2 nd Nine Weeks Exam Study Guide

1. 2nd Nine Weeks Exam Study Guide 1. Mary has two spinners. One is numbered 1-6 and the other is numbered 1-3. If she spins both spinners, what is the probability that both spinners will show the number 3? • Kristin is going to the school dance. She has two dresses, six necklaces, and five pairs of earrings. How many different outfits does she have to choose from if she chooses only one dress, one necklace, and one pair of earrings? 2 x 6 x 5 = 60 3. Set A = { -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5} How many ways can you choose a negative or even number from Set A? Negative or even = {-5, -4, -3, -2, -1} or {-4, -2, 0, 2, 4} but since we don’t count the same element twice {-5, -4, -3, -2, -1, 0, 2, 4} for a total of 8

2. 4. Your teacher randomly selects a number from 1 to 50. What is the probability of you guessing the same number that your teacher selected in 1 try? Express your answer as a percent. 1 out of 50 = 2 out of 100 = 2% • John spins a spinner twice that is divided into 4 equal parts numbered 1 through 4. a. Make a tree diagram and list the outcomes in a sample space. • b. What is the probability that the sum of the two spins would equal 3? 2:16=1:8 • If P(G) = , determine P(G)’ • 7. You are spinning a 4-section spinner and rolling a die. How many events? 2

3. You flip a coin 75 times and document the results. Is this an example of theoretical or experimental probability? Experimental • 9. RHMS Wildcats are playing the Mustangs in a playoff game. When the Wildcats make a touchdown they will score 4 points. When the Mustangs make a touchdown they will score 7 points. Is this a fair game? No!

4. 52+82=102 25 + 64 = 100 89 = 100; false so it will not form a right triangle because it does not satisfy the Pythagorean theorem 2. 1. 3. 4. 6. 52+82=102 25 + 64 = 100 89 = 100; false so it will not form a right triangle because it does not satisfy the Pythagorean theorem 5. 7. Since the square root of 10 is between 3 and 4 the longest side is 10 ft. and should be considered the hypotenuse in the following: 2 + 92=102 10 + 81 = 100 91 = 100; false so it will not form a right triangle because it does not satisfy the Pythagorean theorem.

5. 8. The square roots of 225 are -15 and 15. 9. The square root of 24 is between 4 and 5 so, 11 is greatest. 10. The square root of 6, the square root of 12, 5, 12 11. The square root of 16 is 4 therefore is it rational. 12. The square root of 3 is irrational. The area of the square is 400 sq. ft. The side, s, is the square root of the area. Therefore, the square root of 400 is 20, so the side length is 20 ft. 7 squared = 49 8 squared = 64; therefore the best whole number estimate for the square root of 62 would be 8.

6. Determine if the point is a solutionWe do this by substitution. • y = 2x + 5 (5, 15) 15 = 2(5) + 5 15 = 10 + 5 15 = 15, true; yes this point is a solution 2.y = x + 4 (3, 9) 9 = 3 + 4 9 = 7; false; no, this point is not a solution

7. y < -3x + 2 (3, 7) • 7 < -3(3) + 2 • 7 < -9 + 2 • 7< -7; false, no this point is not a solution Solve for y. • y = 3x + 2 if x = 7 • y = 3(7) + 2 • y = 21 + 2 • y = 23 y = -2x -4 if x = 3 y = -2(3) – 4 y = -6 + (-4) y = -10

8. Solve the following : • 7n + 6n – 5 = 4n +4 13n – 5 = 4n + 4 13n – 4n -5 = 4n – 4n + 4 9n – 5 = 4 9n -5 + 5 = 4 + 5 9n = 9 9n/9 = 9/9 n = 1 • 8 + 8y = -16 y = -3 4. 7p + 4 = 29 + 2p p = 5 5. -3x > 30 6. 10 < x + 7

9. 2. y + 2(y - 5) = 2y + 2y + 2y – 10 = 2y + 2 3y – 10 = 2y + 2 +10 + 10 3y = 2y + 12 -2y -2y y = 12

10. Write each expression with one exponent: 1.7 x 7 x 7 x 7 x 7 x 7 x 7 = 77 • 3∙3∙3∙3∙3∙3∙3∙3∙3 = 39 3. Write with a positive exponent: x-3 4. x2y2 v2

11. Find the missing side length 5 3 • 2. The side is 10. The side is 4. 8 • Solve. • A square lot has an area of 400 ft.2 How long is the side of the square? The side is the square root of the area; therefore, the side length is 20 ft. • 2. Joey has a square bedroom rug with an area of 225 ft2. What is length of one side of the rug? The length of one side is the square root of 225; therefore, the side of the rug is 15 ft. 6

12. Function or Not • 2. NO YES YES • {(-4, -3), (-3, -7), (1, -8), (3, -9), (4, -5)} • {(0, 6), (3, 1), (-2, 5), (-6, 4), (6, 1)} • 5. {(5, -1), (5, 1), (5, -4)} YES NO

13. Simplify. 2. Estimate. 5 + 5 = 10 3. Solve. = 4. What are the square roots of 25? -5 & 5 • Multiply. = 6. Simplify .

14. Determine if each of the following is a rational or irrational number. • 0 rational 2. irrational 3. 3.1415926535…irrational 4. 3.14159 rational 6. -1 rational

15. Scientific Notation • Write 2,008, 050,000 in scientific notation. 2.00805 x 109 2. Write 0.0000603 in scientific notation. 6.03 x 10-5 3. Write 6.7 x 104 in standard notation. 67,000 4. Write 3.6 x 10-2 in standard notation. 0.036

16. For g(x) = 2x2 + 3; find g(2) • g(2) = 2(2)2 + 3 = 2(4) + 3 = 8 + 3 = 11 • For f(x) = 5x – 3; find f(-1) • f(-1) = 5(-1) – 3 = -5 + (-3) = -8 • 3. Name the domain and range for the relation. • {(-1, 2), (3, 5), (-1, 4), (3, -7)} • Domain: {-1, 3} Range: {-7, 2, 4, 5} • 4. Find the range of the relation y = 5 – x for the domain {0, 1, 2, 3} • Range: {2, 3, 4, 5}

17. Write the correct algebraic expression for each phrase. • The quotient of 5 and y 5/y2. The product of 7 and m 7m 3. x less than 6 6 – x4. r less 10 r - 10 5. Twice x 2x Simplify each expression. 3(x + 6) + 2(x – 1)2. -(2b + 8) + 3(b + 2) 3x + 18 + 2x – 2 = -2b – 16 + 3b + 6 5x + 16 b - 10

20. Complete the following statements. • {15, 22, 23, 26} {23, 44, 65} = {15, 22, 23, 26, 44, 65} • {15, 22, 23, 26} {15, 23, 44, 65} = {15, 23} • What is the symbol for “is a subset of”? • What is the symbol for “is an element of”? • What is the symbol for “empty set”? • If two sets having nothing in common they are called disjoint sets.

21. True or False • TRUE{even whole numbers} c{all whole numbers} • True{Snickers, Milky Way} = {candy bars} • FALSE{days of the week} = {March, April, May} 4. TRUE{The letters is the word “stress”} = {s,t,r,e} 5. FALSE{odd numbers} c{even numbers}