eCourse
Don’t miss these video supplements that walk students through the course in an engaging, visual/auditory way!
Helpful Resources
- Free Online Graphing Calculators – These calculators can be used instead of a graphing calculator for this course. (It is recommended that college-bound students get a graphing calculator, however, so they are already familiar with using one.)
- Desmos (suggested, due to ease of identifying values and zooming in and out) – Note that you have to press the keyboard symbol in the bottom left to get a keyboard. Press y = and the values y equals, using x to stand for the independent variable. Use ^ to show exponents (use your right arrow to get back from an exponent to a regular value). Click on the graph of the curve itself to see the value at any particular point. Zoom in or out using the plus or minus signs. Add a second equation by clicking underneath where the first is typed and typing another one.
- Math Is Fun – Use ^ to show exponents; use the first line for inputting the first equation, and the second for the second.
- Free Online Matrix Calculators – These calculators can be used to calculate matrices.
- Desmos – Input a new matrix for each matrix. Press A, A^-1, B to find (A^-1)(B).
- Math Is Fun – Note that in order to calculate (A^-1)(B), you have to first press “inv(A)”, and then press the “to A” button in order to store it as Matrix A. Then press the AB button to calculate A times B, which is really (A^-1)(B), as you stored A^-1 as A (A^-1 is another way of saying the inverse of A).
- The Atheist Delusion – Watch free online or order a DVD.
Corrections/Clarifications
Textbook
Page 152
The top equation on the page should be a(a – b) + b(a – b) = a^2 – ab + ba – b^2.
Page 196, Lesson 7.4
End of first paragraph should read like this: So, the -intercept tells us what input will give us an output of 0.
Page 281, Lesson 9.5
The sidebar should say the square root of 6 instead of the square root of 2.
Page 307, Lesson 10.3
Top right graph should say “…shaded region are ≤ the y…”
Page 315, Lesson 10.4
In the blue box, the second (x + SQRT2i) should really be – SQRT2i rather than +. The > than signs in the graph in the green section should be = signs.
Page 316, Lesson 10.4
Red dashed line should be solid and graph legend should say ≥ 3 + 6.
Page 347, Lesson 11.6
In the first example, it should say “Asymptote is when x = –3.”
Page 359, Lesson 12.3
The first formula should have 1.005 in the dark blue, and the second 1 + 0.005. On the bottom line of each column, the parentheses should have 1.005 not 1.05.
The e in the Carbon-14 equation should be a 2. It is possible to use e to describe Carbon-14 dating, but the rest of the equation would be different.
In the sidebar, 10^3 should be listed as equaling 1,000, not 100.
The example log_2(4), currently under the Quotient Rule, should be listed under the first bullet on the page, and the example log_4(x) – log_4(y) should be listed under the Quotient Rule.
The graph shows movement for 0.02 seconds, not 0.2 seconds.
In the table, under Combinations, it should show 3 – 2 rather than 3 – 1 in the first step.
3rd line of table should be this: F_3 = F_(3-1) + F_(3-2) = F_2 + F_1…; on lines 5-10, simplified subscripts are all one lower than they should be.
The 33 in the sequence that starts {4, 7, 10, 13, …}should be 34, like this: {4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34…}
Row 2, position 1 should be 2 over 2, while row 2 position 2 should be 2 over 1.
In second row of table (when k = 1), 4 – 1 should be 5 – 1. When k = 3 a few rows later, the denominator should start 3! not 5!; when k = 4, the denominator should start 4! not 5!.
In v(t), the third line should be –5, if 1 < t ≤ 6.
Teacher Guide/Solution Manual (2024/2025 Printings)
*Adjusted in Fall 2025 printing.
Worksheet 1.6, Problem 3c, Page 26
Students should be told to round to the second decimal place.
Answer to Worksheet 7.3b
Answer should be multiplied by 10 raised to positive, not negative, 10, and solution show r equaling a value multiplied by 10^5, not 10^8.
Answer to Worksheet 7.8b, Problem 1c
Graph at the top should be of y = x/5 (shown below).
