PARCC Intermediate Mathematics Practice Questions 1 — Questions and Answers

Question 1: 1. Two angles of a triangle each measure 70°. What is the measure of the third angle in degrees?

40° (Correct answer)
80°
100°
120°
140°

Correct answer: 40°

The fundamental property of any triangle is that the sum of its interior angles always equals 180 degrees. Given that two angles each measure 70°, their combined measure is 140°. To find the third angle, subtract this sum from 180° (180° - 140° = 40°), resulting in 40 degrees for the third angle.

Question 2: 2. If Jack needs 2 ½ pints of cream to make a dessert. How many pints will he need to make 3 desserts?

2 ½
3
4
5
7 ½ (Correct answer)

Correct answer: 7 ½

To find the total amount of cream needed, you multiply the amount required for one dessert by the number of desserts Jack wants to make. Jack needs 2 ½ pints (or 2.5 pints) for each dessert. Therefore, for 3 desserts, he will need 2.5 pints/dessert * 3 desserts = 7.5 pints, which is equivalent to 7 ½ pints.

Question 3: 3. A discount store takes 50% off of the retail price of a desk. For the store's holiday sale, it takes an additional 20% off of all furniture. The desk's retail price was $320. How much is the desk on sale for during the holiday sale?

$107
$114
$128 (Correct answer)
$136
$192

Correct answer: $128

First, calculate the price after the initial 50% discount: 50% of $320 is $160, so the desk's price becomes $320 - $160 = $160. Next, apply the additional 20% holiday sale discount to this new price. 20% of $160 is $32. Subtracting this second discount gives the final sale price: $160 - $32 = $128.

Question 4: 4. Which vacation destination is most common for the students?

Beach (Correct answer)
Historical Sites
Cruises
Mountains
Other

Correct answer: Beach

To determine the most common vacation destination, one would examine the provided graph or chart and identify the category with the highest frequency or percentage. Based on the correct answer, the "Beach" category must have represented the largest portion of students' vacation choices, indicating it was the most popular option.

Question 5: 5. If 500 students attend Washington Middle School, how many are going to the mountains for vacation?

25
60 (Correct answer)
75
100
125

Correct answer: 60

To calculate the number of students going to the mountains, you first need to identify the percentage of students choosing mountains from the accompanying chart or graph. If, for example, the chart indicates 12% of students go to the mountains, you would then calculate 12% of the total 500 students. This calculation (0.12 * 500) yields 60 students.

Question 6: 6. If a ¼ of a teaspoon is 1 ml, then how many milliliters are in 6 teaspoons?

10 ml
12.5 ml
15 ml
20 ml
24 ml (Correct answer)

Correct answer: 24 ml

First, determine how many milliliters are in one full teaspoon. Since ¼ of a teaspoon equals 1 ml, a full teaspoon is 4 times that amount (1 ml / (1/4) = 4 ml). Then, to find the total milliliters in 6 teaspoons, multiply 6 by 4 ml, which gives a total of 24 ml.

Question 7: 7. Which of the following is the correct graph for x≥3 or x≤ -2?

Line A
Line B
Line C
Line D (Correct answer)
Line E

Correct answer: Line D

The inequality "x ≥ 3" is represented by a closed circle at 3 with an arrow extending to the right, indicating all numbers greater than or equal to 3. The inequality "x ≤ -2" is represented by a closed circle at -2 with an arrow extending to the left, indicating all numbers less than or equal to -2. Since the condition is "or," the correct graph (Line D) displays both of these separate rays on the number line.

Question 8: 8. A scale on a map states that every ¼ of an inch represents 20 miles. If two cities are 3 ½ inches apart, how many miles are actually between the two cities?

14 miles
20 miles
125 miles
230 miles
280 miles (Correct answer)

Correct answer: 280 miles

First, convert the given distance of 3 ½ inches to a decimal, which is 3.5 inches. Since every ¼ inch represents 20 miles, determine how many ¼-inch segments are in 3.5 inches by dividing 3.5 by 0.25, which equals 14. Finally, multiply this number by the mileage represented by each segment: 14 * 20 miles = 280 miles.

