Download Enriched Pre-Algebra - End of the Year Test Review Short Answer

Enriched Pre-Algebra - End of the Year Test Review
Short Answer
Write each expression using exponents.
1. 8 · 3 · 3 · 3 · 3 · 8 · 8 · 8 · 3
Write each number in scientific notation.
2. 2,825
3. 0.2447
Express each rate as a unit rate.
4. $258 for 6 radios
5. $694 for 40 hours
The points given in each table lie on a line. Find the slope of the line.
6.
x
y
2
–13
3
–18
4
–23
5
–28
Solve each proportion.
7.
Write a proportion to determine the missing measure. Round to the nearest tenth, if necessary.
8. A smokestack of a factory casts a 35-meter shadow at the same time as a 10-meter utility pole casts a 6.3meter shadow. What is the height of the smokestack?
Write a percent proportion to solve each problem. Then solve. Round to the nearest tenth if necessary.
9. 175 is 19% of what number?
Solve each equation using the percent equation.
10. What percent of 4000 is 12?
Find each percent of change. Round to the nearest tenth if necessary. State whether the percent of change is
an increase or a decrease.
11. original: 27
new: 18
Find the simple interest to the nearest cent.
12. $150 at 7.5% for 3 years.
Find the area of each figure.
13. triangle: base, 11 cm; height, 19.6 cm
14. trapezoid: height, 7.4 cm; bases, 12.4 cm and 9.8 cm
Find the area of each circle. Round to the nearest tenth.
15. The radius is 13.4 mm.
Find the volume of each solid. Round to the nearest tenth if necessary.
16. cylinder: radius 6.3 mm; height 11.8 mm
Find the surface area of each solid. Round to the nearest tenth if necessary.
17. cylinder: radius 6.9 ft; height 12.1 ft
Find the mean of each set of data. Round to the nearest tenth if necessary.
18. 26, 35, 13, 15, 33, 40, 23, 17
Evaluate each expression if a = 3, b = 5, and c = 9.
19. 6a – 4b – 6c
Name the property shown by each statement.
20. 4(xy) = (4x)y
21. (3 + 8)6 = 3(6) + 8(6)
Subtract.
22. –5 – 6
23. 11 – (–9)
Multiply.
24. –5(5)(7)
Enriched Pre-Algebra - End of the Year Test Review
Answer Section
SHORT ANSWER
1. ANS:
The common factor is the base. The exponent is the number of times the common factor is used as a factor.
PTS: 1
DIF: Average
OBJ: 2-8.2 Use exponents in expressions.
STA: NSO.3
TOP: Use exponents in expressions.
KEY: Powers | Exponents
MSC: 1999 Lesson 1-2
2. ANS:
2.825  103
When a number is expressed in scientific notation, it is written as a product of a factor and a power of 10. The
factor must be greater than or equal to 1 and less than 10. Multiplying by a positive power of 10 moves the
decimal point to the right the same number of places as the exponent.
PTS: 1
DIF: Average
OBJ: 2-9.1 Express numbers in scientific notation.
STA: NSO.1
TOP: Express numbers in scientific notation.
KEY: Scientific notation | Numbers
MSC: 1999 Lesson 6-9
3. ANS:
2.447  101
When a number is expressed in scientific notation, it is written as a product of a factor and a power of 10. The
factor must be greater than or equal to 1 and less than 10. Multiplying by a negative power of 10 moves the
decimal point to the left the same number of places as the absolute value of the exponent.
PTS: 1
DIF: Average
OBJ: 2-9.1 Express numbers in scientific notation.
STA: NSO.1
TOP: Express numbers in scientific notation.
KEY: Scientific notation | Numbers
MSC: 1999 Lesson 6-9
4. ANS:
$43/radio
The unit cost is the cost of 1 radio.
$258 ÷ 6 = $43/radio
PTS: 1
DIF: Basic
OBJ: 4-1.2 Determine unit rates.
STA: NSO.6
TOP: Determine unit rates.
KEY: Unit rates | Ratios
MSC: 1999 Lesson 3-1
5. ANS:
$17.35/hour
The unit rate is the amount earned for 1 hour.
$694 ÷ 40 = $17.35/hour
PTS: 1
DIF: Average
OBJ: 4-1.2 Determine unit rates.
STA: NSO.6
TOP: Determine unit rates.
KEY: Unit rates | Ratios
MSC: 1999 Lesson 3-1
6. ANS:
–5
Sample:
1
x
20
y
2
25
3
30
4
35
Select two points and use the slope formula:
(1, 20) and (2, 25)
PTS: 1
DIF: Basic
STA: PFA.6 | PFA.13
KEY: Slope | Lines
7. ANS:
6
Sample:
Cross multiply and solve for m.
OBJ: 4-3.2 Find the slope of a line given a table.
TOP: Find the slope of a line given a table.
PTS: 1
DIF: Basic
OBJ: 4-4.1 Use proportions to solve problems.
STA: NSO.6 | MEA.7
TOP: Use proportions to solve problems.
KEY: Proportions | Problem solving
MSC: 1999 Lesson 3-3 | 1999 Lesson 8-1
8. ANS:
55.6 m
Set up a proportion using the sides of the similar triangles. Solve for the height of the smokestack, h.
PTS: 1
DIF: Average
STA: GSS.1 | GSS.3
KEY: Similar triangles | Proportions
9. ANS:
921.1
PTS: 1
DIF: Average
STA: NSO.6 | MEA.7
OBJ: 4-7.1 Solve problems involving similar triangles.