Answer to Worksheet 7.8b, Problem 7a – Explanation
It gets tricky to follow with multiple fractions inside fractions, and students may wonder why we didn’t invert and multiply. The invert and multiply rule works when you have a single fraction over a single fraction, but here the denominator is a fraction minus a value. So instead we used the fact that a/b = a * 1/b (in other words, that you can rewrite the denominator as 1 over that value and it means the same thing). We weren’t changing the meaning at all when we rewrote (1/x^2) – 2 as 1/(1/x^2)-2; in both situations, it’s in the denominator. When you multiply fractions, you multiply the numerators and the denominators, so if you were to multiply the fractions in the second step together you get the first step again. We then had to distribute multiplication and use other techniques to solve since we couldn’t just invert and multiply.
Answer to Worksheet 8.6, Problem 2a
Last line should be 3s, not just s: 3s – 2c + 5l = $2.50.
Worksheet 9.7, Problem 4
Hint should have the same equation as given in the problem.
Worksheet 11.5A, Problem 2
Instructions should begin like this: Remember, to multiply like terms with exponents, we add the coefficients.
Answer to Worksheet 12.1, Problems 1a and 1b
C. should be listed as an answer to 1b, not to 1a.
Worksheet 12.3b and Other Interest Problems
See textbook note about interest problems up above under textbook, page 359.
Answer to Worksheet 13.2, Problem 6a
In the solution itself, every P_f should just be P.
Worksheet 13.2, Problem 6b
Student should be told to solve 5a or 5c rather than 6a. Some printings have the solution for 5c; others for 5a. 5a is the one that will be in the current reprint. If student solves 5a, the answer would be approximately 0.161/day; the second line of the solution would be r = ln(100/20)/10 yr = approximately 0.161/day.
Answer to Worksheet 13.5A, Problem 2b
log should be ln.
Worksheet 14.5B, Problem 2d
The higher dot on the y-axis should be labeled (0, 500), not (0,0).
Worksheet 14.6, Problem 2
In the question, should be “that for values less than 0, f(x) = 5,” not x = 5. The function should be f(x) = { 2x + 5, if x GREATER THAN OR EQUAL TO SYMBOL 0}
Worksheet 14.6, Problem 3
f(t) should be v(t).
Worksheet 14.6, Problem 4b
Should say P($5,000) rather than P(4).
Worksheet 14.7, Problem 1
Should say f(x) = 5ex.
(f(x) rather than f(t))
Answer to 14.7, Problem 5c
There should be a negative sign in front of 2(f(x)).
Answer to 14.9, Problem 4d
The 3 before R should be removed in both the solution and the answer.
Worksheet 15.6, Problem 1e (Grey box)
Should be 2^n, not 2^(n – 1).
*Worksheet 15.7B, Problem 7a
In f(x)=-5x^2 – 2x + 4, the 4 should be a 2. Other points on the graph also need their labels adjusted, but students will get the right answer with what is there.
Answer to Worksheet 15.7B, Problem 7a
Equation should start with +2 instead of +4, making answer +4.
Worksheet 15.10, Problem 4g
The g. Label is missing from the top of page 347. Part g begins “How many tickets would you need…”
Worksheet 16.2, Problem 7d (graph)
Graph labels should be s(t) and t rather than s(x) and x.
Answer to Worksheet 16.2b, Problem 7d
Depending on the zoom level, students may also have graphed the parabola shown.
Worksheet 16.2, Problem 7g, and Answer to Worksheet 16.2
Everywhere in the problem and diagram where it says a, it should say b, and vice versa. If solved the way it is now, the answer should be a ≈ 17.746 b ≈ 10.746 (the an and b are switched from what the solution shows).
Quiz 2 Grading
Problems 2b and 2c should only count as 5 points each.
Quiz 3
2a. Change “Should You Walk Your Dogs on a Leash?” to “Should you Walk Your Dogs?”
Quiz 9, Problem 2a (clarification)
Clarify wording: Which of the expressions you factored resulted in a perfect square after factoring? Mark all that apply.
Test 4, Problem 2e
Formula should be P(t) = Piert
All the xs should really be ts.
Teacher Guide/Solution Manual (Prior Printings)
Worksheet 1.1, Problem 1 (page 19) and *SM page 7
Says refer to pages 3-4 of student book; should say pages 13-14.
Answer to Worksheet 1.5, Problem 2
Answer should be approximately 4.376 yds.
Quiz 1, Problem 3d
The question should read “if the momentum is 12?” instead of “if the momentum is 10?” which would leave the solution correct except for all the 10s would be 12s in it. The answer would then be 8, as it is listed as right now. As it is right now, however the answer would be approximately 6.667, found by multiplying 2 by approximately 3.33.
