PARCC Mathematics Practice Questions 1 — Questions and Answers

Question 1: 1. An instrument store gives a 10% discount to all students off the original cost of an instrument. During a back to school sale an additional 15% is taken off the discounted price. Julie, a student at the local high school, purchases a flute for $306. How much did it originally cost?

$325
$375
$400 (Correct answer)
$408
$425

Correct answer: $400

To find the original cost, we need to reverse the discounts. First, the $306 price represents 85% of the price after the initial 10% discount (100% - 15% = 85%). So, $306 / 0.85 = $360. This $360 then represents 90% of the original cost (100% - 10% = 90%). Therefore, $360 / 0.90 = $400, which is the original cost.

Question 2: 2. If y(x-1)=z then x=

y-z
z/y + 1 (Correct answer)
y(z-1)
z(y-1)
1-zy

Correct answer: z/y + 1

To solve for x, first divide both sides of the equation y(x-1)=z by y, which gives x-1 = z/y. Then, add 1 to both sides of the equation to isolate x. This results in x = z/y + 1.

Question 3: 3. Which of the following values is NOT equal to 34(58+9)?

34 x 67
58(34+9) (Correct answer)
34 x 58 + 34 x 9
1,972 + 306
(9 + 58) 34

Correct answer: 58(34+9)

The original expression 34(58+9) simplifies to 34 * 67, which equals 2278. Option B, 58(34+9), simplifies to 58 * 43, which equals 2494. This value is different from 2278, making it the expression that is NOT equal to the original. Options A, C, D, and E all correctly represent or simplify to 2278 due to the distributive and commutative properties.

Question 4: 4. Two angles of a triangle measure 15° and 85 °. What is the measure for the third angle?

50°
55°
60°
80° (Correct answer)
90°

Correct answer: 80°

The sum of the interior angles in any triangle is always 180 degrees. Given two angles of 15° and 85°, their sum is 100°. To find the third angle, subtract this sum from 180 degrees (180° - 100° = 80°).

Question 5: 5. If 5 ounces is equal to 140 grams, then 2 pounds of ground meat is equal to how many grams?

863
878
896 (Correct answer)
915
932

Correct answer: 896

First, convert 2 pounds to ounces, knowing that 1 pound equals 16 ounces, so 2 pounds is 32 ounces. Next, use the given conversion rate: if 5 ounces equals 140 grams, then 1 ounce equals 140/5 = 28 grams. Finally, multiply 28 grams/ounce by 32 ounces to find the total grams: 28 * 32 = 896 grams.

Question 6: 6. Which year did the most children take swimming lessons?

1990
1991
1992
1994
1995 (Correct answer)

Correct answer: 1995

To determine the year with the most children taking swimming lessons, one would examine the provided data (likely a bar graph or table). The year 1995 would show the highest number of participants compared to all other years listed.

Question 7: 7. Between which year did the largest decrease in children taking swimming lessons occur?

1990-1991
1991-1992
1992-1993 (Correct answer)
1993-1994
1994-1995

Correct answer: 1992-1993

To identify the largest decrease, you would calculate the difference in the number of children taking lessons between consecutive years. The period from 1992 to 1993 would show the greatest negative change, indicating the largest drop in participation.

Question 8: 8. What was the average number of children taking swim lessons from 1990 to 1995?

250
308 (Correct answer)
385
450
1,850

Correct answer: 308

To calculate the average, you need to sum the number of children who took swimming lessons for each year from 1990 to 1995. Then, divide this total sum by the number of years, which is six. The result of this calculation is 308.

Question 9: 9. Which of the following is equal to 5.93 x 10-2?

0.0593 (Correct answer)
0.00593
593
5930
59300

Correct answer: 0.0593

To convert a number from scientific notation with a negative exponent to standard form, move the decimal point to the left. The exponent of -2 indicates that the decimal point should be moved two places to the left. Starting with 5.93, moving the decimal two places left results in 0.0593.

Question 10: 10. On a Map, 1 inch represents 20 miles. The distance between 2 towns is 6 1/5 inches. How many miles are actually between the two towns?

65 miles
84 miles
124 miles (Correct answer)
138 miles
145 miles

Correct answer: 124 miles

First, convert the mixed number 6 1/5 inches to a decimal, which is 6.2 inches. Since 1 inch on the map represents 20 miles in reality, multiply the map distance by the scale factor. Therefore, 6.2 inches * 20 miles/inch = 124 miles.

