Geo - H2 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Find the next item in the pattern 2, 3, 5, 7, 11,... a. 13 c. 15 b. 12 d. 17 2. The table shows the population 65 years and over by age and sex according to the US ensus ureau, ensus 2000 Summary file. Make a conjecture based on the data. Population 65 Years and Over by ge and Sex: 2000 (numbers in thousands) 65 to 74 years 75 to 84 years 85 years and over Women 10,088 7,482 3,013 Men 8,303 4,879 1,227 a. Women outnumbered men in the 65 years and over population. b. Men outnumbered women in the 65 years and over population. c. There are more 65 years old and over in 2000 than in previous years. d. There are fewer 65 years old and over in 2000 than in previous years. 3. Show that the conjecture is false by finding a counterexample. If a > b, then a b > 0. a. a = 11, b = 3 c. a = 3, b = 11 b. a = 11, b = 3 d. a = 11, b = 3 4. There is a myth that a duck s quack does not echo. group of scientists observed a duck in a special room, and they found that the quack does echo. Therefore, the myth is false. Is the conclusion a result of inductive or deductive reasoning? a. Since the conclusion is based on a pattern of observation, it is a result of inductive reasoning. b. Since the conclusion is based on a pattern of observation, it is a result of deductive reasoning. c. Since the conclusion is based on logical reasoning from scientific research, it is a result of inductive reasoning. d. Since the conclusion is based on logical reasoning from scientific research, it is a result of deductive reasoning. 5. etermine if the conjecture is valid by the Law of Syllogism. Given: If you are in alifornia, then you are in the west coast. If you are in Los ngeles, then you are in alifornia. onjecture: If you are in Los ngeles, then you are in the west coast. a. No, the conjecture is not valid. b. Yes, the conjecture is valid.
6. gardener has 26 feet of fencing for a garden. To find the width of the rectangular garden, the gardener uses the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width of the rectangle. The gardener wants to fence a garden that is 8 feet long. How wide is the garden? Solve the equation for w, and justify each step. P = 2l + 2w Given equation 26 = 2(8) + 2w [1] 26 = 16 + 2w Simplify. 16 = 16 10 = 2w Subtraction Property of Equality Simplify. 10 2 = 2w 2 [2] 5 = w Simplify. w = 5 Symmetric Property of Equality a. [1] Substitution Property of Equality [2] ivision Property of Equality The garden is 5 ft wide. b. [1] Simplify [2] ivision Property of Equality The garden is 5 ft wide. 7. Write a justification for each step. c. [1] Substitution Property of Equality [2] Subtraction Property of Equality The garden is 5 ft wide. d. [1] Subtraction Property of Equality [2] Simplify The garden is 5 ft wide. m JKL = 100 m JKL = m JKM + m MKL [1] 100 = (6x + 8) + (2x 4) Substitution Property of Equality 100 = 8x + 4 Simplify. 96 = 8x Subtraction Property of Equality 12 = x [2] x = 12 Symmetric Property of Equality a. [1] Transitive Property of Equality [2] ivision Property of Equality b. [1] ngle ddition Postulate [2] ivision Property of Equality c. [1] ngle ddition Postulate [2] Simplify. d. [1] Segment ddition Postulate [2] Multiplication Property of Equality
8. Fill in the blanks to complete the two-column proof. Given: 1 and 2 are supplementary. m 1 = 135 Prove: m 2 = 45 Proof: Statements Reasons 1. 1 and 2 are supplementary. 1. Given 2. [1] 2. Given 3. m 1 + m 2 = 180 3. [2] 4. 135 + m 2 = 180 4. Substitution Property 5. m 2 = 45 5. [3] a. [1] m 2 = 135 [2] efinition of supplementary angles [3] Subtraction Property of Equality b. [1] m 1 = 135 [2] efinition of supplementary angles [3] Substitution Property c. [1] m 1 = 135 [2] efinition of supplementary angles [3] Subtraction Property of Equality d. [1] m 1 = 135 [2] efinition of complementary angles [3] Subtraction Property of Equality 9. Two angles with measures (2x 2 + 3x 5) and (x 2 + 11x 7) are supplementary. Find the value of x and the measure of each angle. a. x = 5; 60 ; 30 c. x = 5; 60 ; 120 b. x = 6; 85 ; 95 d. x = 4; 40 ; 90 10. Two lines intersect to form two pairs of vertical angles. 1 with measure (20x + 7)º and 3 with measure (5x + 7y + 49)º are vertical angles. 2 with measure (3x 2y + 30)º and 4 are vertical angles. Find the values x and y and the measures of all four angles. a. x = 6; y = 10; 127 ; 127 ; 28 ; 28 c. x = 5; y = 5; 107 ; 107 ; 73 ; 73 b. x = 8; y = 11, 167 ; 167 ; 13 ; 13 d. x = 7; y = 9; 147 ; 147 ; 33 ; 33 Numeric Response
