GRADE 8 MIDTERM
REVIEW PACKET
January 10, 2012
Name: ________________
Teacher: _____________
TOPICS ON MIDTERM EXAM
Format of the exam:
Part I – 15 multiple choice questions – 2 pts. each. No partial credit
Part II – 6 questions – 5 pts. each. Partial credit will be given
Part III – 4 questions – 6 pts. each. Partial credit will be given
Part IV – 2 questions – 8 pts. each. Partial credit will be given
The exam will count as TWO test grades for the 2nd Quarter.
*Please review all notes & tests from 7th Grade & 8th Grade*
- Operations with Sets- Intersection, union, complement
- Interval Notation
- Properties of Numbers – commutative, associative, distributive, identity, inverse
- Scientific Notation- convert from scientific to standard and vice versa; multiplying and dividing in sci. not.
- Algebraic expressions: translating and evaluating, including formulas
- Operations with Polynomials
- Solving equations– including equations with parentheses, combining, variables on both sides, literal
- Solving & Graphing Inequalities
- Factoring quadratic expressions & solving quadratic equations, including factoring completely
- Applications of Solving Equations – number problems, consecutive integer problems, area problems
- Linear Graphing
- Pythagorean Theorem (leg2 + leg2 = hypotenuse2) & Right Triangle Trigonometry (SOH-CAH-TOA)
- Simplifying radicals & performing operations with radicals
- Rate, ratio, & proportion
- Percent of Change
- Area of polygons and figures made up of combinations of polygons
- Volume & Surface Area of Rectangular Prisms (formulas given)
- Transformations – reflections, rotations, dilations & translations
- Geometry- vertical angles, complementary & supplementary angles, parallel lines cut by a transversal
2
Operations with sets- Intersection, Union, Complement
1) Given:
Set A  {( 2,1),( 1,0),(1,8)}
Set B  {( 3,4),( 2,1),( 1,2),(1,8)}.
What is the intersection of sets A and B?
(1) {(1,8)}
(2) {(–2,–1), (1,8)}
2) Given:
(3) {(–2,–1)}
(4) {(–3,–4), (–2,–1), (–1,2), (–1,0), (1,8)}
Set A  {( 2,1),( 1,0),(1,8)}
Set B  {( 3,4),( 2,1),( 1,2),(1,8)}.
What is the union of sets A and B?
(1) {(1,8)}
(2) {(–2,–1), (1,8)}
3) Given:
(3) {(–2,–1)}
(4) {(–3,–4), (–2,–1), (–1,2), (–1,0), (1,8)}
A  {All even integers from 2 to 20, inclusive}
B  {10,12,14,16,18}
What is the complement of set B within the universe of set A?
(1) {4, 6,8}
(2) {2, 4, 6,8}
(3) {4, 6,8, 20}
(4) {2, 4, 6,8, 20}
Interval Notation.
4) Which interval notation represents the set of all numbers from 3 through 7, inclusive?
(1) (3,7]
(3) [3,7)
(2) (3,7)
(4) [3,7]
5) Which interval notation represents the set of all numbers between 3 and 7?
(1) (3,7]
(3) [3,7)
(2) (3,7)
(4) [3,7]
Properties of Numbers - commutative, associative, distributive, identity, inverse
6) If M and A represent integers, M  A  A  M is an example of which property?
(1) commutative
(3) distributive
(2) associative
(4) closure
7) Which equation illustrates the associative property?
(1) a (1)  a
(3) a (b  c)  (ab)  (ac)
(2) a  b  b  a
(4) (a  b)  c  a  (b  c)
3
8) Tori computes the value of 8 95 in her head by thinking 8(100  5)  8  100  8  5.
property is she using?
(1) associative
(3) commutative
(2) distributive
(4) closure
9) Which equation is an illustration of the additive identity property?
(1) x • 1 = x
(3) x – x = 0
1
(2) x + 0 = x
(4) x   1
x
10) Which property of real numbers is illustrated by the equation  3  3  0?
