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MOCK EXAM 1 β Fall 2015 Directions: Be prepared to explain your solution and show your work. This is only a small sample of problems from the topics you studied in MyMathLab modules 1 & 2, and the classroom activities from round 1. If you make any mistakes on this mock exam than you have identified a weakness and you should go to your classroom activities and MML for further practice on similar problem. If you donβt you may get that type of problem wrong on the actual exam. Computational & Conceptual questions 1. Give an example of the associative property; the distributive property; the commutative property. 2. Name the property illustrated in each equation below: a. 3 + (π₯ + 6) = 3 + (6 + π₯) b. 3 + (6 + π₯) = (3 + 6) + π₯ c. 9 + π₯ = π₯ + 9 3. Name the base and the exponent in each of the following, then write in expanded form and evaluate. a. (β5)2 b. β52 c. β(β3)2 d. β(β3)4 4. Will the sum of 4 and β9 be positive or negative? Why? 5. When given an expression containing both multiplication and division, which operation should be performed first? 6. How many factors does a prime number have? How many factors does a composite number have? 7. Define absolute value. 8. Estimate the product of 865 and 171 by rounding to the hundreds first. 9. Find the difference: 4,000 β 103 10. Find the quotient of 5100 and 25. 11. Suppose you wish to fence a yard that is 18 feet by 20 feet. a. How much fencing will you need? (Hint: find the perimeter.) b. How much sod can you plant in the fenced are? (Hint: find the area.) 1 12. Write a mathematical expression for each phrase below. Define a variable for the unknown input. a. Twice the input decreased by 12. b. The sum of the input and six times the same input. c. Two subtracted from twice the input. 13. Find the opposite of the absolute value of β3. 14. Perform the indicated operations. Simplify your solution as much as possible. 18 a. 14 + (β8) β 3 i. 100 ÷ 2 β 10 e. β16 + 2 3 b. β7 β (β4) + 5 f. 2 + (4 β 7)3 3 c. 3β2 g. 24 ÷ 23 β 6 d. β547 β9 h. 15. (a) Find all eight factors of 54. 72 + (β3 + 12 ÷ 3) (b) Find the prime factorization of 108. 16. Circle all the factors of 8 in the following list of numbers {48, 1, 8, 2, 4, 16, 32}. 17. Round 49,624 to the nearest thousand. 2 Activity based questions 1. Rewrite the given expression using the distributive property: β7(π β 3) 2. Take a look at each of the problems below and DO NOT CALCULATE THEM. Instead, write out in words the steps you would take to compute them. a. 1 + 7 β (9 β 10) b. 16 + 7(4 2 β 3 β 6) Now create several of your own ______________ 5 c. 1 + 7 β 3 β 10 3. Now, DO the calculations. Simplify the above order of operations problems ONE STEP AT A TIME, using the steps you described above. 4. Create an expression that encodes the following set of steps: a. Step 1: Square 4. Step 2: Multiply 3 by 9. Step 3: Add the result of step 1 to the result of step 2. Step 4: Multiply the result of step 3 by 7. b. Create your own: Step 1, Step 2, Step 3, Step 4 5. Simple relations between variables Input x -4 -2 0 4 6 Output y -7 -3 1 5 13 a . What pattern do you detect across the π₯ row? b. What pattern do you detect across the π¦ row? c. As the values of π₯ ____________________, the values of π¦ _______________________ d. When the input value, π₯, is 0, what is the output value, π¦? e. When the output value, π¦, is β3, what is the input value, π₯? f. When the input value, π₯, is 1, what is the output value, y? g. What is the formula for finding the π¦ value, if you are given a π₯-value? π¦ = ___________ 3 6. Complete the Evaluation Machine: Verbal Steps Input, x Result of step 1 Result of step 2 Result of step 3 Output , y = 0 0 1 2 β3 β6 1. 3 12 0 3 7. Consider the expression: 9 36 12 39 39 Expression π₯ \ input / 2. 3. π¦= / Output \ 3(2π₯ β 4)2 + 1 The expression above has an implied order of operations, which we need to follow in our steps. Write out the verbal steps in the proper order. \ input / / Output \ 8. Write the symbolic expression based on the given verbal steps \ input / 1. Multiple the input by negative 5 2. Step 1 is subtracted from 3 3. Divide the result of step 2 by 3 / Output \ π₯ π¦= 9. Use any of the strategies you have used in round 1 packet to solve a new Full Parking Lot Problem. In this full parking lot at El Camino College Compton Center, there are 25 parking spots and 90 wheels. Remember the spots are all filled with cars or motorcycles. Find the number of cars and motorcycles in the given parking lot. 4