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GRADE 8 MIDTERM TOPICAL REVIEW PACKET
Midterm: ______
*Show all work! This packet will be graded. 7th Grade Review Topics: ------7-1 - Sets of Real Numbers - Counting, Whole, Integers, Rational, Irrational
1) Rational vs. Irrational? In each box, place an "R" for Rational and an "I" for Irrational.
3 a) b) 12.77 c) –123.4 d) 81 4 e) 83 f) 0.12122… g) h) 9 8 7-2 - Properties of Numbers - commutative, associative, distributive, identity, inverse
2) Name the property that each equation represents. Write down tricks to remember them.
a) x • 1 = x ______
b) x•y = y•x ______
c) x + 0 = x ______
1 d) x 1 ______x
e) x + y = y + x ______
f) x + (-x) = 0 ______
g) x + (y + z) = (x + y) + z ______
h) x (y + z) = xy + xz ______
3) Perform the indicated operation and state the property used: - 6(a - 7)
_____ 4) If M and A represent integers, M A A M is an example of which property? (1) commutative (3) distributive (2) associative (4) closure
_____ 5) 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)
_____ 6) Which equation is an illustration of the additive identity property? (1) x • 1 = x (3) x – x = 0
2 1 (2) x + 0 = x (4) x 1 x _____ 7) Which property of real numbers is illustrated by the equation -3 + 3 = 0? (1) additive identity (3) associative property (2) commutative property (4) additive inverse 7-2 - Exponents (no variables) 8) Using the Laws of Exponents, simplify the following expressions
a) 30 = b) 30 = c) 32 =
d) 32 = e) 32 = f) 32 =
Scientific Notation _____ 9) Expressed in scientific notation, the number 4,600,000,000 is (1) 4.6 108 (3) 4.6 109 (2) 4.6 109 (4) 0.46 100
_____ 10) 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
_____ 11) The number 8.375103 is equivalent to (1) 0.0008375 (3) 0.08375 (2) 0.008375 (4) 8,375
6.3 108 _____ 12) What is the quotient of in scientific notation? 3 104
(1) 2.1 10-2 (3) 2.1 10-4 (2) 2.1 102 (4) 2.1 104
_____ 13) What is the product of 8.4 × 108 and 4.2 × 103 written in scientific notation? (1) 2.0 × 105 (3) 35.28 × 1011 (2) 12.6 × 1011 (4) 3.528 × 1012
------7-3 - Algebraic Expressions & Translating 14) Express each of the following as an algebraic expressions/equations. Let n represent the number.
a) Ten subtracted from twice a number ______
b) The quotient of 6 and a number ______
c) Three times the sum n and 4 ______
3 d) Two times the quantity of four more than a number is equivalent to the product of the number and six. ______
_____ 15) Marie currently has a collection of 58 stamps. If she buys s stamps each week for w weeks, which expression represents the total number of stamps she will have? (1) 58sw (3) 58s w (2) 58 sw (4) 58 s w
16) Evaluate: 5x2 + 5x – 6 if x = -3
7-4a - Solving Linear Equations Algebraically
_____ 17) Which value of p is the solution of 18) Solve for x:
5p – 1 = 2p + 20? 15x – 3(3x + 4) = 6
(1) 3 19 (2) 7 (3) 7 19 (4) 3
_____ 19) If c 2m d, then m is equal to
c d d (1) (3) c 2 2 c (2) d (4) d 2c 2
20) The sum of three consecutive odd integers is 285. Find the integers.
4 7-4b - Inequalities
*What inequality symbols are associated with the following phrases?
at least ______minimum ______greater than ______greater than or equal to ______at most ______maximum ______less than ______less than or equal to ______
_____ 21) 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 most $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
22) 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.
23) 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?
24) Which is the graph of 2x 3 17 ?
(1)
(2)
(3)
(4) 5 7-5 - Rate, ratio, proportion & percent _____ 25) It takes Tammy 45 minutes to ride her bike 5 miles. At this rate, how long will it take her to ride 8 miles? (1) 0.89 hour (3) 48 minutes (2) 1.125 hours (4) 72 minutes
26) 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.
