MATHEMATICS 320 FROM FALL 2003 - Kansas State University

MATHEMATICS 320 OLD FINAL EXAM FROM FALL 2003

Note. Knowing how to solve the following problems will be useful for the final exam, but the actual

problems, or similar problems, to the ones listed below may or may not appear on your final exam.

(1) Write out 499 ? 3434 ? 77 as a single number to a single exponent. In your answer the base must be in the simplest possible form. For example 2 ? 2 ? 2 ? 2 must be written as 24, not 42. (11 points)

(2) The 9th term of an arithmetic sequence is 59 and the 13th term is 87. What is the initial term of

this sequence?

(11 points)

(3) If the side of a cube increases in size by 5%, then by what percentage does the volume increase?

Give your answer to the nearest one percent.

(11 points)

(4) Find a subset of whole numbers that is closed for multiplication but not closed for addition. (11

points )

(5) Use the problem 43 - 27 to explain some of the advantages and disadvantages of using the standard

subtraction algorithm versus the subtract-from-the-base algorithm.

(11 points) (6) Use the figure below to show that any convex 7-gon has the sum of its vertex angles equal to 900.

(11 points)

(7) (a) Complete the following multiplication table in base five. ?1 2 3 4

(7 points)

1

2

3

4

(b) Compute 343five ? 12five. You can use your table from part (a). (8) Determine whether 97 is a prime and explain how you would be sure.

(7 points) (11 points)

(9) If a = 2 ? 32 ? 53, find four possible values of b so that GCF(a, b) = 2 ? 52.

(11 points)

(10) State and Prove the divisibility test for 5 for a three digit number.

(11 points)

Hint: Start by letting abc represent a three-digit number and then expand by powers of ten.

(11)

Calculate

1.8 ? 1025 3.6 ? 1018

and

express

your

final

answer

in

scientific

notation.

(11 points)

(12) Use the following Venn diagram to represent and find the GCF and LCM of 42 and 60. Make sure

to label your diagram.

(11 points)

(13) Let m(1) = m(2), prove that l m.

(11 points)

Hint: Assume that if corresponding angles are equal, then l m.

l 1

2 m

3

Date: Fall 2004.

1

(14) Inga was making a cake that called for 4 cups of flour. However, she could only find a two-thirds

measuring cup. How many two-thirds measuring cups of flour will she need to make her cake? (11

points)

(15) A television set to be sold at a 13% discount, which amounted to $78. How much would the set sell

for after the discount?

(11 points)

(16) Can you use lattice multiplication for decimals? For example, how would you multiply 3.34 times

1.7?

(11 points)

(17) A student in your class says that if the ratio of oil to vinegar in a salad dressing is 3:4, that means

that 75% of the salad dressing is oil. Another student says the dressing is less than 50% oil. Explain

the correct answer.

(11 points)

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