Prerequisite Math Review
for Introductory Statistics
This worksheet is intended for students taking introductory college-level statistics classes, including AP Statistics. These topics are often assumed as working knowledge for students, and professors likely will not spend time in class reviewing them. Use this worksheet at the start of your class (or throughout the class) to revisit this material, ensure it is fresh in your mind, and be able to solve problems of these types with absolute confidence!
If these problems are all straightforward and doable for you, great! You're likely well-prepared to tackle the new material in your course. If not, that's perfectly alright. Use this as an opportunity to review now so that you can focus on the new material in your class when these topics come up.
Algebra Review: Rational functions, absolute value inequalities
Solve for $x$. When your answer includes an interval, express your answer by (i) drawing it on the number line and (ii) writing it in interval notation.
- $\sqrt{2x-5}=3$
- $\frac{15-x}{x}=2$
- $13-3x < 4$
- $|x-3| \geq 5$
Constructing and Interpreting Lines
After much back-and-forth negotiations, a company unveils their new policy for determining worker salaries: Each worker will receive an annual salary $y$ according to the formula $y = 41000 + 3200x$, where $x$ is the number of years an employee has been working for the company.
- What will be the salary of an employee who has worked for this company for 3 years?
- What is the slope of this line? Interpret this value in the context of this problem.
- What is the $y$-intercept of this line? Interpret this value in the context of this problem.
- Before this new policy, a particular employee who had worked at this company for 4 years was making $60,000 per year. Will their salary increase or decrease under this new policy, and if so, by how much?
Summation / Sigma Notation
Suppose we have a set of 4 values: $x_1 = 2, x_2 = 9, x_3=9, x_4=12$. Recall that the summation written below (in sigma notation) is evaluated as follows:
$$\sum_{i=1}^4 x_i =~ 2+9+9+12=~ 32$$
For the same set of values, compute:
- $\sum_{i=1}^4 (2x_i-3)$
- $\sum_{i=1}^4 x_i^2$
- $\left( \sum_{i=1}^4 x_i \right)^2$
Combinatorics
A café offers a choice of 6 different flavors of sandwiches, 6 soups, and 6 salads. How many different ways can you order a combo containing two items, assuming:
(a)a combo can contain any two items (e.g., two BLTs is fine);(b)a combo CAN contain two items of the same type but not identical flavors (e.g., two different soups);(c)a combo CANNOT contain two items of the same type.
A recreational soccer club with 20 members consists of 11 women and 9 men. They break up into teams of 4 for some casual games.* How many unique ways can you create:
(a)A team of 4 members;(b)A team of 4 where one is a goalie, another is a forward, another is a midfielder, and another is a backfielder;(c)A team of 2 women and 2 men?
*Note: My soccer knowledge is almost entirely from Ted Lasso, so please don't get upset with this somewhat unrealistic question!
Calculus Review (Not in every course)
Note: Not every introductory statistics class will use calculus. Please check with your instructor/review the course syllabus to determine whether these topics will be required in your course!
- Evaluate $\int_1^e(x+\frac{1}{x})dx$.
- Solve for $x$: $\int_0^x 2e^{-2t}dt = \frac{1}{4}$
- (Requires Improper Integrals and Integration by Parts): Evaluate $\int_0^\infty xe^{-3x}dx$.
Conclusion
Answers to this worksheet are available here. Please comment below or contact me if you have any questions / clarifications regarding this worksheet! If you're trying to determine whether you're prepared for your particular statistics class, I'd be happy to discuss further, including strategizing on ways to review and prepare for your coursework!
