Math-8 SOLReviewItems 312-13...1$ 13.8$ 2$ 12.2$ 3$ 10.9$ 4$ 10.1$ 5$ 9$ $ $ $ $...

Review Items Vijaya Nallari Math 8 Class

8.1 The student will a) simplify numerical expressions involving positive exponents, using rational numbers,

order of operations, and properties of operations with real numbers; and b) compare and order decimals, fractions, percents, and numbers written in scientific

notation.

8.1a 1. Simplify the following expression.

2 5.2 + 3.8 + (11 − 3)

8.1a 2. Simplify the expression.

12×57×12×1

25

81.a 3. Simplify the following expression. 5 − 2!

4(12 − 3! )

8.1a 4. Simplify the following expression.

−3! +1311 − 2 − (3

15+ 1 + 2

45)

8.1b 5. Which number is the greatest? The least? Show your work. 38%, 3.8×10!!, 3.8, 13 , 3!

!

Order the numbers from greatest to least.

8.2 The student will describe orally and in writing the relationships between the subsets of the real number system.

8.2 6. Describe the difference between rational and irrational numbers.

8.2 7. Which set does not include the number -4? A. Integer B. Rational Number C. Whole Number D. Real Number


8.2 8. Which number belongs to the set of rational numbers? A. 2 B. 5 C. 𝜋 D. 25

8.2 9. What is the difference between the set of natural numbers and whole numbers?

8.2

10. Which of the following numbers are integers? !!"! 2 -‐ !

! 0.4 3 -‐6

8.3 The student will

a) solve practical problems involving rational numbers, percents, ratios, and proportions; and b) determine the percent increase or decrease for a given situation.

8.3a 11. John wants to buy a video game. The video game cost $59.95 and the sales tax is 5%. How much money will John need to purchase the game?

8.3a 12. Samuel has $550 dollars in his savings account. If his bank pays 1.25% annual simple interest and he makes no further withdraws or deposits, how much money will be in the account after 3 years?

8.3a 13. Susan bought a bike on sale for $93.75. If the bike was originally $125, what was the percent of discount?

8.3a 14, Susan ran for class president. In the election 40% of the votes went to the other candidate. There were 440 votes cast. How many votes did Susan get?

8.3b 15. The pool dues in 2012 were $275. The dues increased to $320 for the 2013 season. What was the percent of change? Round your answer to the nearest tenth of a percent.

Circle all the numbers you want to select. You must circle all correct numbers.


8.4 The student will apply the order of operations to evaluate algebraic expressions for given replacement values of the variables.

8.4

16. Evaluate the expression. Write your answer in the blank provide. !

!𝑎 − 𝑏! + 𝑐 when a = 95, b = 2 and c = 25

8.4 17. Use !

!𝐶 + 32 to find the Fahrenheit temperature for the Celsius temperature of 35° 𝐶.

8.5 The student will a) determine whether a given number is a perfect square; and b) find the two consecutive whole numbers between which a square root lies.

8.5a

18. Which of the following is a perfect square? A. 6 B. 13 C. 1 D. 3

8.5b 19. Between which two consecutive whole numbers does 75 lie?

Write the number in the blanks provided.


8.6

The student will a) verify by measuring and describe the relationships among vertical angles, adjacent angles,

supplementary angles, and complementary angles; and b) measure angles of less than 360°.

8.6a

20. Use this diagram to complete the following..

A) 1 & 2∠ ∠ B) 1 & 5∠ ∠ C) 3 & 6∠ ∠

D) 8 & 9∠ ∠ E) 9 & 10∠ ∠ F) 3 & 10∠ ∠

8.6a 21. Use the diagram from the previous problem to fill in the blanks with the correct angle measures. If 𝑚�4 = 34! , 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑚�2 = ______________ If 𝑚�5 = 139! , 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑚�2 = ______________ If 𝑚�9 = 43! , 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑚�10 = ______________ If 𝑚�1 = 144! , 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑚�5 = ______________ If 𝑚�4 = 28! , 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑚�7 = ______________

8.6a 22. Find the value of x.

