Math 2 Finite Mathematics W '95 Allen Klinger
If certain there's only 1 correct statement, select its (a), (b), (c) letter: do not guess. If any answer is clearly wrong choose the letter between the 2-others to best reflect your knowledge. If completely unsure or just unclear about the question and basic answers, choose (m). Answer all questions.
I. Beginning
1. When two quantities, say a and b, are compared, we write a is greater than b (or a is more than b) as: a > b .
Which statement is true?
(a) 1/103 > 1/10-3 (b) 103 > 1/10-3 (c) 103 > 10-3
2. For the given pair of equations which is true about the variables x and y ?
2x + 3y = 2
6x + y = 12
(a) x and y have the same sign.
(b) x and y are whole numbers.
(c) x > y.
3. For the equation x2 + x - 1, solution values are:
(a) Odd. (b) Imaginary. (c) Irrational.
4. We write the logarithm of a number n to base 10 by "log n".
Which statement is true?
(a) log ( n + m) = ( log n ) + ( log m )
(b) log ( n * m) = ( log n ) * ( log m )
(c) log ( n * m) = ( log n ) + ( log m )
5. There are exactly how many ways to arrange 5 things?
(a) 120 (b) 15 (c) 54
I. Intended Answers
| 1 ... b | 2 ... c | 3 ... b | 4 ... c | 5 ... a |
1. When two quantities, say a and b, are compared, we write a is greater than b (or a is more than b) as: a > b . Which statement is true?
(b) 103 > 10-3
Use the ideas of reciprocal and exponents. If you have a number z the reciprocal of it can be written two ways, 1/ z or z -1 . Simply trying to decode the strings of numbers in the answers using these facts eliminates some possiblities.
2. For the given pair of equations which is true about the variables x and y ?
2x + 3y = 2
6x + y = 12
(c) x > y.
Solving is possible if you multiply one equation by 3 and subtract the result from the other. This is because you can eliminate a variable (an x or y ) that way. After doing that you can use either equation to substitute the (now known) x or y value to find the other. Then there is only one possible answer.
3. For the equation x2 + x - 1, solution values are:
(b) Irrational.
Use the quadratic formula to solve general equations of form ax2 + bx + c = 0. In the formula, after the - b there is a radical, a square root. The argument of the square root is b2 - 4 ac . Substitute the coefficients from the above, namely a = 1, b = 1, c = -1 and find the value of that to be 5 and notice that 5 isn't a perfect square (4 and 9 are).
4. We write the logarithm of a number n to base 10 by "log n". Which statement is true?
(c) log (n * m) = ( log n ) + ( log m )
A log is the power you need to raise something (here 10) to, to get a number:
10log 100 = 100 is an easy way to check facts .
So 10log n * m = n * m and
10log n = n both hold, as does the latter when m replaces n .
Since 10a10b = 10(a + b), (c) holds.
5. There are exactly how many ways to arrange 5 things?
a) 120
Any of 5 in the first place, any of 4 in the second, etc. All of the first times all the remainder.
Product of 5(4)(3)(2)(1) is 120.