Simplify this expression.

4(8x + 3) + 3(2x + 6)

A) 36x + 6

B) 38x + 30 (Correct Answer)

C) 44x + 36x

D) 80x

Explanation:

Using the Distributive Property:

4(8x + 3) = 4(8x) + 4(3) = 32x + 12

3(2x + 6) = 3(2x) + 3(6) = 6x + 18

Combining the terms: 32x + 12 + 6x + 18 = 38x + 30

Related Common Core State Standard: Expressions & Equations: 7.EE.2

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If Ron walks 1/2 mile in a quarter of an hour and Maria walks 1/3 mile in the same time period, how many miles have Ron and Maria walked in 3 hours?

A) 1 1/3 miles

B) 4 miles

C) 6 miles

D) 10 miles (Correct Answer)

Explanation:

If Ron walks 1/2 mile in a quarter of an hour he can walk 2 miles in an hour.

If Maria walks 1/3 mile in a quarter of an hour, she can walk 1 1/3 miles in an hour.

In 3 hours Ron will have walked 2 x 3 = 6 miles. Maria will have walked 1 1/3 x 3 = 4 miles. 6 + 4 = 10 miles

Related Common Core State Standard: Statistics & Probability: 7.RP.1

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Examine the chart:

Which of the following statements is true based on the information in the chart?

A) The same students are tardy each day.

B) Each day more boys did not wear their uniform compared to girls.

C) On the hottest days, most girls did not wear their uniform. (Correct Answer)

D) There are more boys not in uniform than girls during the week.

Explanation:

Rationale:

On the hottest days, Tuesday and Wednesday, more girls are not in uniform than boys.

Related Common Core State Standard: Statistics & Probability: 7.SP.1

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The figure is drawn such that 3cm = 1 mile

What is the distance one would travel between these two locations?

A) 1 mile

B) 3 miles

C) 1/3 of a mile (Correct Answer)

D) This cannot be determined

Explanation:

If 3cm = 1 mile, then traveling 1 cm as shown on the map is equal to 1/3 of a mile in actual distance traveled.

Related Common Core State Standard: Geometry: 7.G.1

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A rectangular garden has an area of 432 square feet. The length

of the garden is 24 feet. What is the width of the garden?

A) 20 feet

B) 18 feet (Correct Answer)

C) 24 feet

D) It cannot be determined.

Explanation:

The area of the garden is the product of its length and its width. The area is 432 and the length is 24.

The width is equal to 432 divided by 24, which is 18. The garden is 18 feet wide.

Related Common Core State Standard: Geometry: 7.G.6

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x^{6} · x^{10} = ?

A) x^{60}

B) x^{30}

C) x^{16} (Correct Answer)

D) x^{-4}

Explanation:

When a multiplication expression involves factors with the same base being raised to powers, add the powers.

x^{6} · x^{10} = x^{16}

Related Common Core State Standard: The Number System: 7.NS.2c

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Simplify the following expression:

10 (2 + 3) – 8 · 3

A) 126

B) 74

C) 26 (Correct Answer)

D) 18

Explanation:

Using the Order of Operations, do parentheses first:

10 (2 + 3) – 8 · 3 = 10(5) – 8 · 3

Then do multiplication and division, from left to right:

10(5) – 8 · 3 = 50 – 24

Finally, subtract.

50 – 24 = 26

Related Common Core State Standard: Expressions & Equations: 7.EE.1

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In 1954, Great Britain’s Diane Leather was the first to break the 5-minute

mile in woman’s track and field. If She ran a mile in 4:59.6, what would

be her speed at the half mile mark?

A) 2:30.3

B) 2:29.8 (Correct Answer)

C) 9:59.2

D) 8:30.6

Explanation:

To find half of 4 minutes, 59.6 seconds, divide by 2.

Related Common Core State Standard: Ratios & Proportional Relationships :7.RP.1

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A table top is in the shape of an equilateral triangle. If the perimeter of

the table top is 420 cm, what is the length of one side of the table?

A) 140 cm (Correct Answer)

B) 180 cm

C) 35 cm

D) 105 cm

Explanation:

An equilateral triangle has 3 equal length sides: 3x = 420; x = 140

Related Common Core State Standard: Geometry: 7.G.2

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Roger wraps presents at a local gift shop. If it takes 1.4 meters of ribbon

to wrap a present, how many can he wrap if he has 40 meters of ribbon?

A) 27

B) 28 (Correct Answer)

C) 29

D) 30

Explanation:

To determine how many presents Roger can wrap with 40 meters of ribbon, divide 40 by 1.4.