(1) additive identity
(2) commutative property of addition
(3) associative property of addition
(4) additive inverse
Scientific Notation
11) What is the value of n if the number 0.0000082 is written in the form 8.2  10n ?
(1) -6
(3) 5
(2) -5
(4) 6
12) Expressed in scientific notation, the number 4,600,000,000 is
(1) 4.6  108
(3) 4.6  109
(2) 4.6  109
(4) 0.46  100
13) The number 8.375  103 is equivalent to
(1) 0.0008375
(3) 0.08375
(2) 0.008375
(4) 8,375
14) What is the value of
(1) 2.1 10-2
(2) 2.1102
6.3 108
in scientific notation?
3 104
(3) 2.1 10-4
(4) 2.1104
15) What is the quotient of 8.05  106 and 35
.  102 ?
(1) 2.3  103
(3) 2.3  108
(2) 2.3  104
(4) 2.3  1012
4
Which number
Algebraic Expressions
16) Express each of the following as an algebraic expression. Let n represent the number.
a) 3 less than a number
___________________
b) Twice a number decreased by 10 ________________
c) The quotient of 6 and a number ___________________
17) Write an equation to express the situation. Four times a number is nine more than the number.
(Let n = number)
______________________________________________________________________________________
18) Translate each algebraic expression into a verbal expression
a) 3x + 2
________________________________________________________________________
b) 7-5x ___________________________________________________________________________
19) If A = ½ bh and b = 6 and h = 2.5, find A.
20) Evaluate: 5x2 + 5x – 6 if x = -3
Operations with Polynomials
21) The sum of 8 x 2  x  4 and x  5 is
(1) 8 x 2  9
(3) 8x 2  2 x  9
(2) 8x 2  1
(4) 8x 2  2 x  1
22) The expression (2 x 2  6 x  5)  (6 x 2  3x  5) is equivalent to
(1)  4 x 2  3 x
(3) 4 x 2  3 x  10
(2) 4 x 2  3x
(4) 4 x 2  3 x  10
5
23) When 3a 2  2a  5 is subtracted from a 2  a  1 , the result is
(1) 2a 2  3a  6
(3) 2a 2  3a  6
(2) 2a 2  3a  6
(4) 2a 2  3a  6
24) (9r 3 s)(5r 5 s)
25) m(m 2 )( m 3 )
26) (5 y 2 ) 3
27) (b x ) y
28)
x5 y8 z 7
x 2 yz 3
29)
 4a 3 b 7 c 8
2abc
30) (2x7)(9x3)
3x2
31) 3x (4x2 + 6x – 7)
32) 64y4 + 16y2
8y
33) (x + 6) (x + 2)
34) (x + 2)2
35) (x + 4) (x – 3)
6
Solving equations
36) Solve for x: 15x – 3(3x + 4) = 6
37) What is the value of n in the equation 0.6(n +10) = 3.6?
38) If c  2m  d , then m is equal to
cd
d
(1)
(3) c 
2
2
c
(2)  d
(4) d  2c
2
Solving Inequalities
39) Mr. Jones wrote "Sixteen less than four times a number is greater than three" on the board.
If x represents the number, write an inequality representing this statement.
40) An electronics store sells DVD players and cordless telephones. The store makes a $75 profit on the sale of
each DVD player (d) and a $30 profit on the sale of each cordless telephone (c). The store wants to make a
profit of at least $255.00 from its sales of DVD players and cordless phones. Which inequality describes this
situation?
(1) 75d  30c  255
(3) 75d  30c  255
(2) 75d  30c  255
(4) 75d  30c  255
7
41) A prom ticket at Smith High School is $120. Tom is going to save money for the ticket by walking his
neighbor’s dog for $15 per week. If Tom already has saved $22, what is the minimum number of weeks
Tom must walk the dog to earn enough to pay for the prom ticket?