11. Find a value for x that provides a counterexample for this conjecture. For all real numbers x, 4x 8 3x 6 = 4 3. 12. In the quadrilateral, m 1 + m 2 + m 3 + m 4 = 360. If m 2 = 3m 1, m 3 = m 1 + 6, and m 4 = m 1, find m 3 in degrees. Matching Match each vocabulary term with its definition. a. conjecture b. inductive reasoning c. deductive reasoning d. conclusion e. biconditional statement f. hypothesis g. counterexample h. conditional statement 13. an example that proves that a conjecture or statement is false 14. a statement that is believed to be true 15. the part of a conditional statement following the word then 16. the part of a conditional statement following the word if 17. the process of reasoning that a rule or statement is true because specific cases are true Match each vocabulary term with its definition. a. conclusion b. converse c. inverse d. negation e. hypothesis f. truth value g. contrapositive 18. a statement can have a truth value of true (T) or false (F) 19. operations that undo each other
20. the contradiction of statement by using not, written as 21. the statement formed by exchanging the hypothesis and conclusion of a conditional statement 22. the statement formed by both exchanging and negating the hypothesis and conclusion
Geo - H2 Practice Test nswer Section MULTIPLE HOIE 1. NS: The prime numbers make up the pattern. The next prime is 13. The prime numbers make up the pattern. What is the next prime number? The prime numbers make up the pattern. What is the next prime number? Is there a prime number that is greater than 11 but smaller than 17? PTS: 1 IF: asic REF: Page 74 OJ: 2-1.1 Identifying a Pattern NT: 12.5.1.a TOP: 2-1 Using Inductive Reasoning to Make onjectures 2. NS: For every age group 65 years and over, the number of women is greater than the number of men. The data supports the conjecture that women outnumbered men in the 65 years and over population. Look at the table's data. re there more men or women 65 years and over? Look at the table's data. Is there any information about previous years? Look at the table's data. Is there any information about previous years? PTS: 1 IF: verage REF: Page 75 OJ: 2-1.3 pplication NT: 12.3.5.a TOP: 2-1 Using Inductive Reasoning to Make onjectures 3. NS: Pick values for a and b that follow the condition a > b. Then substitute them into the second inequality to see if the conjecture holds. Values of a and b a > b Let a = 4 and b = 1. 4 > 1 Let a = 11 and b = 3. 11 > 3 Let a = 11 and b = 3. 11 > 3 a b > 0 onclusion 4 > 0 1 The conjecture holds. 11 > 0 3 The conjecture holds. 11 3 < 0 The conjecture is false. a = 11 and b = 3 is a counterexample. The conjecture is false when a is positive and b is negative.
In this case, a/b is greater than zero, so it is not a counterexample. In this case, a is not greater than b. The counterexample should have a > b and a/b less than or equal to 0. In this case, a is not greater than b. a > b is the condition of the conjecture. The counterexample should have a > b and a/b less than or equal to 0. PTS: 1 IF: verage REF: Page 76 OJ: 2-1.4 Finding a ounterexample NT: 12.3.5.a TOP: 2-1 Using Inductive Reasoning to Make onjectures 4. NS: The scientists determined the myth was false because they heard an echo by observing the duck. Inductive reasoning is based on a pattern of observation. eductive reasoning is based on logical reasoning. Inductive reasoning is based on observation. This conclusion was based on observation instead of logical reasoning. PTS: 1 IF: asic REF: Page 88 OJ: 2-3.1 pplication NT: 12.3.5.a TOP: 2-3 Using eductive Reasoning to Verify onjectures 5. NS: Let p, q, and r represent the following. p: You are in alifornia. q: You are in the west coast. r: You are in Los ngeles. You are given that p q and r p Since p is the conclusion of the second statement and the hypothesis of the first statement, reorder the statements like this r p and p q. y the Law of Syllogism, if r p and p q are true, then r q is true. r q is the statement, If you are in Los ngeles, then you are in the west coast. The Law of Syllogism states that if (if p, then q) and (if q, then r) are true statements, then (if p, then r) is a true statement. PTS: 1 IF: verage REF: Page 89 OJ: 2-3.3 Verifying onjectures by Using the Law of Syllogism