TOP: Solve problems involving similar triangles.
MSC: 1999 Lesson 8-8
OBJ: 5-3.1 Solve problems using the percent proportion.
TOP: Solve problems using the percent proportion.
KEY: Percent proportion | Problem solving
10. ANS:
0.3%
MSC: 1999 Lesson 8-2
PTS: 1
DIF: Average
OBJ: 5-6.1 Solve problems using the percent equation.
STA: NSO.6
TOP: Solve problems using the percent equation.
KEY: Percent equation | Problem solving MSC: 1999 Lesson 8-3
11. ANS:
33.3%, decrease
Subtract the new number from the original number. Then divide the difference by the original number.
PTS: 1
DIF: Average
OBJ: 5-7.2 Find and use the percent of decrease.
STA: NSO.6
TOP: Find and use the percent of decrease.
KEY: Percent of decrease | Problem solving
MSC: 1999 Lesson 8-5
12. ANS:
$33.75
PTS: 1
DIF: Basic
OBJ: 5-8.1 Solve problems involving simple interest.
STA: NSO.6
TOP: Solve problems involving simple interest.
KEY: Simple interest | Problem solving
MSC: 1999 Lesson 8-6
13. ANS:
107.8 cm2
Sample:
triangle: base, 7.2 mm; height, 18 mm
Use the formula
.
mm2
PTS: 1
DIF: Basic
OBJ: 7-1.2 Find the areas of triangles.
STA: MEA.9
TOP: Find the areas of triangles.
KEY: Area | Triangles
MSC: 1999 Lesson 7-6
14. ANS:
82.14 cm2
Sample:
trapezoid: height, 5.2 m; bases, 15.6 m and 8.9 m
Use the formula
.
PTS: 1
DIF: Basic
OBJ: 7-1.3 Find the areas of trapezoids.
STA: MEA.9
TOP: Find the areas of trapezoids.
KEY: Area | Trapezoids
MSC: 1999 Lesson 7-6
15. ANS:
564.1 mm2
Sample:
The radius is 13 cm.
Use the formula
.
PTS: 1
DIF: Average
OBJ: 7-2.2 Find the area of circles.
STA: MEA.9
TOP: Find the area of circles.
KEY: Area | Circles
MSC: 1999 Lesson 7-7 | 1999 Lesson 11-1
16. ANS:
1471.3 mm3
Sample:
cylinder: radius 4.4 m; height 9.9 m
Use the formula V = Bh.
PTS: 1
DIF: Average
STA: MEA.9 | MEA.10
KEY: Volume | Cylinders
17. ANS:
823.7 ft2
Sample:
cylinder: radius 4.8 m; height 10.2 m
Use the formula
.
OBJ: 7-5.2 Find the volume of cylinders.
TOP: Find the volume of cylinders.
MSC: 1999 Lesson 11-3
PTS: 1
DIF: Average
STA: MEA.9 | MEA.10
KEY: Surface area | Cylinders
18. ANS:
OBJ: 7-7.2 Find the surface area of cylinders.
TOP: Find the surface area of cylinders.
MSC: 1999 Lesson 11-5 | 1999 Lesson 11-6
25.3
The mean of a set of data is the sum of the data divided by the number of pieces of data.
PTS: 1
DIF: Basic
OBJ: 9-4.1 Find the mean of a set of data.
STA: DAP.4
TOP: Find the mean of a set of data.
KEY: Mean | Analyzing data
MSC: 1999 Lesson 4-4
19. ANS:
–56
Substitute the appropriate values and simplify.
Sample:
PTS: 1
DIF: Basic
OBJ: 1-2.2 Evaluate algebraic expressions.
STA: PFA.8
TOP: Evaluate algebraic expressions.
KEY: Evaluating expressions | Algebraic expressions
MSC: 1999 Lesson 1-3
20. ANS:
Associative Property of Multiplication
The order of the factors does not change, just the position of the grouping symbols.
PTS: 1
DIF: Average
OBJ: 1-2.3 Identify properties.
STA: NSO.4
TOP: Identify properties.
KEY: Identifying properties | Properties
MSC: 1999 Lesson 1-3
21. ANS:
Distributive Property
The 6 is distributed over the sum of 3 + 8.
PTS: 1
DIF: Average
OBJ: 1-2.3 Identify properties.
STA: NSO.4
TOP: Identify properties.
KEY: Identifying properties | Properties
MSC: 1999 Lesson 1-3
22. ANS:
–11
To subtract an integer, add its additive inverse.
Sample:
4–9
4 + (–9)
–5
PTS: 1
DIF: Basic
OBJ: 1-5.1 Subtract integers.
STA: NSO.4
TOP: Subtract integers.
KEY: Subtraction | Integers
MSC: 1999 Lesson 2-5
23. ANS:
20
To subtract an integer, add its additive inverse.
Sample:
–2 – (–16)
–2 + (16)
14
PTS: 1
DIF: Average
OBJ: 1-5.1 Subtract integers.
STA: NSO.4
TOP: Subtract integers.
KEY: Subtraction | Integers
MSC: 1999 Lesson 2-5
24. ANS:
–175
The product of two integers with the same sign is positive. The product of two integers with different signs is
negative.
Sample:
–7(3)(–6)
(–21)(–6)
126
PTS: 1
DIF: Average
OBJ: 1-6.1 Multiply integers.
STA: NSO.4
TOP: Multiply integers.
KEY: Multiplication | Integers
MSC: 1999 Lesson 2-7 | 1999 Lesson 2-8