27) The world population in 1997 was 5,840,324,240. The world population in 2011 has reached 6,894,177,686 and is expected to reach 7 billion sometime this year! Find the percent of change in the world population from year you were born to today to the nearest tenth.
------7-6 - Converting Measurements Relative Error
6 28) Alexis calculated the surface area of a gift box as 600 square inches. The actual surface area of the gift box is 592 square inches. Find the relative error of Alexis' calculation expressed as a decimal to the nearest thousandth.
7-7a - Area of Polygons 29) 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. a) What is the area of the window? Leave in terms of pi.
b) What is the perimeter of the window? Leave in terms of pi.
30) 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.
31) In the diagram below, the circumference of circle O is 16 inches. The length of BC is three-quarters of the length of diameter AD and CE = 4 inches. Calculate the area, in square inches, of trapezoid ABCD.
7 7-7b - Volume and Surface Area of Rectangular Prisms 32) Find the volume, in cubic inches, and the surface area, in square inches, of the rectangular prism shown below.
------7-8 - Polynomials reviewed in 8th grade - Unit #5 (8-5) ------7-9 - Simplifying Radicals & Operations with Radicals Simplify the following expressions to simplest radical form.
33) 34) 35) 4 60 5 2 18 15 20 3 5
7-10 - Graphing Linear Equations 8 _____ 36) Find the slope of the line that passes through the points (3, 5) and (-2,2).
1 5 (1) m (3) m 5 3
3 (2) m (4) m 5 5
_____ 37) Which of the following points satisfies the equation y 2x 10 ? (1) (4, -3) (3) (-3, 4) (2) (2, 10) (4) (10, 2)
38) Complete the table below with the missing values for y. Based on the data in the table, write the equation (in y = form that represents the relationship between x and y.
39) In the diagram to the right, what is the slope of the line passing through points A and B?
40) Graph the line that passes through the points (4,-3) and (6,-5).
a) slope:______
b) y - intercept:______
9 c) Equation:______
------7-11 - Statistics - Mean, median, mode, and range 41) Given the set {85, 11, 10, 12, 10, 10, 8}, Find the following
a) Mean = b) Median = c) Mode = d) Range = e) Outlier = 8th Grade Review Topics: 8-1 - Operations with sets- Intersection, Union, Complement 42) Match the decimals from the top row with the equivalent fractions from the bottom row.
a) 0.12 = b) 0.12 = c) 3.6 = d) 3.6 =
18 3 11 4 5 25 3 33
43) Simplify the following expressions.
a) 52 = b) 53 = c) 64 = d) 3 64 =
Set A {(2,1),(1,0),(1,8)} 44) Given: Set B {(3,4),(2,1),(1,2),(1,8)}.
_____ a) What is the intersection of sets A and B? (1) {(1,8)} (3) {(–2,–1)} (2) {(–2,–1), (1,8)} (4) {(–3,–4), (–2,–1), (–1,2), (–1,0), (1,8)}
_____ b) What is the union of sets A and B? (1) {(1,8)} (3) {(–2,–1)} (2) {(–2,–1), (1,8)} (4) {(–3,–4), (–2,–1), (–1,2), (–1,0), (1,8)}
10 A = {All even integers from 2 to 20, inclusive} 45) Given: B = {10,12,14,16,18}
_____ What is the complement of set B within the universe of set A? (1) {4,6,8} (3) {4,6,8, 20} (2) {2, 4,6,8} (4) {2, 4,6,8, 20}
Interval Notation
_____ 46) Which interval notation represents the set of all numbers greater than 3 and less than or equal to 7? (1) (3,7] (3) (3,7) (2) [3,7) (4) [3,7]
8-2 - Transformations 47) On the axes below, plot ABC using the points A(-2, 0), B( -3, 4), C(-1,2). a) Reflect ABC over the y-axis. Label the image A'B'C'.
b) Dilate ABC by a scale factor of 2. Label the image A''B''C''.
