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Q2 Benchmark Review (A.4a) 1. 9 Solve for C: F C 32 . 5 Set 4 3. Solve the following for r: C 2π r A 5 C F 32 9 A 2C π B 9 C F 32 5 B π 2C C 5 C (F 32) 9 C C 2π D 2π C D 2. A B C 5 F 32 9 Solve for h: V 3V π r2 V 3π r 2 C 3r 2 Vπ D 3Vπ r 2 1 π r 2h 3 4. Solve for h: A = A h= B h= C h= 2b A D h= A 2b Ab 2 2A b 1 bh 2 Q2 Benchmark Review 5. Which property of equality does this illustrate? Set 4 9. The first step in solving 2a + (a + 3) > 8 leads to (2a + a) + 3 > 8. This step is an example of which property? A B C D associative property of inequality commutative property of inequality distributive property of inequality addition property of inequality If x y z , then z x y . A B C D reflexive property transitive property addition property symmetric property 6. Which property of equality is this? “Every number is equal to itself”; for example, 3 = 3. A B C D reflexive property transitive property addition property symmetric property 7. Which property of the real numbers is illustrated? (3x )y 3(xy ) A B C D closure property commutative property associative property transitive property 8. Which property of the real numbers is used here? 4(x 2) 4x 8 A B C D distributive property associative property commutative property closure property Q2 Benchmark Review Set 4 Use this sequence to answer the next three questions. 3(x + 4) + x = (3x + 3 4) + x (3 4 + 3x) + x 12 + (3x + x) 12 + 4x Step 1 Step 2 Step 3 Step 4 1 1 4 x , step I 4 through step IV below were completed. 13. To simplify = 1 1 1 4 x 4 4 II. = 1 1 1 4 x 4 4 III. = 1 1 1 x 4 IV. = 1 x 4 I. 1 1 4 x 4 10. How do you justify Step 1? A B C D associative property of multiplication commutative property of multiplication distributive property of multiplication additive identity Which properties were used for steps I and II? 11. How do you justify Step 2? A B C D associative property of multiplication commutative property of addition distributive property of multiplication additive identity 12. How do you justify Step 3? A B C D associative property of addition commutative property of multiplication distributive property of multiplication additive identity A the distributive and associative properties of multiplication B the distributive property of multiplication and the property of reciprocals C the identity and the distributive properties of multiplication D the identity property of multiplication Q2 Benchmark Review Set 4 14. In solving the equation, 2x 5 33 , the following steps and reasons are given. Step 1. 2x 5 33 Reason 1. given 2. (2x 5) 5 33 5 2. subtraction property of equality 3. 2x (5 5) 33 5 3. ??? 4. 2x 0 28 4. additive inverse property 5. 2x 28 5. addition 6. 2x 28 2 2 7. x 14 6. division property of equality 7. division Which of the following properties correctly justifies step #3? A B C D commutative property of addition subtraction property of equality additive inverse property associative property of addition Q2 Benchmark Review (A.4d) 15. What is the solution to 5n 4 21 ? A B C D n = 5 n = 3 n= 3 n= 5 16. What is the solution to 4(n 1) 2(11 n ) ? A B C D n=3 n=4 n=7 n = 13 17. What is the solution to 2 n 24 ? 3 A B C D n = 12 n = 16 n = 36 n = 72 Set 4 18. What is the solution to 4(x 1) 8 ? A B x= 1 x= 2 C x= D 3 2 4 x= 3 19. Solve this equation for y. (2y – 5) – 8 = (3 – y) + 2 A B C D y=2 y=4 y=6 y = 18 20. Mrs. Corbett rented a truck to move some furniture. The rental charge is $60 plus $0.25 per mile. She wants to spend no more than $180, not including tax. What is the maximum number of miles that she can drive the truck? A B C D 85 miles 360 miles 480 miles 720 miles