Answer to Quiz 1, Problem 3d
The question should read “if the momentum is 12?” instead of “if the momentum is 10?” which would leave the solution correct except for all the 10s would be 12s in it. The answer would then be 8, as it is listed as right now. As it is right now, however the answer would be approximately 6.667, found by multiplying 2 by approximately 3.33.
Answer to Worksheet 1.6, Problem 3a
The 0.9144 in the solution should be 0.914. The answer should be 3.282275711.
Answer to Worksheet 1.6, Problem 3b
3.282275711 should be used instead of 3.28083989501; the answer should be 0.001864929.
Answer to Worksheet 1.6, Problem 3c
The answer should be approximately 6.71, with a note that it is okay if students have more decimal places shown; calculators vary in how many digits are kept for other steps of the problem, which is why we rounded to the second decimal place.
Answer to Worksheet 1.7, Problem 3a
The answer should be approximately 295.405 yd/min, and the 0.9144 changed to 0.914.
Answer to Worksheet 1.8, Problem 4a
The xb should be bx to follow the general convention of listing letters in alphabetical order.
Answer to Worksheet 2.1, Problem 6b
The formula for a cylinder is Bh; in the Solution Manual , it lists πr^2h as the formula…which is the same thing if you substitute πr^2 (how you find the area of the circular base) for B. Future printings will show this extra step.
Answer to Worksheet 2.5a, Problem 1b
0.0579 should be rounded to 0.058.
Answer to Worksheet 2.6A, 1f and 2f
There should not be a +- sign in front of the answer.
Answer to Worksheet 2.6B, Problem 4c
The 2.40642274 in in the solution should be 2.40642274 in^2 (same thing, except square the inches). (The answer is the same; this correction is just in the solution portion.)
Note that students may get a slightly different answer depending on how they round pi. If the answer is far off, check to make sure they are putting parentheses around the exponent of 1/2 when inputting into a calculator or inputting the exponent of 1/2 as 0.5; otherwise, the calculator might be viewing it as an exponent of 1 and then division by 2.
Worksheet 2.7A, Problem 1i, Page 48
The student worksheet states “Solve problem 2f for when d is 4.” There is no problem 2f, so it should state “Solve problem 1f for when d is 4.”
The hint should also be removed. This book follows the convention where all fractional exponents are defined as meaning the positive root, as that is how most books/calculators treat them. This is explained in the lesson book on page 69. So unless there’s a +- sign, the positive root is meant in this course.
Answer to Worksheet 2.7B, Problem 3a-3c
The answer to 3a is approximately 50.797 and the answer is 4 to 3b and 3c.
Worksheet 2.7B, Problem 3
The instructions should say, “find the answer if the unknown equals 2” rather than “if the unknown equals 2.”2b
Answer to 2.7B, Problem 4d, Page 50 (Page 36 of Solution Manual)
Answer should be 0.049 to keep with general rounding instructions.
Worksheet 3.2A, Problem 1b
Please ignore problem, as complex numbers haven’t been introduced yet. Will be updated in next printing to show that x must be an element of the set of all real numbers instead.
Worksheet 3.4B (Page 64)
The worksheet lists problems as 5d, 5e, 5f, and 5g. They should be 5a, 5b, 5c, and 5d.
Answer to Worksheet 3.7B, Problem 5b
Answer should be times 10 to the positive, not negative, 3.
Answer to Worksheet 4.1, Problem 2a
Seconds should be cubed in the solution, not squared, until the final step.
Worksheet 4.1, Problem 2d (Page 70)
The instructions should say “force” not “fore.”
Worksheet 4.1, Problem 2b
The problem is confusing as it is. Count as correct if students do not have a negative sign in their answer, as the scenario is unclear, or reword to “50 mi/hr in the negative direction and need to travel 300 mi in the negative direction, how long will it take you?” and remove the hint. Then the answer should be 6 hr.
Answer to Worksheet 5.1, Problem 1a
Answer should start with 2y not 2x.
Answer to Worksheet 4.7, Problem 4c
The answer should be equals, not approximately equals.
Worksheet 6.4, Problem 1
“A certain sum of money (P) at simple interest grows…”
should be
“A certain sum of money (P_i) at simple interest grows…”
All the _i should be unitalicized.
