |
8X |
X |
8 |
|
Slow Car |
8(X – 15) |
X – 15 |
8 |
|
Total |
840 |
|
|
Fill in the 4 x 4 chart with the given information.
To fill in the distance column use the formula Distance = Rate x Time
You now have the formula:
8X + 8(X – 15) = 840
Distributive Property: 8X + 8X – 120 = 840
Combine Like Terms: 16X -120 = 840
+ 120 +120
Solve for X: 16X = 960
16 16
X = 60
Substitute X into the chart and answer the question:
|
Type |
D |
R |
T |
|
Fast Car |
8(60) = 480 miles |
60 mph |
8 |
|
Slow Car |
8(60– 15) = 360 miles |
60 – 15 = 45 mph |
8 |
|
Total |
840 miles |
|
|
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10. UMMMMMMMMMMMMMMMMM!!!!!!! The answer is YES!!!
The competency exam is very important.
To pass MAT0024C Elementary Algebra you need an 80% or better on the competency exam.
Note: Use test taking strategies like eliminating the incorrect answers first, then look at the possible choices.