Full-Length CLEP College Algebra Practice Test-Answers and Explanations

47- Choice D is correct
\(0.5x=(0.25)×38→x=19→(x-3)^3=(16)^3=4,096\)

48- Choice C is correct
It is given that \(g(4)=6\). Therefore, to find the value of \(f(g(4))\), then \(f(g(4))=f(6)=5\)

49- Choice C is correct
The best way to deal with changing averages is to use the sum. Use the old average to figure out the total of the first 5 scores: Sum of first 5 scores: \((5)(80)=400\), Use the new average to figure out the total she needs after the \(6^{th}\) score: Sum of 6 scores: \((6)(82)=492\) To get her sum from 400 to 492, Mary needs to score \(492-400=92.\)

50- Choice C is correct
To solve a quadratic equation, put it in the \({ax}^2+bx+c=0\) form, factor the left side, and set each factor equal to 0 separately to get the two solutions. To solve \(2x^2=7x-3\), first, rewrite it as\( 2x^2-7x+3=0\). Find the value of the discriminant. \(b^2-4ac=7^2-4(2)(3)=49-24=25,∆>0\), Since the discriminant is positive, the quadratic equation has two solutions \(x=3\) Or \(x=\frac{1}{2}\), There are two solutions for the equation.

51- Choice B is correct
\(y=5a^2 b-3ab+4b^2\).Plug in the values of a and b in the equation: \(a=2\) and \(b=-2\)
\(y=5(2)^2 (-2)-3(2)(-2)+4(-2)^2=-40+12+16=-12\)

52- Choice D is correct
\(f(x)=2x-8,g(x)=x^2+3x-9,\)
\((f-2g)(x)=(2x-8)-2(x^2+3x-9)=2x-8-2x^2-6x+18=-2x^2-4x+10\)

53- Choice A is correct
Let the number be A. Then: \(x=y\% ×\)A.
Solve for A. \(x=\frac{y}{100}×\)A
Multiply both sides by \(\frac{100}{y}: x×\frac{100}{y}=\frac{y}{100}×\frac{100}{y}×\)A→A\(=\frac{100x}{y}\)

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54- Choice C is correct
The line passes through the origin, (8,m) and (m,18).
Any two of these points can be used to find the slope of the line. Since the line passes through (0, 0) and (8,m), the slope of the line is equal to \(\frac{m-0}{8-0}=\frac{m}{8}\). Similarly, since the line passes through (0, 0) and (m,18), the slope of the line is equal to \(\frac{18-0}{m-0}=\frac{18}{m}\). Since each expression gives the slope of the same line, it must be true that \(\frac{m}{8}=\frac{18}{m}\), Using cross multiplication gives
\(\frac{m}{8}=\frac{18}{m}→m^2=18×8=144 →m^2=144→m=12\)

55- Choice E is correct
\(1.23 per minute to use the car. This per-minute rate can be converted to the hourly rate using the conversion 1 hour \(=60\) minutes, as shown below. \(\frac{1.23}{minute}×\frac{60 minutes}{1 hours}=\frac{\)(1.23×60)}{hour}\)
Thus, the car costs \($(1.23×60)\) per hour. Therefore, the cost c, in dollars, for h hours of use is c\(=(1.23×60)\)h, Which is equivalent to c\(=1.23(60\)h)

56- Choice D is correct
Plug in each pair of numbers in the equation:
A. \((-1, 2): 6(-1)-3(2)=-12\) Nope!
B. \((0, 3): 6(0)-3(3)=-9\) Nope!
C. \((1, 4): 6(1)-3(4)=6-12=-6\) Nope!
D. \((3, 2): 6(3)-3(2)=18-6=12\) Bingo!
E. \((4, 1): 6(4)-3(1)=24-3=21\) Nope!

57- Choice C is correct
Here we can substitute 8 for \(x\) in the equation. Thus, \(y-4=3(8+6), y-4=3(14)=42\) Adding 4 to both side of the equation: \(y=42+4, y=46\)

58- Choice C is correct
Let’s review the options:
I. \(|a|<1→-1<a<1\)
Multiply all sides by b. Since, \(b>0→-b<ba<b\)
II. Since,\( -1<a<1\) and \(a<0→ -a>a^2>a\) (plug in \(-\frac{1}{2}\), and check!)
III.\( -1<a<1\),multiply all sides by 4,then: \(-4<4a<4\),subtract 2 from all sides,then:
\(-4-2<4a-2<4-2→-6<4a-2<2\), I and III are correct.

59- Choice C is correct
The equation can be rewritten as \(c-d=ac\)→(divide both sides by c) \(1-\frac{d}{c}=a\), since \(c > 0\) and \(d < 0\), the value of \(-\frac{d}{c}\) is positive. Therefore, 1 plus a positive number is positive. a must be greater than 1.\( a > 1\)

60- Choice B is correct
\(f(x)=-x^3+4x^2-8x+2,g(x)=2, then f(g(x))=f(2)=-(2)^3+4(2)^2-8(2)+2=-6\)

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How to use Full-Length CLEP College Algebra Practice Test-Answers and Explanations as real practice

Full-Length CLEP College Algebra Practice Test-Answers and Explanations works best when it is used as a short, focused study session rather than a quick click-through activity. The goal is not simply to finish the questions. The goal is to notice which skills feel automatic, which skills still need review, and which mistakes happen when you rush.

Start with a clean piece of scratch paper. For each item, answer the questions under realistic conditions, then review every missed problem before retaking a similar set. If you get something wrong, do not immediately move on. Write the correct step, circle the part that caused the mistake, and try one similar item before continuing. That small correction habit is what turns an online practice test into lasting math improvement.

A three-round study routine

This routine is simple, but it solves a common problem: students often practice only until an answer looks familiar. Real readiness means you can solve a fresh problem without hints, explain the first step, and check whether the final answer is reasonable.

What to write down while you practice

Keep a tiny mistake log next to the activity. You only need three columns: the topic, the mistake, and the correction. For example, a student might write “fractions,” “forgot common denominator,” and “rewrite both fractions before adding.” A log like that is more useful than a long list of scores because it tells you exactly what to review next.

• If the mistake is a fact or formula, review it before the next round.
• If the mistake is a setup error, copy one worked example and label each step.
• If the mistake is from rushing, slow down and require written work for the next five items.
• If the same mistake appears twice, stop and review that topic before continuing.

When you are ready to move on

You are ready for the next topic when you can get several items correct in a row and explain why the method works. A score by itself is helpful, but it is not the whole story. You should also be able to describe the rule, formula, or pattern that the activity is testing.

For test preparation, come back to Full-Length CLEP College Algebra Practice Test-Answers and Explanations after a day or two and try a fresh round. If the skill still feels easy after a short break, it is much more likely to stay with you during a quiz, unit test, or standardized test. If it feels shaky, that is useful information too: it tells you exactly where to spend your next study session.

Study tips for parents and teachers

When using this page with a student, ask for the reasoning before the answer. Questions such as “What is the first step?”, “Why did you choose that operation?”, and “How can you check it?” help students build mathematical language. That matters because many test questions measure more than calculation; they also measure whether the student can read the problem, choose a method, and explain a result.

Short sessions are usually best. Ten to fifteen minutes of careful practice can be more productive than a long session full of guessing. End by naming one skill that improved and one skill to review next time. That keeps practice positive, specific, and easy to continue.