Question 11: 11. Which of the following is a correct graph of x>1, x<4 ?

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

Correct answer: Line A

The inequalities x > 1 and x < 4 describe all numbers greater than 1 but less than 4. On a number line, this is represented by an open interval between 1 and 4. This means there should be open circles (or parentheses) at 1 and 4, with the line segment between them shaded.

Question 12: 12. How many cubed pieces of fudge that are 3 inches on an edge can be packed into a Christmas tin that is 9 inches deep by 12 inches wide by 9 inches high with the lid still being able to be closed?

18
24
32
36 (Correct answer)
43

Correct answer: 36

To find how many cubes fit, calculate how many can fit along each dimension of the tin. For the 12-inch width, 12/3 = 4 cubes fit. For the 9-inch depth, 9/3 = 3 cubes fit. For the 9-inch height, 9/3 = 3 cubes fit. Multiply these numbers together (4 * 3 * 3) to get the total number of cubes that can be packed, which is 36.

Question 13: 13. Sarah is twice as old as her youngest brother. If the difference between their ages is 15 years. How old is her youngest brother?

10
15 (Correct answer)
20
25
30

Correct answer: 15

Let the youngest brother's age be 'B'. Sarah is twice as old, so her age is '2B'. The difference between their ages is 15 years, which can be written as 2B - B = 15. Solving this equation, we find that B = 15. Therefore, her youngest brother is 15 years old.

Question 14: 14. Which of the following fractions is equal to 5/6?

20/30
15/24
25/30 (Correct answer)
40/54
2/7

Correct answer: 25/30

To find a fraction equal to 5/6, you need to multiply both the numerator and the denominator by the same non-zero number. In this case, multiplying both by 5 gives (5 * 5) / (6 * 5) = 25/30. This process creates an equivalent fraction that represents the same value.

Question 15: 15. What will it cost to tile a kitchen floor that is 12 feet wide by 20 feet long if the tile cost $8.91 per square yard?

$224.51
$237.60 (Correct answer)
$246.55
$271.38
$282.32

Correct answer: $237.60

First, calculate the area of the kitchen floor: 12 feet * 20 feet = 240 square feet. Since the tile cost is given per square yard, convert the area to square yards by dividing by 9 (as 1 square yard = 3 feet * 3 feet = 9 square feet): 240 sq ft / 9 sq ft/sq yd = 26.666... square yards. Finally, multiply the area in square yards by the cost per square yard: 26.666... * $8.91 = $237.60.

Question 16: 16. In a writing competition, the first place winner receives ½ of the prize money. The second runner up receives ¼ of what the winner won. What was the total amount of prize money distributed if the winner receives $6,000?

$6,000
$8,500
$12,000 (Correct answer)
$15,000
$18,500

Correct answer: $12,000

The winner received $6,000, which is stated to be 1/2 of the total prize money. To find the total prize money, you simply multiply the winner's amount by 2. Therefore, $6,000 * 2 = $12,000 was the total amount of prize money distributed. The information about the second runner-up is extraneous for this calculation.

Question 17: 17. You are lying 120 ft away from a tree that is 50 feet tall. You look up at the top of the tree. Approximately how far is your hear from the top of the tree in a straight line?

50 feet
75 feet
120 feet
130 feet (Correct answer)
150 feet

Correct answer: 130 feet

This problem forms a right-angled triangle, where the distance from you to the tree (120 ft) and the height of the tree (50 ft) are the two legs. The straight-line distance from your head to the top of the tree is the hypotenuse. Using the Pythagorean theorem (a² + b² = c²), we calculate 50² + 120² = c², which simplifies to 2500 + 14400 = 16900. Taking the square root of 16900 gives c = 130 feet.

Question 18: 18. A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?

8.1
8.3
8.6
8.9 (Correct answer)
9.0

Correct answer: 8.9

To find the average rate, divide the total distance by the total time. Let 'x' be the one-way distance, so the total distance for the round trip is 2x. The time going is x/10 hours, and the time returning is x/8 hours. The total time is x/10 + x/8 = (4x + 5x)/40 = 9x/40 hours. The average rate is (2x) / (9x/40) = 2x * (40/9x) = 80/9, which approximately equals 8.9 miles per hour.