Worksheet 7.9, Problem 3a
(1,0)
Worksheet 8.3b, Problems 1b and 1c.
Add clarification: “On 1b and 1c, look carefully at the second example in the Textbook on page 243 to make sure you correctly identify if the value is positive or negative.”
Answer to Worksheet 9.3b, Problem 6a
The last part of the solution and the answer should have -12x instead of +12x.
Answer to Worksheet 10.1A
Answer to problem 4b should be “odd.”
Answer to Worksheet 10.1A, Problem C
Solution should show 27 instead of 216 from the second step on, and a factored out 8x, not just x.
Answer to Worksheet 10.4, Problem 3c
Answer should be “Even.”
Answer to Worksheet 11.4A, Problem 2b
The denominator in the answer should be -9.8, not positive 9.8.
Worksheet 11.4A, Problems 5c and 5d
Problems should reference 1e instead of 1d.
Answer to Worksheet 11.4B, Problem 2f (Solutions Manual)
The formula for r(t) should be the same as in 2c, just without the units written out (for simplicity). This yields an answer of approximately $0.09.
Answer to Worksheet 11.5B, Problem 1c (Solution Manual)
The line with (x^2 – 2) should be (-x^2 – 2). The final answer is the same as is, only that – sign is missing.
Answer to Worksheet 11.5B, Problem 6b (Solution Manual)
The line with (300t – 40) should not have a – sign in front of it.
Worksheet 13.2, Question 2
The second sub-problems a-d should be e-h.
Answer to Worksheet 13.2, Problem 6b
Solution Manual should show problem 5a rather than 5c, as currently shown. Or students should solve 5c.
Answer to Worksheet 14.5B, Problem 2a
Solution Manual should have p greater than or equal to 100, not 0, to match worksheet.
Worksheet 14.5B, Problem 2b
The x coordinate in the middle point in the transformed function should be 150 not 50.
Worksheet 15.7A, Problem 1c (page 333)
The hint should say “11th term” not “15th term.”
Worksheet 15.7A, Problems 2b, 2d, 3b, and 3d (pages 333 + 334)
The subscripts should be 0, 1, and 2 rather than 1, 2, and 3.
Answer to Quiz 1, Problem 3d
Solution should have the 10s replaced with 12s.
Quiz 2, Problem 1f
Answer as the problem is should be a^4. Problem should be updated in future printings to be (a^2)^-2, in which case the current solution and answer is correct.
Quiz 2, Problem 1k
Problem should be clarified to be -(2)^2(-3)^2.
Answer to Quiz 2, Problem 1k
Solution should be clarified like this: -(2)^2(-3)^2 = (-1)(2^2)(-3)^2 = (-1)(4)(9) = -36.
Answer to Quiz 7, Problem 1e
Answer should be r = 0 (all bold).
Answer to Quiz 7, Problem 1g
Answer should be (0,0) and the l = 0 should be removed. This note in the sidebar should be added: Found by graphing F(l) = 5l, which gets inputted into the calculator as y = 5x, and looking at the point where the line intercepts the x-axis.
Quiz 8, Grading
Each problem in sections 1 and 3 should be worth 3 instead of 4 points; those in section 5 should be worth 4 instead of 5 points.
Quiz 9, Grading
Each problem in Section 3 should be worth 4 instead of 5 points.
Quiz 10, Problem 2b
In future printings, the instructions should be adjusted to include complex roots.
Answer to Quiz 10, Problem 2b
As it is right now, the answer of approximately +- sqrt 4/5i should not be listed, as it is complex and the instructions say not to list complex roots. However, students who list it should not be penalized. The references to real solutions should be removed in the solution. If we were just looking for real roots, we could just graph to see the x = 0.
Answer to Quiz 11, Problem 1e
Answer should be + or – since we took a square root to solve.
Answer to Quiz 12, Problem 1e
The first part of solution should be removed–it’s just a repeat of problem above.
Make sections 1 ,3, 4, and 5 worth 3 points, each problem in section 2 worth 2 points (except the bonus question), and each problem on sections 6-10 worth 5 points.
Below is a more in-depth solution.
Answer should have 1/0.3 rather than just 0.3. If students struggle with compressing by 0.3, you can change the problem to have them compress by 3 instead of by 0.3, in which case the answer would be -f(1/3(x-3)).
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