Question 9: 9. Michelle wants to expand her flowerbed by increasing the length and width each by 2 ft. What will the new area of the flowerbed be, if L and W represent the original dimensions of the flowerbed's length and width?

2 LW
2 (L+W)
2L +2W
(L+2) (W+2) (Correct answer)
LW/2

Correct answer: (L+2) (W+2)

The original dimensions of the flowerbed are represented by L for length and W for width. When Michelle increases the length by 2 ft, the new length becomes (L+2). Similarly, increasing the width by 2 ft results in a new width of (W+2). The area of a rectangle is calculated by multiplying its length and width, so the new area of the expanded flowerbed will be (L+2) multiplied by (W+2).

Question 10: 10. Melinda's lights went out. She has 3 pairs of red socks in her drawer, 2 pairs of black socks, and 5 pairs of white socks. What is the minimum number of pairs she must remove from the drawer to ensure that she has a pair of each color?

3
5
7
9 (Correct answer)
10

Correct answer: 9

This is a classic "worst-case scenario" problem. To guarantee she has at least one pair of each color, Melinda must first draw all the pairs of the two most numerous colors. She has 5 white and 3 red pairs, so she could draw all 5 white pairs and all 3 red pairs (5 + 3 = 8 pairs) without getting a black pair. The very next pair she draws (the 9th pair) is guaranteed to be black, ensuring she has one of each color.

Question 11: 11. Which of the following fractions are correctly placed from the least in value to the greatest in value?

1/4, 17/25, 3/4, 11/16
17/25, 1/4, 11/16, 3/4
1/4, 17/25, 11/16, 3/4 (Correct answer)
1/4, 17/25, 3/4, 11/16
3/4, 17/25, 11/16, 1/4

Correct answer: 1/4, 17/25, 11/16, 3/4

To correctly order the fractions from least to greatest, convert each fraction into its decimal equivalent. 1/4 is 0.25, 17/25 is 0.68, 11/16 is 0.6875, and 3/4 is 0.75. Arranging these decimals in ascending order gives 0.25, 0.68, 0.6875, and 0.75, which corresponds to the original fractions 1/4, 17/25, 11/16, and 3/4 respectively.

Question 12: 12. What is the mathematical average of the number of days in a typical year, the number of days in a week, and the number of hours in a day?

100
115
132 (Correct answer)
158
224

Correct answer: 132

To find the mathematical average, first identify the three numbers: a typical year has 365 days, a week has 7 days, and a day has 24 hours. Next, sum these three values: 365 + 7 + 24 = 396. Finally, divide the sum by the count of numbers (which is 3) to get the average: 396 / 3 = 132.

Question 13: 13. 1.75 x 105=

175,000 (Correct answer)
17,500
1,750
0.00175
0.000175

Correct answer: 175,000

Scientific notation 1.75 x 105 indicates that the decimal point in 1.75 should be moved 5 places to the right. Starting with 1.75, moving the decimal five places to the right results in 175,000. Each move to the right effectively multiplies the number by 10.

Question 14: 14. The electric company charges 3 cents per kilowatt-hour. George used 2800 kilowatt-hours in April, 3200 kilowatt-hours in May, and 3600 kilowatt-hours in June. What was his average cost of electricity for the 3 months?

$72
$88
$96 (Correct answer)
$102
$113

Correct answer: $96

First, calculate the total kilowatt-hours used over the three months: 2800 + 3200 + 3600 = 9600 kWh. Next, determine the total cost by multiplying the total kilowatt-hours by the rate of 3 cents ($0.03) per kilowatt-hour: 9600 * $0.03 = $288. Finally, divide the total cost by the number of months (3) to find the average cost per month: $288 / 3 = $96.

Question 15: 15. On a map, 1/3 inch equals 15 miles. The distance between two towns on a map is 3 2/3 inches. How many miles are actually between the two towns?

11
16
88
132
165 (Correct answer)

Correct answer: 165

First, determine the mileage represented by one full inch. Since 1/3 inch equals 15 miles, one inch would be 3 times that distance, or 45 miles (15 * 3). Next, convert the distance between the towns, 3 2/3 inches, into an improper fraction, which is 11/3 inches. Finally, multiply the mileage per inch by this fraction: (11/3) * 45 miles = 11 * 15 miles = 165 miles.