48) On the axes below, plot DEFG using the points D(1, 2), E(1, 7), F(4, 7), G(4, 2).
a) Translate DEFG using (x + 2, y – 4).. Label the image D'E'F'G'. 11 b) Rotate DEFG 90 degrees clockwise. Label the image D''E''F''G''.
8-3 - Plane Geometry (vertical angles, complementary and supplementary angles, parallel lines cut by a transversal) 49) In the accompanying diagram, line a intersects line b.
What is the value of x?
(1) -10 (3) 10 (2) 5 (4) 90
*Vertical angles:
50) The measures of two complementary angles are represented by (3x 15) and (2x 10). What is the value of x? (1) 17 (3) 35 (2) 19 (4) 37
51) In the accompanying figure, what is one pair of alternate interior angles? Prove your answer by identifying what each pair is. (corresponding, vertical, alternate interior, alternate exterior, a linear pair, or supplementary)
a) 1 and ∠ 2 are ______b) 4 and ∠ 5 are ______12 c) 4 and ∠ 7 are ______d) 6 and ∠ 8 are ______e) 1 and ∠ 7 are ______f) 4 and ∠ 6 are ______
52) 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.
53) Triangles: Interior and Exterior Angles
8- a) Find the value of x. What is mF ? 4 -
Pythagorean Theorem (leg 2 leg 2 hypotenuse2 or a 2 b 2 c 2 ) Pythagorean Triples:
_____ 54) The set of integers {3,4,5} is a Pythagorean triple. Another such set is (1) {6,7,8} (3) {6,12,13} (2) {6,8,12} (4) {8,15,17}
_____ 55) 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 (3) 34 ft (2) 30 ft (4) 46 ft
13 56) 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?
_____ 57) If the length of the legs of a right triangle are 5 and 7, what is the length of the hypotenuse?
(1) 2 (3) 2 6 (2) 2 3 (4) 74
O A O 8-4 Trigonometry ( S C T ) H H A
_____ 58) 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 13 (1) (3) 85 84 84 84 (2) (4) 85 13
59) A communications company is building a 30-foot antenna to carry cell phone transmissions. As shown in the diagram below, a 50-foot wire from the top of the antenna to the ground is used to stabilize the antenna. Find to the nearest degree, the measure of the angle the wire makes with the ground.
14 60) A stake is to be driven into the ground away from the base of a 50-foot pole, as shown in the diagram below. A wire from the stake on the ground to the top of the pole is to be installed at an angle of elevation of 52°. How far from the base of the pole should the stake be driven in, to the nearest foot?
8-5 - Operations with Polynomials
_____ 61) The sum of 8x2 x 4 and x 5 is
(1) 8x2 9 (3) 8x2 2x 9 (2) 8x2 1 (4) 8x2 2x 1
_____ 62) When 3a2 2a 5 is subtracted from a2 a 1, the result is
(1) 2a2 3a 6 (3) 2a2 3a 6 (2) 2a2 3a 6 (4) 2a2 3a 6
63) 64) (9r 3s)(5r 5 s) (5y 2 ) 2
15 65) 66) 4a 3b7c8 64y 4 16y 2 8y
2ab9c 8y
67) 68) 69) 3x4x 2 6x 7 (x + 4)(x – 3) (x + 2)2
8-5 - Factoring Quadratic Expressions 3 Methods of Facoring: 1) 2) 3)
_____ 70) Which expression is a factor of x2 2x 15 (1) (x - 3) (3) (x + 15) (2) (x + 3) (4) (x – 5)
71) Factor completely: a) b) c) 3x 2 15x 42 x3 – 16x xyz + 3x2y3z4
8-6 - Solving Quadratic Equations Algebraically _____ 72) What is the solution set of the equation 3x 2 48? (1) {–2,–8} (3) {4,–4} (2) {2,8} (4) {4,4}
16 _____ 73) The solution set for the equation x 2 5x 6 is (1) {1,-6} (3) {-1,6} (2) {2,-3} (4) {-2,3}
74) The square of a number decreased by four times the number equals 21. What is the negative solution? Solve algebraically.
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