Question 19: 19. If edging cost $2.32 per 12-inch stone, and you want a double layer of edging around your flower bed that is 6 yards by 1 yard. How much will edging you flower bed cost?

$32.48
$64.96
$97.44
$129.92
$194.88 (Correct answer)

Correct answer: $194.88

First, calculate the perimeter of the flower bed in yards: 2 * (6 yards + 1 yard) = 14 yards. Convert this to inches: 14 yards * 3 feet/yard * 12 inches/foot = 504 inches. Since a double layer of edging is desired, the total length needed is 2 * 504 inches = 1008 inches. Each stone is 12 inches, so 1008 inches / 12 inches/stone = 84 stones are needed. Finally, multiply the number of stones by the cost per stone: 84 * $2.32 = $194.88.

Question 20: 20. If 3x=6x-15 then x + 8=

5
10
11
12
13 (Correct answer)

Correct answer: 13

First, solve the equation 3x = 6x - 15 for x. Subtract 6x from both sides to get -3x = -15, then divide by -3 to find x = 5. The question asks for the value of x + 8. Substitute x = 5 into the expression: 5 + 8 = 13.

Question 21: 21. The number of milliliters in 1 liter is

10,000
1,000 (Correct answer)
0.1
0.01
0.001

Correct answer: 1,000

The metric system uses prefixes to denote multiples or submultiples of base units. The prefix 'milli-' means one-thousandth (1/1000). Therefore, 1 liter is equal to 1000 milliliters.

Question 22: 22. The cost to ride on a ferry is $5.00 per vehicle and driver with an additional cost of 50 cents per passenger. If the charge to get on the ferry is $6.50, how many people were in the vehicle?

1
2
3
4 (Correct answer)
5

Correct answer: 4

The base cost for the vehicle and driver is $5.00. Subtract this from the total charge of $6.50 to find the cost attributed to additional passengers: $6.50 - $5.00 = $1.50. Since each additional passenger costs $0.50, divide the remaining cost by $0.50: $1.50 / $0.50 = 3 additional passengers. Including the driver, the total number of people in the vehicle is 1 (driver) + 3 (passengers) = 4 people.

Question 23: 23. What is 1/9 of 9?

1/9
0
1 (Correct answer)
2
3

Correct answer: 1

In mathematics, 'of' typically indicates multiplication. So, '1/9 of 9' means (1/9) * 9. When you multiply a fraction by its denominator, the result is the numerator. Therefore, (1/9) * 9 = 9/9 = 1.

Question 24: 24. In his pocket, a boy has 3 red marbles, 4 blue marbles, and 4 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color?

3
7
8
9 (Correct answer)
11

Correct answer: 9

To guarantee at least one of each color, consider the worst-case scenario. You could pick all of the marbles of the two most numerous colors first. There are 4 blue and 4 green marbles, so you could pick 4 + 4 = 8 marbles without getting a red one. The very next marble you pick (the 9th marble) must be red, ensuring you have at least one of each color.

Question 25: 25. Which fraction is equal to 0.20%?

1/20
1/40
1/50
1/400
1/500 (Correct answer)

Correct answer: 1/500

To convert a percentage to a fraction, first divide the percentage by 100. So, 0.20% becomes 0.20 / 100 = 0.002. Next, convert the decimal to a fraction: 0.002 is equivalent to 2/1000. Finally, simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, 2, resulting in 1/500.

Question 26: 26. Find the missing term in the following sequence: 4, 9, 19, __, 79

36
37
38
39 (Correct answer)
40

Correct answer: 39

Examine the differences between consecutive terms in the sequence: 9 - 4 = 5, and 19 - 9 = 10. This shows a pattern where the difference is doubling. Following this pattern, the next difference should be 10 * 2 = 20. Adding this difference to the last known term gives the missing term: 19 + 20 = 39. To verify, the next difference would be 20 * 2 = 40, and 39 + 40 = 79, which matches the sequence.

Question 27: 27. How much money did Jessica's budget allow for housing in April of 2001?

$617.80
$620.92
$622.50 (Correct answer)
$626.38
$633.20

Correct answer: $622.50

This question requires information from an external budget chart or table for April 2001. To find the correct answer, you would locate the row or entry for 'Housing' in April 2001 on Jessica's budget chart. The value listed there for housing in that specific month is $622.50.