40 ÷ 1.4 = 28 4/7. Roger can wrap 28 presents with the ribbon. Note: The extra 4/7 of a present was disregarded.

Related Common Core State Standard: 7.NS.3

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As a mixed number, 240% is equal to ___________ .

A) 24

B) 240

C) 2 4/5

D) 2 2/5 (Correct Answer)

Explanation:

By definition, 100% = 1 whole. Therefore, 240% = 2.4 or 2 2/5.

Related Common Core State Standard: 7.NS.2

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A restaurant owner spends $892 for 65 pounds of produce. Which equation could you use to find the price per pound?

A) 892 (65) = x

B) 892 = 65 / x

C) 892 = 65x (Correct Answer)

D) 892 = 65 + x

Explanation:

To find the price per pound of produce, the total cost is equal to the number of pounds

of produce multiplied by the price per pound.

Related Common Core State Standard: 7.RP.2

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Evaluate if a = 4, b = 6, c = -3.

5ab ÷ c

A) 108

B) 40

C) -40 (Correct Answer)

D) 33

Explanation:

Substituting the values for a, b, and c:

5(4)(6) ÷ (-3). Then simplifying:

120 ÷ (-3) = -40

Related Common Core State Standard: 7.EE.4

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Jasmin takes three walks a day. If her walks last 30 minutes, 47

minutes, and 1 hour, respectively, and she walks a total of 4 miles

a day, which of the following reflects the approximate pace she walks?

A) two and a quarter miles per hour

B) two and a half miles per hour

C) one half mile per hour (Correct Answer)

D) one quarter mile per hour

Explanation:

First, determine the total number of minutes Jasmine walks: 30 minutes + 47 minutes + 1 hour = 2 hours, 17 minutes.

This is approximately 2 and a quarter hour or 2.25 hours.

Next, since Jasmin walked a total of 4 miles, divide the distance travelled by time. 4 miles/(9/4) hours.

The result is approximately equal to one and half mile per hour.

Related Common Core State Standard: 7.RP.1

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Simplify the following expression:

4 (x + 3) + (7 – 4)

A) 15x

B) 7x + 13

C) 4x + 15 (Correct Answer)

D) 12x + 3

Explanation:

Using the Distributive Property, 4 (x + 3) = 4(x) + 4(3) = 4x + 12.

(7 – 4) simplifies to 3. The entire expression becomes 4x + 12 + 3 = 4x + 15.

Related Common Core State Standard: 7.EE.2

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You’ve been given a scholarship of $10,000. If you invest it at a 3.4%

annual interest rate, how much interest will you have earned in a

year’s time?

A) $34,000

B) $340 (Correct Answer)

C) $10,340

D) $10,000

Explanation:

simple interest = the initial amount x interest rate x time period

simple interest = $10,000 (3.4) 365 days

Related Common Core State Standard: 7.RP.3

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An architect is planning a triangular pool with a perimeter of 99 ft.

If two of the sides measure 20 and 42, respectively, what is the

length of the missing side?

A) 35 feet

B) 37 feet (Correct Answer)

C) 39 feet

D) 41 feet

Explanation:

To solve, set up the equation, and subtract 20 and 42 from each side:

20 + x + 42 = 99

20 + x + 42 – 20 – 42 = 99 – 20 – 42. Then simplify.

x = 37

Related Common Core State Standard: 7.EE.4

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A student at a large middle school is planning to survey students about

their favorite cafeteria meal. Which of the following would ensure the

survey is valid?

A) choose a sample that represents the student population (Correct Answer)

B) only ask friends about their food choices

C) only ask students about your favorite foods

D) only ask sixth graders to participate in the survey

Explanation:

To be a valid survey, the sample must represent the general population.

Related Common Core State Standard: 7.SP.1

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**Danny rolls two number cubes (dice), one red and one blue. What is**

the probability that he will roll a 2 on the red cube and a 6 on the

blue cube?

A) 1/6

B) 2/15

C) 1/18

D) 1/36 (Correct Answer)

**Explanation:**

The probability of both events happening is the product of the probabilities of each event happening individually. The probability of rolling a 2 on the red cube is 1/6. The probability of rolling a 6 on the blue cube is 1/6. The probability of both events happening is 1/6 x 1/6 = 1/36.

Related Common Core State Standard: 7.SP.6

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**Which of the following formulas can be used to find the area of a circle?**

A) C = (pi)d

B) C = 2(pi)r

C) A = (pi)r2 (Correct Answer)

D) D = C/(pi)

Explanation:

The formula for the area of a circle is the circumference multiplied by the radius, squared.

Related Common Core State Standard: 7.G.4

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