NT: 12.3.5.a TOP: 2-3 Using eductive Reasoning to Verify onjectures 6. NS: P = 2l + 2w Given equation 26 = 2(8) + 2w [1] Substitution Property of Equality 26 = 16 + 2w Simplify. 16 = 16 10 = 2w Subtraction Property of Equality Simplify. 10 2 = 2w 2 [2] ivision Property of Equality 5 = w Simplify. w = 5 Symmetric Property of Equality The variables P and l are substituted, not simplified. Use the Substitution Property. heck the properties. heck the justifications. PTS: 1 IF: verage REF: Page 105 OJ: 2-5.2 Problem-Solving pplication NT: 12.5.2.e TOP: 2-5 lgebraic Proof 7. NS: m JKL = m JKM + m MKL [1] ngle ddition Postulate 100 = (6x + 8) + (2x 4) Substitution Property of Equality 100 = 8x + 4 Simplify. 96 = 8x Subtraction Property of Equality 12 = x [2] ivision Property of Equality x = 12 Symmetric Property of Equality heck the properties. heck the justifications. The Segment ddition Postulate refers to segments, not angles. PTS: 1 IF: verage REF: Page 106 OJ: 2-5.3 Solving an Equation in Geometry NT: 12.5.2.e TOP: 2-5 lgebraic Proof 8. NS: Proof: Statements Reasons 1. 1 and 2 are supplementary. 1. Given
2. m 1 = 135 2. Given 3. m 1 + m 2 = 180 3. efinition of supplementary angles 4. 135 + m 2 = 180 4. Substitution Property 5. m 2 = 45 5. Subtraction Property of Equality heck to the given information. To get from Step 4 to Step 5, use subtraction, not substitution. The angles are supplementary, not complementary. PTS: 1 IF: verage REF: Page 111 OJ: 2-6.2 ompleting a Two-olumn Proof TOP: 2-6 Geometric Proof 9. NS: Step 1 reate an equation The angles are supplements and their sum equals 180. (2x 2 + 3x 5) + (x 2 + 11x 7) = 180 NT: 12.3.5.a Step 2 Solve the equation 3x 2 + 14x 12 = 180 3x 2 + 14x 192 = 0 (3x + 32)(x 6) = 0 x = 32 3 or 6. When x = 32 3 x 2 + 11x 7 = 10.6. ngles cannot have negative measurements, so x = 6., the measurement of the second angle is Step 3 Solve for the required values The measurement of the first angle is 2x 2 + 3x 5 = 2(6) 2 + 3(6) 5 = 85. The measurement of the second angle is x 2 + 11x 7 = (6) 2 + 11(6) 7= 95. The angles are supplements. Use the definition of supplements to solve for x. heck for algebra mistakes. When x equals 5, the second angle is not 120 degrees. The angles are supplements. Use the definition of supplements to solve for x. PTS: 1 IF: dvanced NT: 12.2.1.f TOP: 2-6 Geometric Proof 10. NS: Step 1 reate a system of equations.
m 1 = m 3 20x + 7 = 5x + 7y + 49 15x 7y = 42 The sum of the measures of supplementary angles equals 180. m 1 + 2 = 180 20x + 7 + 3x 2y + 30 = 180 23x 2y = 143 reate a system of equations. 15x 7y = 42 23x 2y = 143 Step 2 Solve the system of equations. 15x 7y = 42 23x 2y = 143 30x + 14y = 84 Multiply the first equation by 2. 161x 14y = 1001 Multiply the second equation by 7. 131x = 917 dd the two equations together. x = 7 ivide both sides by 131. Solve for y. Substitute x = 7 into 15x 7y = 42. 15(7) 7y = 42 y = 9 The values are x = 7 and y = 9. Step 3 Solve for the four angles. ngle 1: (20(7) + 7) = 147 ngle 2: (3(7) 2(9) + 30) = 33 ngle 3: (5(7) + 7(9) + 49) = 147 ngle 4 and angle 2 are vertical and thus have equal measures. The measurement of angle 4 is 33. The measures of all four angles are 147, 147, 33, and 33. Use the definitions of supplementary and vertical angles to create a solvable system of equations. Use the definitions of supplementary and vertical angles to create a solvable system of equations. Use the definitions of supplementary and vertical angles to create a solvable system of equations. PTS: 1 IF: dvanced NT: 12.2.1.f TOP: 2-7 Flowchart and Paragraph Proofs
NUMERI RESPONSE 11. NS: 2 PTS: 1 IF: dvanced NT: 12.3.5.a TOP: 2-1 Using Inductive Reasoning to Make onjectures 12. NS: 65 PTS: 1 IF: verage NT: 12.2.1.f TOP: 2-5 lgebraic Proof MTHING 13. NS: G PTS: 1 IF: asic REF: Page 75 TOP: 2-1 Using Inductive Reasoning to Make onjectures 14. NS: PTS: 1 IF: asic REF: Page 74 TOP: 2-1 Using Inductive Reasoning to Make onjectures 15. NS: PTS: 1 IF: asic REF: Page 81 16. NS: F PTS: 1 IF: asic REF: Page 81 17. NS: PTS: 1 IF: asic REF: Page 74 TOP: 2-1 Using Inductive Reasoning to Make onjectures 18. NS: F PTS: 1 IF: asic REF: Page 82 19. NS: PTS: 1 IF: asic REF: Page 83 20. NS: PTS: 1 IF: asic REF: Page 82 21. NS: PTS: 1 IF: asic REF: Page 83 22. NS: G PTS: 1 IF: asic REF: Page 83