1 2 3 4 5 6 9 10

7 8

Adjacent Angles Complementary Angles

Supplementary Angles Vertical Angles

No relationship

2x + 3 x -‐ 6

Write the corresponding letter for the following angle pairs in the appropriate box. A letter may be used more than once

What is the relationship of the angle pairs listed below? Write the letter of the angle pair in all appropriate boxes below.


8.6b 23. Which of the following angles would appear to be closest to 77O ?

8.7 The student will a) investigate and solve practical problems involving volume and surface area of prisms,

cylinders, cones, and pyramids; and b) describe how changing one measured attribute of a figure affects the volume and surface

area. 8.7a

24. Circle all of the following that have a volume of greater than 250 cubic units.

8.7a 25. What is the surface area of a square based pyramid with a height of 7.2 feet, slant height

of 8.4 feet and base length of 8.8 feet?

8.7b 26. A candy company packages its product in boxes (a rectangular prism) that measures 4 in x 2 in x 5 in. The new supply clerk, by mistake, ordered boxes that measure 4 in x 4 in x 5 in. If the selling price of the original box was $4.50, what should be the cost of new box of candy?

10 cm

3 mm

4 mm 10 mm

5 cm

10 cm

10 ft 4 in

10 in 4 ft

A B C


8.8 The student will a) apply transformations to plane figures; and b) identify applications of transformations.

8.8a

8.8a 28. Use the graph to answer the two following questions.

The transformation of figure ABCD onto figure A’B’C’D’ is a ______

Rotation 180O Clockwise

Dilation with a scale factor of 2

Reflection across the y-‐axis

Translation down 8 units and left 6 units

A B

C

D

27. Use this diagram for the following questions.

Give the coordinates of G’ and H’ after a reflection across the y-‐axis.

G’ ( , )

H’ ( , )

Give the coordinates of A’, B’ and C’ after a rotation of 90o clockwise.

A’ ( , )

B’ ( , )

C’ ( , )

A

B C

G

H

Circle the all the statements you wish to select. You must select all the correct statements.

Transformations may affect the congruency, orientation or location of an image. For the given transformation, what did not change?

Congruency Orientation Location

A’ B’

C’

D’


8.8b 29. The following picture is an example of which type of transformation?

8.9 The student will construct a three-dimensional model, given the top or bottom, side, and front views.

8.9 30. Sketch the top, front and side view of the following figure.

8.9

31. Which of the figures below would have the following views? Front Side Top

A. Reflection

B. Dilation

C. Translation

D. Rotation

Circle the figures that correctly answer the question. You must circle all correct figures.


810 The student will a) verify the Pythagorean Theorem; and b) apply the Pythagorean Theorem.

8.10a 32. 32. Each of the following groups of numbers represents the lengths of the sides of a triangle. Which lengths would produce a right triangle? I. 3, 5, 4 II. 12, 13, 5 III. 8, 9, 10 IV. 10, 24, 26 A. I only B. I, II, and IV C. I and III D. I, II and III

8.10a 33. Find the length of the hypotenuse of a right triangle with legs that measure 8 cm and 13 cm. (Round your answer to the nearest hundredth)

8.10b

34. Albino was enjoying flying a kite on a windy day in March. He wanted to determine how high his kite was flying. He knew that he had let out almost 90 feet of string and he estimated that his dog had run about 65 feet from him to get to a spot directly under the kite. Approximately how high above the ground is his kite?

Solution: _________________________

For this problem you will be using approximate measures.


8.11 The student will solve practical area and perimeter problems involving composite plane figures. 8.11

8.11 36. Find the area of the figure shown. The measurements given are in inches (use 3.14 for π).

20

18

20

For the following problem, round your answer to the nearest tenth of a meter. Use 3.14 for pi.

35. Consider the diagram of a track. If a runner stays on the interior lane, running as close to the field as possible, about how far will he run in 3 laps?


8.12 The student will determine the probability of independent and dependent events with and without replacement.

8.12 37. A deck of cards contained 5 red cards, 9 purple cards, 4 green cards and 2 blue cards. What is the probability that you draw a blue card, replace it, then draw a red card?

