Intermediate Algebra links & errata

Below are some of the links that are referenced in the book Intermediate Algebra. (Note: Art of Problem Solving is not responsible for the content on any external site.)

How to Use This Book

Cellular Automata Links

Chapter 10

Chapter 15

References

Unfortunately, the book is not perfect. If you find an error in the text or solutions, we would appreciate a short email to books@artofproblemsolving.com describing the error.

First Printing
Text

• Page 77, Problem 3.47. The problem should specify that a and b are real.
• Page 101, Problem 4.24. In the third line from the end, the 12 in the coefficient of k should be a 13.
• Page 114, Problem 5.5. The directrix formula stated between the Important boxes should be x = h - 1/(4a), not y = h - 1/(4a).
• Page 138, Problem 5.24 part (a). The foci are 4*sqrt(2) apart, not 2*sqrt(2) apart. So, the foci are (4+2sqrt(2), -2) and (4-2sqrt(2),2) .
• Page 166, Problem 6.5. Part (b) should start "Let g_1(x) = x^2 + g_2(x)...", not "Let g_2(x) = x^2 + g_1(x)".
• Page 194, Problem 7.2. The first sentence of the fourth paragraph should start "If a is a root of...".
• Page 198, Exercise 7.1.5. The second term of the polynomial should be -20x^2, not -20^2.
• Page 215. The warning box should read, "The rule above does not apply if a is negative."
• Page 224, Exercise 7.6.4. The last equation should be 64a + 16b + 4c + d = 256, not 64a + 16b + 4b + d = 256.
• Page 228, Problem 7.52. The term bx^3 should be bx^2.
• Page 240, Problem 8.10(b). A factor of 2 was left out of the denominator of the application of the quadratic formula, so the two nonreal roots should be 1/2 the ones shown in the text
• Page 242, Problem 8.13. In both equations where -d^2 appears, the equation should include +d^2 instead. This does not affect the argument presented in the problem.
• Page 265, Problem 9.5. In this line that starts "Next, we check...", both instances of -xy should be +xy.
• Page 369, Problem 11.43. The problem should state that n > 1.
• Page 411, Problem 12.70. The problem should state that n is a position integer.
• Page 414, Problem 13.3. The exponent of 25 in part (a) should be just x, not 2x. (The problem is correctly stated on page 415.)
• Page 418, Problem 13.10(b). The base of the second logarithm in the problem should be 5, not 3.
• Page 438, Problem 13.28. In the first sentence of the final block of the solution, we incorrectly explain that 10/b^2 must be an integer. We should have noted that x is an integer when b = sqrt(10) and omitted the first two sentences in that block.
• Page 558, Problem 17.14. The value of B is -9, not 9. This does not change the rest of the solution; as the correct value of B is used in the algebraic manipulations that follow.

• Page 17, Problem 2.4.2(f). The left end of the interval for the domain should be -5, not 5.
• Page 20, Problem 2.28. The f(g(x)) in the last sentence should be g(f(x)).

• Page 194, Problem 10.6.6. Two entries in the last two matrices of the final displayed equation have the wrong sign. The first row, second column entry should not be negated, and the second row, first column entry should be negated.
• Page 206, Problem 13.58. The answer is correct, but there are two logical flaws that cancel each other. The statement "a < b if and only if ln a > ln b" should be "a < b if and only if ln a < ln b". This flips the inequality sign in several ensuing steps. But later in the solution, when we divide by ln(0.9), we should flip the inequality sign back!
• Page 233, Problem 15.48. A = 1/2 is also a solution, since x=0 is the only solution to the original equation when A = 1/2.
• Page 248, Problem 16.55. The value 11/2 should not be included in the domain, since it would cause division by 0. The correct answer is -8 <= x < 11/2.
• Page 261, Problem 17.4.1(c). The solution given is for the sum of (5n-4)/2^n, not (5n-1)/2^n. The correct solution to the original problem would have S = 4/2 + 9/2^2 + 14/2^3 + 19/2^4+..., so 2S = 4 + 9/2 + 14/2^2 + 19/2^3 + .... Subtracting the first equation from the second gives S = 4 + 5/2 + 5/2^2 + 5/2^3 + ... = 4 + 5(1/2 + 1/2^2 + 1/2^3 + ...) = 4 + 5 = 9.
• Page 276, Problem 18.2.4. The cases a>=b>=c and a>=c>=b must be tackled separately.
• Page 309-10, Problem 20.3.1. In the middle of the solution, the exponent was dropped from the bx^2 term, causing the rest of the solution to be incorrect. The correct answer is b = -2.

Second Printing
Text

• Page 77, Problem 3.47. The problem should specify that a and b are real.
• Page 114, Problem 5.5. The directrix formula stated between the Important boxes should be x = h - 1/(4a), not y = h - 1/(4a).
• Page 138, Problem 5.24 part (a). The foci are 4*sqrt(2) apart, not 2*sqrt(2) apart. So, the foci are (4+2sqrt(2), -2) and (4-2sqrt(2),2) .
• Page 194, Problem 7.2. The first sentence of the fourth paragraph should start "If a is a root of...".
• Page 242, Problem 8.13. In both equations where -d^2 appears, the equation should include +d^2 instead. This does not affect the argument presented in the problem.
• Page 369, Problem 11.43. The problem should state that n > 1.
• Page 411, Problem 12.70. The problem should state that n is a position integer.
• Page 418, Problem 13.10(b). The base of the second logarithm in the problem should be 5, not 3.
• Page 438, Problem 13.28. In the first sentence of the final block of the solution, we incorrectly explain that 10/b^2 must be an integer. We should have noted that x is an integer when b = sqrt(10) and omitted the first two sentences in that block.
• Page 558, Problem 17.14. The value of B is -9, not 9. This does not change the rest of the solution; as the correct value of B is used in the algebraic manipulations that follow.

• Page 194, Problem 10.6.6. Two entries in the last two matrices of the final displayed equation have the wrong sign. The first row, second column entry should not be negated, and the second row, first column entry should be negated.
• Page 206, Problem 13.58. The answer is correct, but there are two logical flaws that cancel each other. The statement "a < b if and only if ln a > ln b" should be "a < b if and only if ln a < ln b". This flips the inequality sign in several ensuing steps. But later in the solution, when we divide by ln(0.9), we should flip the inequality sign back!
• Page 233, Problem 15.48. A = 1/2 is also a solution, since x=0 is the only solution to the original equation when A = 1/2.
• Page 248, Problem 16.55. The value 11/2 should not be included in the domain, since it would cause division by 0. The correct answer is -8 <= x < 11/2.
• Page 261, Problem 17.4.1(c). The solution given is for the sum of (5n-4)/2^n, not (5n-1)/2^n. The correct solution to the original problem would have S = 4/2 + 9/2^2 + 14/2^3 + 19/2^4+..., so 2S = 4 + 9/2 + 14/2^2 + 19/2^3 + .... Subtracting the first equation from the second gives S = 4 + 5/2 + 5/2^2 + 5/2^3 + ... = 4 + 5(1/2 + 1/2^2 + 1/2^3 + ...) = 4 + 5 = 9.
• Page 276, Problem 18.2.4. The cases a>=b>=c and a>=c>=b must be tackled separately.
• Page 309-10, Problem 20.3.1. In the middle of the solution, the exponent was dropped from the bx^2 term, causing the rest of the solution to be incorrect. The correct answer is b = -2.