October 25, 2017

CLEP College Algebra PT-LSG Exam Answer Key

1. B
2. C
3. C
4. C
5. E
6. B
7. D
8. C
9. D
10. A

1. B.  or or 

2. C. To find the value of g(f(−1)), first find f(−1), which equals 2(−1)−1 or −3.
Next, place −3 into the g function or find g(−3) : g(−3) = (−3)2 + 3 or 9 + 3 = 12.

3. C. To find the zeroes of x3 – 3x + 2, first use the rational root theorem that states that a rational root of the polynomial must be any factor of the last term, 2, divided by any rational factor of the first term’s coefficient, 1. In this case, that would be (±2 or ±1) / ± 1 or (±2 or ±1). These are the only four possible rational roots of this polynomial. Each of these values is then substituted for x in the polynomial. The values that produce “zero” for the polynomial are “zeroes” of the polynomial.
f(1) = (1)3 − 3(1) + 2 = 0
f(−1) = (−1)3 − 3(−1) + 2 = 4
f(2) = (2)3 − 3(2) + 2 = 4
f(−2) = (−2)3 − 3(−2) + 2 = 0

1 and -2 are the only rational roots of this polynomial. Note: One of these must have a multiplicity of two – that is, a double zero. Why? Since the polynomial is a cubic, there are three zeroes, and, since imaginary zeroes must come in pairs, the third zero must be real.

4. C. Since log a = 0.30 and log b = 0.47, the problem is asking for the log of what number = 0.77 or the sum of log a and log b. log a + log b = log (a·b)

5. E. To solve for x in 8x+1 = 42x−1, first recognize 8 and 4 can both be written with a base 2 – that is, 8 = 23 and 4 = 22. Now, re-write using the base 2 notation:
8x+1 = 42x−1 or (23)x + 1 = (22)2x − 1, which equals 23x + 3 = 24x − 2 since (na)b = nab, where n is any base. In 23x + 3 = 24x−2, since both have equal bases, their exponents must also be equal.

3x + 3 = 4x − 2 or x = 5

6. B. In , first multiply the two factors in the numerator to get:= .

Remember that i−2 = −1, or = . Then, multiply both numerator and denominator by the complex conjugate of the denominator. The complex conjugate of 1 + i is 1 − i: or . Further reduce to obtain.

Dividing numerator and denominator by 2 yields: 1 − 2i.

7. D. When multiplying expressions such as “x” with the same base, the rule is to ADD the exponents, but remember to MULTIPLY the coefficients.
= or

8. C. | 3x − 9 | > 4 translates to 3x − 9 > 4 or 3x − 9 < −4 or 3x > 13 or 3x < 5 or x > or x <

9. D. To find the inverse of a function such as f(x) = 3x − ½, re-write f(x) with y, or y = 3x − ½.
Then, reverse the x and y to obtain: x = 3y − ½. Now, solve for y:

2x = 6y − 1 or 6y = 2x + 1.

Divide all terms by 6: . Since this is the inverse function, use the f−1(x) notation for y to obtain: f−1(x).

 

 

10. A. Rewrite the equation, 2x + 5y − 8 = 0, in slope intercept form, or solve for y:  .
The slope for this line, as well as for any line parallel to it, is , the coefficient of x.

Therefore, knowing the parallel line’s slope and given its y-intercept, we obtain from y = mx + b, where m is the slope and b is the y-intercept:

.

To express in standard form, first multiply by 5: 5y = −2x − 15. Then, set the equation equal to zero to obtain: 2x + 5y + 15 = 0