Factoring Quadratic Expressions & Solving Quadratic Equations
*The three ways to factor are: 1) _________ 2) _________
42) If 3x is one factor of 3x 2 - 9x , what is the other factor?
(1) 3x
(2) x 2 - 6x
(3) x – 3
(4) x + 3
43) Which expression is a factor of x 2  2 x  15 ?
(1) (x - 3)
(2) (x + 3)
(3) (x + 15)
(4) (x – 5)
44) Factor completely: 3x 2  15 x  42
45) Factor completely: 3x 2 - 27
(1) 3(x - 3)2
(2) 3(x 2 - 27)
(3) 3(x + 3)(x – 3)
(4) (3x + 3)(x – 9)
9 x 4  27 x 6
is equivalent to
3x 3
(1) 3x(1  3x)
(3) 3x (1  9 x 5 )
(2) 3x (1  3x 2 )
(4) 9 x 3 (1  x)
46) The expression
8
3) ________________
47) Simplify: x2 – x – 6
x-3
48) What is the solution set of the equation 3x 2  48 ?
(1) {–2,–8}
(2) {2,8}
(3) {4,–4}
(4) {4,4}
49) The solution set for the equation x 2  5 x  6 is
(1) {1,-6}
(2) {2,-3}
(3) {-1,6}
(4) {-2,3}
Applications of Solving Equations –number, consecutive integer, area problems
*Only an algebraic solution will be accepted. Be sure to define a variable!
50) Four less than a number is 172. Find the number.
51) The sum of three consecutive odd integers is 285. Find the integers.
52) The product of two consecutive integers is 20. Find the integers.
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53) The base of a parallelogram measures 7 centimeters more than its altitude. If the area of the parallelogram
is 30 square centimeters, find the measure of its base and its altitude.
Linear Graphing
54) Find the slope of the line that passes through the points (-3, 5) and (-5,-8).
(1) m = 1/80
(2) m = -6.5
(3) m = 6.5
(4) m = - .375
55) Find the equation of the line that passes through the points (-2, 3) and (1, -6).
(1) y = - 3x – 3
(2) y = - 1/3x – 3
(3) y = 1/3x – 3
(4) y = - 3x + 3
56) Which of the following points satisfies the equation y = 2x + 10?
(1) (4, -3)
(2) (2, 10)
(3) (-3, 4)
(4) (10, 2)
57) What is an equation for the line that passes through the coordinates (2,0) and (0,3)?
3
2
(1) y   x  3
(3) y   x  2
2
3
3
2
(2) y   x  3
(4) y   x  2
2
3
10
58) Using the tables below, identify the slope and y-intercept. Then write the equation of the line.
a)
b)
x
-2
0
2
4
6
y
12
8
4
0
-4
feet
1
3
7
11
13
min.
0
1
3
5
6
Slope:_____________
Slope:_____________
Y-intercept:_____________
Y-intercept:_____________
Equation:_______________
Equation:_______________
59) Draw the line that passes through the points (4,-3) and (6,-5). Identify the slope and y-intercept.
Then write the equation of the line.
Slope:_____________
Y-intercept:_____________ Equation:_______________
Pythagorean Theorem (leg2 + leg2 = hypotenuse2) & Trigonometry (SOH-CAH-TOA)
60) The set of integers {3,4,5} is a Pythagorean triple. Another such set is
(1) {6,7,8}
(2) {6,8,12}
(3) {6,12,13}
(4) {8,15,17}
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61) A builder is building a rectangular deck with dimensions of 16 feet by 30 feet. To ensure that the sides
form 90° angles, what should each diagonal measure?
(1) 16 ft
(2) 30 ft
(3) 34 ft
(4) 46 ft
62) If the length of the legs of a right triangle are 5 and 7, what is the length of the hypotenuse?
