** Math 2 Finite Mathematics** W '95

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*

Which statement is true?

(a) 1/10^{3} > 1/10^{-3} (b) 10^{3} > 1/10^{-3} (c) 10^{3} > 10^{-3}

2. For the given pair of equations which is true about the variables **x** and **y **?

2**x **+ 3**y = **2

6**x **+ **y = **12

(a) **x** and **y **have the same sign.

(b) **x** and **y **are whole numbers.

(c) **x** > **y**.

3. For the equation **x**^{2} + **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*

(b) 10^{3} > 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 **?

2**x **+ 3**y = **2

6**x **+ **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 **x**^{2} + **x** - 1, solution values are:

(b) Irrational.

Use the quadratic formula to solve general equations of form a**x**^{2} + b**x ** + 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:

10^{log 100} = 100 is an easy way to check facts .

So 10^{log n * m }= **n ***** m **and

10^{log n }= **n ** both hold, as does the latter when **m ** replaces **n** .

Since 10^{a}10^{b} = 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.