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ACT Math : Expressions

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Example Questions

Example Question #4 : Evaluating Expressions

Evaluate 4x²+ 6x – 17, when x = 3.

Possible Answers:

Correct answer:

Explanation:

Plug in 3 for x, giving you 36 + 18 – 17, which equals 37.

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Example Question #5 : Evaluating Expressions

John has a motorcycle. He drives it to the store, which is 30 miles away. It takes him 30 minutes to drive there and 60 minutes to drive back, due to traffic. What was his average speed roundtrip in miles per hour?

Possible Answers:

45 mph

30 mph

40 mph

50 mph

60 mph

Correct answer:

40 mph

Explanation:

The whole trip is 60 miles, and it takes 90 minutes, which is 1.5 hours.

Miles per hour is 60/1.5 = 40 mph

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Example Question #7 : Evaluating Expressions

If (xy/2) – 3w = –9, what is the value of w in terms of x and y?

Possible Answers:

w = 3 + (xy/6)

3xy – 6

3xy + 6

(1/2)xy – 3

(1/3)xy + 6

Correct answer:

w = 3 + (xy/6)

Explanation:

–3w = –9 – (xy/2)

w = 3 + (xy/6)

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Example Question #8 : Evaluating Expressions

Evaluate 5x²+ 16x + 7 when x = 7

Possible Answers:

361

364

363

362

365

Correct answer:

364

Explanation:

Plug in 7 for x and you get 5(49) + 16(7) + 7 = 364

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Example Question #6 : Evaluating Expressions

Let $\dpi{100} \small a\&hash;b=(2a-b)^{2}$ for all integers $\dpi{100} \small a$ and $\dpi{100} \small b$ . Which of the following is the value of $\dpi{100} \small -2\&hash;5$ ?

Possible Answers:

$\dpi{100} \small 1$

$\dpi{100} \small 81$

$\dpi{100} \small -81$

$\dpi{100} \small 144$

$\dpi{100} \small -9$

Correct answer:

$\dpi{100} \small 81$

Explanation:

In order to solve the expression, replace $\dpi{100} \small a$ with $\dpi{100} \small -2$ and $\dpi{100} \small b$ with $\dpi{100} \small 5$ in the definition given:

$\dpi{100} \small a\&hash;b=(2(-2) -5)^{2}$

$\dpi{100} \small a\&hash;b=(-4 -5)^{2}$

$\dpi{100} \small a\&hash;b=(-9)^{2}$

$\dpi{100} \small a\&hash;b=81$

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Example Question #41 : Expressions

What is the value of $x$ that satisfies the equation $5(x+2)=12x-5$ ?

Possible Answers:

$\frac{15}{7}$

$-\frac{15}{17}$

$\frac{15}{11}$

$1$

$0$

Correct answer:

$\frac{15}{7}$

Explanation:

Distributing the 5 on the left side of the equation gives you $5x+10=12x-5$ .

Subtracting $5x$ from both sides of the equation gives you $10=7x-5$ .

Adding 5 to both sides of the equation gives you $15=7x$ .

Dividing each side of the equation by 7 gives you $\frac{15}{7}=x$ .

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Example Question #11 : How To Evaluate Algebraic Expressions

If $\small a = 2$ and $\small b = 4$ , what is $\small -4(ab)^{3} + (3a - 2b)$ ?

Possible Answers:

$-2050$

$-32,770$

$2050$

$2046$

$-2046$

Correct answer:

$-2050$

Explanation:

$\small -4(2\times 4)^{3} + \left ( 3\times 2 - 2\times 4 \right )$

$\small -4(512) + (6-8)$

$\small -2048 -2$

$\small -2050$

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Example Question #12 : How To Evaluate Algebraic Expressions

8 less than 4 times a number is 76. Find the number.

Possible Answers:

Correct answer:

Explanation:

4x - 8 = 76

4x = 76 + 8

4x = 84

$x = \frac{84}{4} = 21$

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Example Question #13 : How To Evaluate Algebraic Expressions

Let x = 2 , y = 3 and z = 4 . Solve $zx^{y}$

Possible Answers:

Correct answer:

Explanation:

Substitute the given values into the variables to get:

$4(2^{3})= 4(8)= 32$

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Example Question #13 : How To Evaluate Algebraic Expressions

Bob needs to order 700 candy bars from a warehouse. The website he is ordering from shows that the candy bars come in cases of boxes with candy bars in each box. It is not possible to order partial cases. What is the fewest amount of cases that Bob should order?

Possible Answers:

Correct answer:

Explanation:

The answer is .

Bob must order full cases, which contain boxes of candy bars with bars per box. This comes out to a total of 15*10= 150 candy bars per case. An order of cases comes out to 150*4= 600 candy bars which is not enough. However if he orders one more case, the total comes out to 150*5=750 candy bars which allows him to barely surpass his needed amount of 700 bars.

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ACT Math : Expressions

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #4 : Evaluating Expressions

Example Question #5 : Evaluating Expressions

Example Question #7 : Evaluating Expressions

Example Question #8 : Evaluating Expressions

Example Question #6 : Evaluating Expressions

Example Question #41 : Expressions

Example Question #11 : How To Evaluate Algebraic Expressions

Example Question #12 : How To Evaluate Algebraic Expressions

Example Question #13 : How To Evaluate Algebraic Expressions

Example Question #13 : How To Evaluate Algebraic Expressions

All ACT Math Resources

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