(1) 2
(2) 2 3
(3) 2 6
(4) 74
63) The accompanying diagram shows a kite that has been secured to a stake in the ground with a 20-foot
string. The kite is located 12 feet from the ground, directly over point X. What is the distance, in feet,
between the stake and point X?
64) A wall is supported by a brace 10 feet long, as shown in the diagram below. If one end of the brace is
placed 6 feet from the base of the wall, how many feet up the wall does the brace reach?
65) Draw and label a diagram of a path of an airplane climbing at an angle of 11 degrees with the ground. Find,
to the nearest foot, the ground distance the airplane has traveled when it has attained an altitude of 400 feet.
12
66) Use the diagram to find the value of x to the nearest tenth of a foot.
x
20 feet
15°
67) In triangle MCT, the measure of T  90 , MC  85 cm, CT  84 cm, and TM = 13 cm. Which ratio
represents the sine of C ?
13
85
84
(2)
85
(1)
13
84
84
(4)
13
(3)
Simplifying Radicals & Operations with Radicals
68) 5 8  18  2
69)
3 6 
2
70) 15 20  3 5
Rate, ratio, & proportion
71) Sam runs 4 miles in 2400 seconds. How many minutes take it him to run each mile?
(1) 10
(2) 160
(3) 600
(4) 9600
13
72) Jake drove 330 miles from Montauk to home and used 32.2 gallons of gasoline. His friend, Sue, drove 420
miles from Montauk to her home and used 40 gallons of gasoline. Whose vehicle had better gas mileage?
Justify your answer.
Percent of Change
73) The Hudson Record Store is having a going-out-of-business sale. CDs normally sell for $18.00. During the
first week of the sale, all CDs will sell for $15.00. What is the percent of change to the nearest tenth?
74) The world population was 4.2 billion people in 1982. The population in 1999 reached 6 billion. Find the
percent of change from 1982 to 1999 to the nearest tenth.
Area of Polygons
75) A designer created the logo shown below. The logo consists of a square and four quarter-circles of equal
size. Express, in terms of  , the exact area, in square inches, of the shaded region.
14
76) A window is made up of a single piece of glass in the shape of a semicircle and a rectangle, as shown in the
diagram below. What is the perimeter of the window? Leave in terms of pi.
77) The first base of a trapezoid is 6 cm. The second base of the trapezoid is 2/3 the length of the first base.
If the height of the trapezoid is 4 cm, find the area.
Volume and Surface Area of Rectangular Prisms
78) Find the volume and surface area of the figure below if: V= lwh & SA = 2lw + 2wh + 2lh
15
Transformations
79) On the axes below, plot the points A (-2, 0) B( -3, 4) C (-1,2). Perform a reflection in the y-axis.
80) What are the coordinates of point A’, the image of point A (-3, 4) under a dilation of 2?
(1) (-6,8)
(2) (6,8)
(3) (-1,6)
(4) (2,0)
81) What are the coordinates of point A’, the image of point A (-3, 4) under a translation T2,-3?
(1) (-6,12)
(2) (-1,4)
(3) (-1,1)
(4) (6,2)
82) On the axes below, plot the points A (-2, 0) B( -3, 4) C (-1,2). Perform a rotation of 90 degrees.
16
Geometry- Vertical angles, complementary and supplementary angles, parallel lines cut by
a transversal
83) In the accompanying diagram, line a intersects line b.
What is the value of x?
(1) -10
(2) 5
(3) 10
(4) 90
84) The measures of two complementary angles are represented by (3x  15) and (2 x  10).
What is the value of x?
(1) 17
(2) 19
(3) 35
(4) 37
85) Two parallel roads, Elm Street and Oak Street, are crossed by a third, Walnut Street, as shown in the
accompanying diagram. Find the number of degrees in the acute angle formed by the intersection of Walnut
Street and Elm Street.
86) In the accompanying figure, what is one pair of alternate interior angles?
(1)  1 and   2
(2)  4 and   5
(3)  4 and   6
(4)  6 and   8
17