Question 16: 16. James invested $4,000 at 5% interest per year; how long will it take him to earn $200 in simple interest?

1 year (Correct answer)
2 years
3 years
4 years
5 years

Correct answer: 1 year

To find the time it takes to earn $200 in simple interest, use the formula I = PRT (Interest = Principal × Rate × Time). We have I = $200, P = $4000, and R = 5% or 0.05. Plugging these values in gives $200 = $4000 * 0.05 * T. This simplifies to $200 = $200 * T, so dividing both sides by $200 reveals that T = 1 year.

Question 17: 17. John pays $650 in property tax. What is the assessed value of his property if property taxes are 1.2% of assessed value?

$28,800.27
$41,328.90
$43,768.99
$54,166.67 (Correct answer)
$64,333.39

Correct answer: $54,166.67

To find the assessed value, you need to set up an equation where the property tax is 1.2% of the assessed value. Let 'A' represent the assessed value. So, $650 = 0.012 * A. To solve for A, divide the property tax by the tax rate: A = $650 / 0.012. This calculation yields an assessed value of approximately $54,166.67.

Question 18: 18. A lamp is marked with a sale price of $23.80, which is 15% off of the regular price. What is the regular price?

$26
$28 (Correct answer)
$30
$32
$43

Correct answer: $28

If the lamp is on sale for 15% off, the sale price of $23.80 represents 85% (100% - 15%) of the original regular price. To find the regular price, divide the sale price by the percentage it represents in decimal form. So, $23.80 / 0.85 equals $28, which is the lamp's original regular price.

Question 19: 19. A mattress store sells their stock for 15% off of retail. If someone pays cash, they take an additional 10% off of the discounted price. If a mattress's retail price is $750, what is the price after the store discount and the cash discount?

$550.75
$562.50
$573.75 (Correct answer)
$637.50
$675.00

Correct answer: $573.75

First, calculate the price after the initial 15% store discount. 15% of $750 is $112.50, making the discounted price $750 - $112.50 = $637.50. Next, apply the additional 10% cash discount to this new discounted price. 10% of $637.50 is $63.75. Subtracting this second discount gives the final price: $637.50 - $63.75 = $573.75.

Question 20: 20. 85% of what number is 136?

160 (Correct answer)
170
180
190
220

Correct answer: 160

To find the original number, convert the percentage to a decimal by dividing it by 100 (85% = 0.85). Then, set up the equation: 0.85 multiplied by the unknown number (x) equals 136. Dividing 136 by 0.85 gives the result of 160.

Question 21: 21. A building that is 150 ft tall casts a shadow of 20 feet long. At the same time a tree casts a shadow of 2 ft. How tall is the tree?

10
15 (Correct answer)
20
25
30

Correct answer: 15

This problem involves similar triangles, where the ratio of an object's height to its shadow length is constant at a given time. Set up a proportion: 150 ft (building height) / 20 ft (building shadow) = x ft (tree height) / 2 ft (tree shadow). Solving for x gives (150 * 2) / 20 = 300 / 20 = 15 feet.

Question 22: 22. Which of the following is a true statement?

The product of two negative numbers is negative.
The product of one negative and one positive number is positive.
When dividing a positive number by a negative number, the results are negative. (Correct answer)
When dividing a negative number by a positive number, the results are positive.
When dividing a negative number by a negative number the results are negative.

Correct answer: When dividing a positive number by a negative number, the results are negative.

The rules for dividing signed numbers state that if the two numbers have different signs (one positive and one negative), their quotient will always be negative. For example, 10 divided by -2 equals -5. The other options describe incorrect rules for operations with signed numbers.

Question 23: 23. What is the fractional equivalent of 12.5%?

1/4
2/9
1/5
1/8 (Correct answer)
2/7

Correct answer: 1/8

To convert a percentage to a fraction, first express it as a decimal by dividing by 100, so 12.5% becomes 0.125. Next, write the decimal as a fraction: 0.125 is equivalent to 125/1000. Finally, simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, 125, which results in 1/8.

Question 24: 24. Change 4 3/5 to an improper fraction.

