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ACT Math : How to evaluate algebraic expressions

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Example Question #31 : Evaluating Expressions

If $x\ \blacklozenge \ y$ is defined by the formula $(x^{3}-y)^{2}-x$ , what is $2\ \blacklozenge \ 1$ equivalent to?

Possible Answers:

Correct answer:

Explanation:

The function $x\ \blacklozenge \ y$ is defined by $(x^{3}-y)^{2}-x$ . This means that for whatever value is in the space of the before the symbol $\blacklozenge$ , in our case 2, is inserted into any in the defined function:

$\dpi{100} (2^{3}-y)^{2}-2$

For the value that follows $\blacklozenge$ , the value of 1 in our case, is inserted into any variable in the defined function.

$\dpi{100} (2^{3}-1)^{2}-2$

Then simplify:

$(8-1)^{2}-2$

$7^{2}-2$

49-2

is our correct answer after all the simplification.

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Example Question #67 : Expressions

A dress that normally costs $80 before tax is on sale for 15% off. After the discount is subtracted, a 7% sale tax is added. What is the final price of the dress?

Possible Answers:

$\$72.76$

$\$50.76$

$\$65.00$

$\$72.00$

Need more information

Correct answer:

$\$72.76$

Explanation:

The word problem can be simplified into two steps. First, subtracting the 15% discount:

$New Price = (Original Price - (Original Price \cdot 0.15))$

Second, adding the sales tax to the result from the first step:

$Final Price = (New Price + (New Price \cdot 0.07))$

The percentage is represented as a decimal by dividing the percentage by 100.

So, for the numbers provided:

New Price = $(\$80.00-(\$80.00\cdot 0.15))=\$68.00$

Final Price = $\$68.00+(\$68.00\cdot 0.07)=\$72.76$

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Example Question #68 : Expressions

Evaluate the expression:

3(x-2) + y^2-xy

for x = 2 and y = -3

Possible Answers:

Correct answer:

Explanation:

Plug in the values for the variables and use PEMDAS to dictate the order of the operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. Using this order of operations we get

(x-2) = 0 so the first part of the expression is .

Next we deal with the exponents,

-3^2 .

Then, we deal with the multiplication,

$2\cdot -3 = -6.$

Finally, we plug these simplified values back into the equation and solve,

9 - (-6) = 15 .

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Example Question #69 : Expressions

Tickets for a circus show cost $\$ 5$ each when bought in advance and $\$7$ each when bought at the door. The circus show's goal is to acquire at least $\$ 2,000$ in ticket sales. The show group sold 153 opening-night tickets in advance.

What is the minimum number of tickets they need to sell at the door on opening night to reach their goal?

Possible Answers:

293

177

154

176

200

Correct answer:

177

Explanation:

Since 153 tickets were sold in advance, the group earned a revenue of $153*\$ 5= \$ 765$ . In order to reach their goal of $\$ 2,000$ , they would still need to earn an extra $(\$ 2000-\$ 765)= \$ 1235.$

Since each ticket costs $\$ 7$ at the door, the theatre would need to sell $\$ 1235/7$ tickets, or 177 tickets (rounded to the next whole number).

Note: the answer is NOT 176 tickets, because if 176 tickets are sold, the revenue would be $(176*7) + (153*5) = \$ 1997$ , which does not reach the goal of $\$ 2,000$ .

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Example Question #70 : Expressions

If x=-4 , what is the value of $\frac{x^2-1}{x+1}$ ?

Possible Answers:

Correct answer:

Explanation:

Since x=-4 this value can be substituted for in the function.

$\frac{x^2-1}{x+1}}$

$=\frac{(-4)^2-1}{(-4)+1}$

$=\frac{16-1}{-3}$

Here, the denominator becomes , while the numerator becomes .

$=\frac{15}{-3}$

Hence,

$\frac{15}{-3} = -5$ .

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Example Question #31 : How To Evaluate Algebraic Expressions

If f(x) = 4x^2 + 2x - 4 , then f(-2) equals?

Possible Answers:

Correct answer:

Explanation:

When substituting (-2) for in the provided equation, we get

4(-2)^2 +2(-2) -4 ,

which can be simplified to

16-4-4 , or .

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Example Question #971 : Algebra

Question 20

In which month has Abraham collected the most stamps?

Possible Answers:

October

July

November

May

April

Correct answer:

May

Explanation:

May corresponds to the month Abraham collected the most stamps, adding 24 to his collection. April, July, October, and November correspond to 18, 6, 21, 12, respectively.

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Example Question #33 : How To Evaluate Algebraic Expressions

A company establishes a rewards program such that the bonus received by an employee is given by the model $b = \frac{s^3}{10}$ , where is the number of sales an employee completed. If Alex earned $2700 at the end of the month, how many sales has he completed?

Possible Answers:

300

27000

Correct answer:

Explanation:

Alex’s bonus of

$2700 = \frac{s^3}{10} \rightarrow 27000 = s^3\rightarrow s = 30.$

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Example Question #31 : Evaluating Expressions

2x + 7 = |-7| , then $x = \:?$

Possible Answers:

-3.5

Correct answer:

Explanation:

|-7| = 7 . Thus

$2x + 7 = 7\rightarrow 2x = 0 \rightarrow x = 0$

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Example Question #32 : Evaluating Expressions

Evaluate the folling expression given x=2 .

$x^3+\frac{2}{x}-4x^2+x!$

Possible Answers:

Correct answer:

Explanation:

To evaluate, simply plug in for . Thus:

$2^3+\frac{2}{2}-4*2^2+2!=8+1-16+2=-5$

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ACT Math : How to evaluate algebraic expressions

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #31 : Evaluating Expressions

Example Question #67 : Expressions

Example Question #68 : Expressions

Example Question #69 : Expressions

Example Question #70 : Expressions

Example Question #31 : How To Evaluate Algebraic Expressions

Example Question #971 : Algebra

Example Question #33 : How To Evaluate Algebraic Expressions

Example Question #31 : Evaluating Expressions

Example Question #32 : Evaluating Expressions

All ACT Math Resources

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