Type of Event

Dependent Event Independent Event

Simple Event

Probability

35%

20%

2.5%

8.12 38. You were so hungry when you came home from school that you reached in bag of mixed types of cookies and gobbled up the first cookie you grabbed. It was so good, you reached in for another. If the bag contained 9 chocolate chip cookies, 10 sandwich cookies and 3 peanut butter cookies, what is the probability that the first cookie you ate was a sandwich cookie and the second was a chocolate chip cookie? Write your answer is simplest fraction form.

Select an event and probability from each table. Write the type of event and probability in the blank provided below each table.


8.13 The student will a) make comparisons, predictions, and inferences, using information displayed in graphs; and b) construct and analyze scatterplots.

8.13a 39. This scatterplot shows the relationships between the heights of 10 pairs of

mothers and daughters.

Based on the scatterplot, which of the following statements is true? A The tallest mother has the tallest daughter. B The shortest mother has the shortest daughter. C Taller mothers tend to have taller daughters. D Shorter mothers tend to have taller daughters.

8.13b 40. a) Construct a scatterplot for the following data b) Sketch a line of best fit c) Predict the time to run the mile after 7 weeks of practice.

Weeks of practice

Time to run the mile (in minutes)

1 13.8 2 12.2 3 10.9 4 10.1 5 9


8.13b 41. Describe the relationship that exists between the independent and dependent variables in the previous problem.

A. Positive Relationship C. Negative Relationship

B. No Relationship D. Constant Relationship

8.14 The student will make connections between any two representations (tables, graphs, words, and rules) of

a given relationship. 8.14 42. Which graph would represent the following situation.

A. B.

C. D.

Carlita has $5 saved and plans to save an additional $2 per week .


8.14 43. Which of the following equations best represents the data in the table?

A y = -4x + 2 C y = -2x + 6 B y = -5x D y = -7x - 4

X Y -2 10 0 2 1 -2 3 -10

8.15 The student will a) solve multistep linear equations in one variable with the variable on one and two sides of

the equation; b) solve two-step linear inequalities and graph the results on a number line; and c) identify properties of operations used to solve an equation.

8.15a 44. Solve for x in the following equation.

16𝑥 − 5 = 2

8.15a 45. What value of t makes −2 𝑡 − 4 = 12 a true statement?

8.15a 46. What is the value of c in the following equation? 15 + 4𝑐 = 𝑐

8.15b 47. Graph the solution to the following inequality. 4𝑥 − 8 ≥ 8


8.15b 48. Use the graph to fill in the circle. 5𝑥 + 1 11

8.15b

49.. Solve the inequality and choose all the solutions below. −2𝑥 − 8 ≤ 10 -‐10 9 -‐9 0 -‐21 15

8.15c 50. What property would you use to justify the first step in solving 3 𝑑 − 8 = 21?

A. Associative property of Addition B. Additive inverse property C. Distributive Property D. Commutative Property of Addition

8.15c 51. What property is used to justify the following step?

7𝑥 − 3.5 = 7.5 7𝑥 = 11

Circle all the numbers you want to select. You must circle all correct numbers.


8.16 The student will graph a linear equation in two variables. 8.16

52. Graph 𝑦 = !!𝑥 − 3

8.16 53. Complete the table of values and graph the equation 𝑦 = −3𝑥 − 1 . x -‐1 0 1

y


8.16 54. Choose the table that represents the equation 𝑦 = −𝑥 + 1 A. x -‐2 0 2

y -‐1 1 3

B. x -‐2 0 2

y 3 1 -‐1

C. x -‐2 0 2

y 3 -‐1 -‐1

D. x -‐2 0 2

y -‐1 -‐1 3

8.17 The student will identify the domain, range, independent variable, or dependent variable in a given situation.

8.17 55. Give the domain and range for the function in the table below.

Hours worked(x) 3 6 8 10 Pay(y) $24 $48 $64 $80

8.17 56. The following table shows the number of lawns William mowed(n) and the amount of money he earned(m). Identify the independent and dependent variables in this situation.

Number of Lawns Mowed(n)

Amount of Money Earned(m)

2 $50

3 $75

5 $125

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Math-8 SOLReviewItems 312-13...1$ 13.8$ 2$ 12.2$ 3$ 10.9$ 4$ 10.1$ 5$ 9$ $ $ $ $...

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