23/5 (Correct answer)
7/5
12/20
20/12
12/5

Correct answer: 23/5

To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fraction. Then, add the numerator to this product. The result becomes the new numerator, while the denominator remains the same. For 4 3/5, this is (4 * 5) + 3 = 20 + 3 = 23, so the improper fraction is 23/5.

Question 25: 25. The fine for a driver riding in the carpool lane without any passengers is $133. A driver is issued a bench warrant for $2,294.25, which includes a 15% fee for late charges and court costs. How many tickets has the driver not paid?

10
12
13
14
15 (Correct answer)

Correct answer: 15

First, determine the total original amount of the fines before the 15% fee was added. Since $2,294.25 represents 115% (100% original + 15% fee), divide $2,294.25 by 1.15 to get the total original fine amount, which is $1,995. Then, divide this total original fine amount by the cost of a single ticket ($133) to find the number of unpaid tickets. This calculation yields 1995 / 133 = 15 tickets.

Question 26: 26. Brett started a race at 6:30 A.M., and he did not cross the finish line until 1:05 P.M. How long did it take for Brett to finish the race?

6 hours and 15 minutes
6 hours and 35 minutes (Correct answer)
7 hours and 5 minutes
7 hours and 15 minutes
7 hours and 35 minutes

Correct answer: 6 hours and 35 minutes

To calculate the duration, first find the time from 6:30 A.M. to 12:30 P.M., which is exactly 6 hours. Then, calculate the remaining time from 12:30 P.M. to 1:05 P.M., which is 35 minutes. Adding these two durations together gives a total race time of 6 hours and 35 minutes.

Question 27: 27. What is the fraction equivalent of the shaded region in the following circle?

2/3 (Correct answer)
3/8
4/5
3/4
7/16

Correct answer: 2/3

Assuming the image shows a circle divided into three equal sections, with two of those sections shaded. The total number of equal parts in the circle represents the denominator of the fraction, which is 3. The number of shaded parts represents the numerator, which is 2. Therefore, the fraction equivalent of the shaded region is 2/3.

Question 28: 28. Multiply 2.345 x 0.023

0.53935
0.053935 (Correct answer)
0.0053935
10.195652
101.95652

Correct answer: 0.053935

To multiply decimals, first multiply the numbers as if they were whole numbers: 2345 * 23 = 53935. Next, count the total number of decimal places in both original numbers. 2.345 has three decimal places and 0.023 has three decimal places, totaling six decimal places. Finally, place the decimal point six places from the right in the product, resulting in 0.053935.

Question 29: 29. A men's basketball team won 24 games and lost 32. What is the ratio of games lost to the number of games played?

32:24
4:3
3:4
4:7 (Correct answer)
3:7

Correct answer: 4:7

First, calculate the total number of games played by adding the games won and games lost: 24 + 32 = 56 games. The question asks for the ratio of games lost to games played, which is 32:56. To simplify this ratio, divide both numbers by their greatest common divisor, which is 8. This yields a simplified ratio of 4:7.

Question 30: 30. Which of the following choices is equivalent to 5/6?

5/12
10/6
20/30
15/24
15/18 (Correct answer)

Correct answer: 15/18

An equivalent fraction is created by multiplying or dividing both the numerator and the denominator by the same non-zero number. For the fraction 5/6, if you multiply both the numerator (5) and the denominator (6) by 3, you get 15/18. This confirms that 15/18 is an equivalent fraction to 5/6.

Question 31: 31. Jill earns $120 for 8 hours of work. At the same pay rate, how much will she earn for 15 hours of work?

$180
$225 (Correct answer)
$245
$280
$310

Correct answer: $225

First, determine Jill's hourly pay rate by dividing her earnings ($120) by the number of hours worked (8 hours), which gives $15 per hour. Then, to find out how much she will earn for 15 hours of work, multiply her hourly rate ($15) by 15 hours. This calculation results in $225.

Question 32: 32. Which two years were the least number of tires sold?

1998 and 1999
1998 and 2000 (Correct answer)
1998 and 2001
1999 and 2000
2000 and 2001

Correct answer: 1998 and 2000

Assuming the question refers to a provided data set, such as a bar graph or table showing tire sales per year. To identify the years with the least number of tires sold, one must visually inspect or compare the sales figures for each year. The correct answer indicates that 1998 and 2000 had the lowest sales volumes compared to the other years in the given period.

