Work: The converse of the statement If p, then q is If q, then p. Thus choice C is correct.

Transcription

1 Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the specified statement. 1) State the converse of the following: 1) If you study hard, then your grades will be good. A) If you study hard, then your grades will not be good. B) If you do not study hard, then your grades will not be good. C) If your grades are good, then you studied hard. D) If your grades are not good, then you did not study hard. Work: The converse of the statement If p, then q is If q, then p. Thus choice C is correct. Determine the validity of the argument. 2) Martians are green. Frogs are green. Therefore frogs are Martians. A) Not valid B) Valid 2) Indicate whether the sequence is arithmetic, geometric, or neither. 3) 25, 175, 1225, 8575, 60,025,... 3) A) Arithmetic B) Neither C) Geometric Work: Each term is obtained by multiplying 7 to its preceding term. Therefore it is a geometric sequence with first term 25 and common ratio 7. For the number represented by the given Hindu-Arabic numeral, write an equivalent numeral from the indicated system. 4) 100; Mayan 4) A) B) C) D) Work: The Mayan numeration system also included the use of place value, with the place value positions arranged vertically and increasing by factors of 20, except for position three, which increased by a factor of 18. The lower symbol is equivalent to zero and one horizontal line is equivalent to 5. Thus would be = 100. Write a multiplication equation and find the area of the rectangle.

2 5) A rectangle 15 units high and 11 units wide 5) A) = 82.5 square units B) 15 units + 11 units = 26 square units C) (2 15 units) + (2 11 units) = 52 square units D) 15 units 11 units = 165 square units Work: Area of the rectangle = length * width = 15 units * 11 units = 165 square units. Decide whether or not the set is closed under addition. 6) { 8} 6) A) Closed B) Not closed Work: As there is only one member in the set so it is close under addition. Estimate the answer by rounding as indicated. 7) Estimate by rounding to the leftmost digit A) 40,000 B) 48,000 C) 52,000 D) 50,000 7) Work: Rounding 995 to left most digit, we get Rounding 51 to the left most digit, we get 50 Thus estimated value of is 1, = 50,000 Perform the calculation mentally. 8) ) A) 825 B) 633 C) 5000 D) 500 Work: I saw that 25 times 8 equals 200, and multiplying by 200 is easy. Then, 25 times 200 is The product is Find all the factors of the number. 9) 56 9) A) 2, 4, 7, 8, 14, 28 B) 1, 2, 4, 7, 8, 14, 28, 56 C) 1, 2, 3, 4, 7, 8, 14, 18, 28, 56 D) 1, 2, 4, 7, 8, 14, 18, 28, 56 Work: 56 is divisible by each of the numbers: 1, 2, 4, 7, 8, 14, 28, 56 Determine whether the statement is true or false. 10) If a natural number is divisible by 7, then it must also be divisible by ) A) True B) False Work: Counter example is: 28 is divisible by 7 but not divisible by 21.

3 Solve the problem. 11) The city bridge has 9 lanes, all carrying equal numbers of cars. If 414 cars drive across the bridge, how many cars cross in each lane? A) 46 cars B) 55 cars C) 47 cars D) 423 cars 11) Work: 414 cars are divided into 9 lanes equally, so number of cars in each lane = = 46 Complete the magic (addition) square. 12) Use each number 5, 6, 7, 8, 9, 10, 11, 12, and 13 once. 12) A) B) C) D) Work: The sum in any ways comes 27 (horizontally, vertically or diagonally). So option D is correct choice. Find the mixed number or rational fraction in lowest terms represented by the repeating decimal. 13) ) A) B) C) D) Work: Let r = then multiply by 100 gives100r = Subtracting gives 99r = 69 Or r = r = Solve the problem. 14) Find the amount of money in an account after 7 years if $3600 is deposited at 8% annual interest compounded annually. A) $ B) $ C) $ D) $ )

4 Work: Using the formula A = P 1 + r n, we get A = $ A = $ A = $ ) A man earned $3000 the first year he worked. If he received a raise of $400 at the end of each year, what was his salary during the 15th year? A) $ 9000 B) $ 8600 C) None of these D) $ ) Work: The salary will be in arithmetic sequence with common difference $400 and first term $3000. Therefore salary during 15 th year is given by a + n 1 d = $ $400 = $ $400 = $ $5600 = $8600 Write or illustrate the number in the indicated form. 16) , using expanded notation with exponents 16) A) 7( ) + 5( ) + 8( ) + 9( ) B) 7( ) + 5( ) + 8( ) + 9( ) C) 7( ) + 5( ) + 8( ) + 9( ) D) 7( ) + 5( ) + 8( ) + 9( ) Evaluate on a calculator. 17) ( ) - ( ) 17) A) 7808 B) 7856 C) 7832 D) 7592 Determine whether the number is abundant or deficient. 18) ) A) Abundant B) Deficient Work: When the sum of the proper factors of a number is less than the number, it is called a deficient number When the sum of the proper factors of a number is greater than the number, it is called an abundant number. Now the proper factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 75. Their sum = = 172. Since the sum of the proper factors of 150 is greater than 150 so it is abundant.

5 Perform the computation. 19) -3 + ( -20) 19) A) 23 B) -17 C) 17 D) -23 Work: = 3 20 = 23 Write the decimal as a fraction in lowest terms. 20) ) A) B) C) D) Work: 4.07 = = Solve the problem. 21) The trim for a costume costs $38.25 for 4.5 yd. Find the unit price in dollars per yard. 21) A) $ 8.50 per yd B) $ per yd C) $ per yd D) $ per yd Work: Unit price = $ yd = $8.5 per yd 22) A rose garden has 16 bushes in one row, 13 bushes in the next row, then 10, and so on. If there are 51 bushes in the garden, in how many rows are they planted? A) 6 B) 7 C) 5 D) 3 22) Work: It is an arithmetic sequence with first term 16 and common difference -3. Thus we have = 29 [Two rows] = 39 [Three rows] = 46 [Four rows] = 50 [Five rows] = 51 [Six rows] Thus there are 6 rows. For U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z} identify the following. 23) 23) A) {r, t, v, x, z} B) {q, y} C) {q, s, u, w, y} D) { }

6 Work: A is the set of all numbers of U which are not in A. Thus A = { r, t, v, x, z} Solve. 24) An electrician needs 766 feet of 12-gauge wire to do a wiring job. He has 140 feet of 12-gauge wire in stock. How much more wire does he need? A) 766 feet B) 626 feet C) 906 feet D) 622 feet 24)

7 Work: Out of 766 feet he already have 140 feet. So he need 766 feet 140 feet = 626 feet. Determine whether the number is abundant or deficient. 25) 34 A) Abundant B) Deficient Work: When the sum of the proper factors of a number is less than the number, it is called a deficient number When the sum of the proper factors of a number is greater than the number, it is called an abundant number. Now the proper factors of 34 are: 1, 2, 17. So their sum = = 20. Since the sum of the proper factors is less than 34 so it is deficient.