## Level of Mathematical Background Required

This course assumes mathematical facility in the following topics usually associated with "precalculus" and introductory statistics

- Ordered Pairs, n-tuples
- Linear_equation
- Sets
- Solving inequalities and equations
- Properties of functions
- Composite_functions
- Matrices
- Frequency_distribution
- axioms Basic probability through simple conditional probability
- Basics of Boolean algebra

You have some familiarity with these concepts:

- Polynomial_functions
- Rational_functions
- Exponential_functions
- Logarithmic_functions
- Sequence]s and [[series_(mathematics) series]
- Mathematical_induction
- Limits

## Self Test

[[table]]

[[row]]

[[cell style="vertical-align: top;"]]

On the grid to the right …

**1.**

**Q124.** On the grid below …

…draw the line $y=2x + 1$

…shade the area for $x>5$ and the area for $y < 3$

…shade the area for y >= 2x + 1

**Q125.** Write an equation for the line passing through the points (3,2) and (0,5).

#### Sets and Logic

**4.** Write an equation for the line passing through the points (3,2) and (0,5).

If A = {red, blue, yellow, green} and B = {blue, green, violet, orange},

**5.** what is A B?

**6.** what is A intersection B?

If A and B are sets that are neither identical nor disjoint, sketch them in a VENN Diagram, and label the areas representing…

**7**. …A and B

**8.** …A but not B

#### Inequalities

**9.**If a > b and b > c what do we know about a and c?

$a > c$ | $a < c$ | $a = c$ | $a \leq c$ | $a \geq c$ | depends what c is |

If a < b then

**10.**

**11.**

**12.** If $3 x + 2 y = 7$ and $x + y = 10$, what are $x$ and $y$?

**13.** If $a > 0$ and $b > 0$ and $a < b$ then $\frac{1} {a} \bigcirc \frac{1}{b}$?

#### Algebra

**14.** Simplify $(ab + ac)=$

**15.** Simplify $\frac{(a + b) (3a + 4c)}{(a + b) (a - b)}=$

**16.** Simplify $\frac{(a + b) (3a + 4c)}{(a^2 - b^2)}=$

**17.** Simplify $\frac{(a - b) (c - d)}{(d - c) (b - a)}=$

#### Functions

**18.** If $f(x) = x^2$, what is the range of $f(x)$?

**19.** If $1000 = 10^x$ what is $x$?

**20.** If $f(x) = 3x + 2$ and $g(x) = x^2$, what is f(g(4))?

#### Notation and such

**21.** Consider the matrix below. What is element **a _{2,3}**?

$A = \left( \begin{tabular} {c c c} 3 & 4 & 2 \\ 1 & 1 & 7 \\ 1 & 8 & 8 \\ 4 & 0 & 5 \end{tabular} \right)$

**22.**If $S_{n+1} = 2 S_n + 3$, and $S_4 = 33$, what is $S_5$?

#### Matrices

23. $\left( \begin{tabular} {c c c} 3 & 4 & 2 \\ 1 & 1 & 7 \\ \end{tabular} \right) \times \left( \begin{tabular} {c c} 3 & 4 \\ 1 & 1 \\ 1 & 8 \end{tabular} \right) =$

#### Probability and Statistics

**24.** Suppose we have age, years of education, and income data on four individuals:

Express the third individual's data as an ordered 3-tuple.

**25.** What is the median income?

**26.** Sketch a plot of income as a function of years of education.

**27.** Sketch a normal distribution

**28.** Sketch a uniform distribution

**29.** If you throw a single six-sided fair die 300 times, what will the frequency distribution of the results look like? What do we call this distribution?

**30.** If you throw two six sided fair dice 300 times, what will the frequency distribution of the results look like? What do we call this distribution?

**31.** If you measure the height of all the students at Mills College what will the frequency distribution of the results look like? What do we call this distribution?

**32.** What are the possible outcomes from throwing a single die?

**33.** If we write P(event) to represent the probability of event, what is P(outcome is odd)?

**34.** What is P(outcome > 4)?

**35.** What is the probability that the outcome is both odd and greater than four?

**36.** What is the probability that the outcome is either odd or greater than four?

#### Logs and exponents

**37. An** investment of $100 earns 10% annual simple interest. What is it worth in three years?

**38.** If $y = 10^x$, what is $\log_{10} y$?

**39.** $10^3 \times 10^6 =$

**40.** $a^b + a^c =$

**41.** $5 a^5 + 3 a^3 =$