Question 33: 33. Which year did the store sell 1/3 more tires than the year before?

1998
1999 (Correct answer)
2000
2001
This did not occur during the 4 year span.

Correct answer: 1999

Assuming a data set is provided, to find the year where sales increased by 1/3 compared to the previous year, calculate 1/3 of the previous year's sales and add it to that year's total. For example, if 1998 sales were 7,500, then 1/3 of 7,500 is 2,500. Adding this to 7,500 gives 10,000. If 1999 sales were 10,000, then 1999 is the year that sold 1/3 more tires than the year before.

Question 34: 34. What was the average number of tires sold by the store from 1998 to 2001?

9,000
9,375 (Correct answer)
9,545
9,770
9,995

Correct answer: 9,375

To calculate the average number of tires sold, first sum the total number of tires sold for each year from 1998 to 2001. Then, divide this total sum by the number of years, which is four. For instance, if the total sales were 37,500 over four years, the average would be 37,500 / 4 = 9,375 tires.

Question 35: 35. A salesman sold 20 cars in the month of July, and 40 cars the month of August. What is the percent increase in the number of cars the salesman sold?

50%
100% (Correct answer)
150%
200%
250%

Correct answer: 100%

To find the percent increase, first calculate the absolute increase in sales, which is 40 cars (August) - 20 cars (July) = 20 cars. Then, divide this increase by the original amount (July's sales) and multiply by 100 to express it as a percentage. So, (20 / 20) * 100% equals a 100% increase.

Question 36: 36. If one side of a square is 5 units, what is the area of the square?

10
10
20
25 (Correct answer)
30

Correct answer: 25

The area of a square is calculated by multiplying the length of one side by itself, or side squared (Area = side * side). Given that one side of the square is 5 units, the area is 5 units * 5 units. Therefore, the area of the square is 25 square units.

Question 37: 37. If 8x + 5 = 21, then 3 x + 4 =

5
2
10 (Correct answer)
16
17

Correct answer: 10

First, solve the given equation 8x + 5 = 21 for the variable x. Subtract 5 from both sides to get 8x = 16, then divide by 8 to find x = 2. Next, substitute this value of x into the expression 3x + 4. This yields 3(2) + 4, which simplifies to 6 + 4, resulting in 10.

Question 38: 38. In triangle ABC, AB=BC and (C's measure is 65°.) What is the measure of angle B?

40°
50° (Correct answer)
60°
65°
75°

Correct answer: 50°

Since AB=BC, triangle ABC is an isosceles triangle, meaning the angles opposite these equal sides are also equal. Therefore, if angle C is 65°, then angle A must also be 65°. The sum of all angles in a triangle is 180°. So, angle B = 180° - (angle A + angle C) = 180° - (65° + 65°) = 180° - 130°, which equals 50°.

Question 39: 39. If the average arithmetic mean of 8, 12, 15, 21, x and 11 is 17 then what is x?

3
15
17
35 (Correct answer)
42

Correct answer: 35

The arithmetic mean is calculated by summing all values and dividing by the count of values. In this case, the sum of the five known numbers (8, 12, 15, 21, 11) is 67. Since there are six numbers in total and their average is 17, their total sum must be 17 * 6 = 102. Therefore, to find x, subtract the sum of the known numbers from the total sum: 102 - 67 = 35.

Question 40: 40. Sarah has a 20 dollar bill and a 5 dollar bill. If she purchases two items, one for $11.23 and the other for $8.32, then how much money does she have left over?

$3.75
$5.45 (Correct answer)
$6.34
$7.77
$8.12

Correct answer: $5.45

First, calculate Sarah's total money by adding her two bills: $20 + $5 = $25. Next, find the total cost of her purchases by adding the prices of the two items: $11.23 + $8.32 = $19.55. Finally, subtract the total cost of the purchases from her total money to find the amount left over: $25.00 - $19.55 = $5.45.

PARCC Intermediate Mathematics Practice Questions 1

1.
Two angles of a triangle each measure 70°.
What is the measure of the third angle in degrees?