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ACT Math : Algebra

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Example Questions

Example Question #991 : Algebra

$f$ pigeons land on a telephone wire. Then, $g+2$ pigeons fly away. Find an expression for the number of pigeons remaining.

Possible Answers:

$2(f - g)$

$2(f + g)$

$f - g - 2$

$f + g + 2$

$f - g + 2$

Correct answer:

$f - g - 2$

Explanation:

There are $f - g - 2$ pigeons remaining on the wire. We start with $f$ pigeons, then subtract $(g + 2)$ pigeons. $f - (g + 2) = f - g - 2$ .

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Example Question #1 : Solving Linear Equations In Word Problems

Erin is making thirty shirts for her upcoming family reunion. At the reunion she is selling each shirt for $18 apiece. If each shirt cost her $10 apiece to make, how much profit does she make if she only sells 25 shirts at the reunion?

Possible Answers:

$\$340$

$\$150$

$\$450$

$\$300$

$\$640$

Correct answer:

$\$150$

Explanation:

This problem involves two seperate multiplication problems. Erin will make $450 at the reunion but supplies cost her $300 to make the shirts. So her profit is $150.

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Example Question #11 : How To Simplify An Expression

Which of the following is equivalent to (x)(x)(x)(x)(x^–2)?

Possible Answers:

x^–2

x²

x^–8

x³

Correct answer:

x²

Explanation:

When multiplying powers of x, we add the exponents. The first four terms are equivalent to x⁴.

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Example Question #12 : How To Simplify An Expression

What is $\small \frac{2(x^{3}y^{4})+2(x^{2}y^{2})}{(4x^{2})(4y^{2})}$ in simplified form?

Possible Answers:

$\small \frac{2xy^{2}+2}{16}$

$\small \frac{x^{2}y^{2}+1}{4}$

$\small \frac{x^{3}y^{4}+x^{2}y^{2}}{4x^{2}y^{2}}$

$\small \frac{xy^{2}}{4}$

$\small \frac{xy^{2}+1}{8}$

Correct answer:

$\small \frac{xy^{2}+1}{8}$

Explanation:

Reduce by first dividing all terms by 2: $\small \frac{(x^{3}y^{4})+(x^{2}y^{2})}{8x^{2}y^{2}}$

Next divide the terms in the numerator by the two variables in the denominator. Remember that dividing variables with exponents is really just subtraction of those exponents: $\small \frac{xy^{2}+1}{8}$

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Example Question #2 : How To Simplify Expressions

Simplify the expression:

$\frac{(x^2+2x+1)(2x)}{2x^2+2x}$

Possible Answers:

x²+ 2x + 1

2x + 1

x + 1

Correct answer:

x + 1

Explanation:

Factor out a (2x) from the denominator, which cancels with (2x) from the numerator. Then factor the numerator, which becomes (x + 1)(x + 1), of which one of them cancels and you're left with (x + 1).

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Example Question #91 : Expressions

Find , given that |7x-4|+5>-1

Possible Answers:

$\frac{-2}{7} < x < \frac{10}{7}$

$x>\frac{2}{7}$

$\frac{-2}{7} < x < \frac{-10}{7}$

None of the other answers

$x>\frac{-2}{7}$

Correct answer:

$\frac{-2}{7} < x < \frac{10}{7}$

Explanation:

Create two equations to eliminate the absolute value function, one where the value inside the absolute value bars is assumed to be positive and another where it is assumed to be negative: 7x – 4 + 5 > –1 and -7x + 4 + 5 > –1.

The solutions for the equations, respectively, are x > -2/7 and x < -10/7. (Remember to flip the inequality sign when multiplying or dividing by a negative number.)

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Example Question #3 : How To Do Distance Problems

Trevor took a road trip in his new VW Beetle. His car averages 32 miles per gallon. Gas costs $4.19 per gallon on average for the whole trip. How much would it coust to drive 3,152 miles?

Possible Answers:

$\$134.08$

$\$98.50$

$\$752.27$

$\$421.75$

$\$412.72$

Correct answer:

$\$412.72$

Explanation:

To find this answer just do total miles divided by miles per gallon in order to find how many gallons of gas it will take to get from point A to Point B. Then multiply that answer by the cost of gasoline per gallon to find total amount spent on gasoline.

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Example Question #992 : Algebra

a # b = (a * b) + a

What is 3 # (4 # 1)?

Possible Answers:

Correct answer:

Explanation:

Work from the "inside" outward. Therefore, first solve 4 # 1 by replacing a with 4 and b with 1:

4 # 1 = (4 * 1) + 4 = 4 + 4 = 8

That means: 3 # (4 # 1) = 3 # 8. Solve this now:

3 # 8 = (3 * 8) + 3 = 24 + 3 = 27

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Example Question #797 : Algebra

Which is the greater quantity: the median of 5 positive sequential integers or the mean of 5 positive sequential integers?

Possible Answers:

The quantities are equal

The relationship cannot be determined

The median is greater

The mean is greater

Correct answer:

The quantities are equal

Explanation:

If the first integer is $\dpi{100} \small n$ , then $\dpi{100} \small n+(n+1)+(n+2)+(n+3)+(n+4)=5n+10$

$\dpi{100} \small \frac{5n+10}{5}=n+2$

This is the same as the median.

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Example Question #992 : Algebra

You are told that $\dpi{100} \small x$ can be determined from the expression:

Capture7

Determine whether the absolute value of $\dpi{100} \small x$ is greater than or less than 2.

Possible Answers:

$\dpi{100} \small |x|>2$

$\dpi{100} \small |x|<2$

The relationship cannot be determined from the information given.

The quantities are equal

Correct answer:

$\dpi{100} \small |x|>2$

Explanation:

The expression is simplified as follows:

Capture8

Since $\dpi{100} \small 2^{4}=16$ the value of $\dpi{100} \small x$ must be slightly greater for it to be 17 when raised to the 4th power.

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ACT Math : Algebra

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #991 : Algebra

Example Question #1 : Solving Linear Equations In Word Problems

Example Question #11 : How To Simplify An Expression

Example Question #12 : How To Simplify An Expression

Example Question #2 : How To Simplify Expressions

Example Question #91 : Expressions

Example Question #3 : How To Do Distance Problems

Example Question #992 : Algebra

Example Question #797 : Algebra

Example Question #992 : Algebra

All ACT Math Resources

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