Question 28: 28. What was the average amount of money that Jessica's budget allowed for clothing the first six months of 2001?

$249.90
$250.40
$251.32
$253.33
$255.75 (Correct answer)

Correct answer: $255.75

To find the average amount, you would need to sum Jessica's clothing budget allotments for each of the first six months of 2001 (January through June) from the provided budget chart. Once you have the total sum for these six months, divide that sum by 6 to calculate the average. The correct average amount, based on the data, is $255.75.

Question 29: 29. If Jessica only spent 20% instead of the 25% allotment for food in May of 2001, how much did she save?

$131.10 (Correct answer)
$144.30
$148.32
$152.22
$153.33

Correct answer: $131.10

To determine the savings, first identify Jessica's total budget for May 2001 from the provided chart (which is $2622, derived from the correct answer). The original allotment for food was 25% of this budget, while she only spent 20%. The difference in percentage is 25% - 20% = 5%. Therefore, she saved 5% of her total May budget: 0.05 * $2622 = $131.10.

Question 30: 30. Jonathan can type a 20 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document?

5 minutes
10 minutes (Correct answer)
15 minutes
18 minutes
20 minutes

Correct answer: 10 minutes

First, determine each person's typing rate as a fraction of the document per minute: Jonathan (1/40), Susan (1/30), and Jack (1/24). Add their rates to find their combined rate: 1/40 + 1/30 + 1/24. Using a common denominator of 120, this becomes 3/120 + 4/120 + 5/120 = 12/120 = 1/10 document per minute. The time it takes them to type the document together is the reciprocal of their combined rate, which is 10 minutes.

Question 31: 31. Of the following fractions, which is less than 2/3?

7/8
5/6
3/4
3/5 (Correct answer)
5/7

Correct answer: 3/5

To compare fractions, convert them to decimals or find a common denominator. 2/3 is approximately 0.666... Comparing the options: 7/8 = 0.875, 5/6 ≈ 0.833, 3/4 = 0.75, 3/5 = 0.6, and 5/7 ≈ 0.714. Of these, 3/5 (0.6) is the only fraction that is less than 2/3 (0.666...).

Question 32: 32. A hockey team won 6 games and lost 8. What is the ratio of wins to number of games?

6/8
8/6
3/7 (Correct answer)
8/14
6/7

Correct answer: 3/7

First, calculate the total number of games played: 6 wins + 8 losses = 14 games. The ratio of wins to the total number of games is expressed as wins/total games. So, the ratio is 6/14. To simplify this fraction, divide both the numerator and the denominator by their greatest common divisor, which is 2, resulting in 3/7.

Question 33: 33. Sue receives a base salary of $90 weekly plus a 12% commission on all sales. Sue had $3,000 in sales this week. How much did she make total?

$375
$450 (Correct answer)
$480
$510
$525

Correct answer: $450

33. B: The amount of money she made may be represented by the expression, 90 + 0.12x, where x represents the amount of sales. Substituting 3000 for x gives 90 + 0.12(3000), which equals 450. So, she made $450 this week.

Question 34: 34. If the perimeter of a rectangular house is 25 1/3 yards, and the length is 22 feet. What is the width?

16 feet (Correct answer)
35 feet
37 feet
40 feet
42 feet

Correct answer: 16 feet

First, convert the perimeter from yards to feet: 25 1/3 yards * 3 feet/yard = 76 feet. The perimeter of a rectangle is given by the formula P = 2 * (length + width). Substitute the known values: 76 feet = 2 * (22 feet + width). Divide both sides by 2 to get 38 feet = 22 feet + width. Finally, subtract 22 feet from both sides to find the width: width = 38 feet - 22 feet = 16 feet.

Question 35: 35. Jimmy made a 15% profit on the sale of a custom designed boat, and the original cost of the boat was $15,000. The boat sold for how much?

$17,250.00 (Correct answer)
$16,540.44
$16,230.34
$15,980.55
$15,870.88

Correct answer: $17,250.00

To find the selling price, first calculate the profit amount. A 15% profit on an original cost of $15,000 is 0.15 * $15,000 = $2,250. Then, add this profit to the original cost to find the selling price: $15,000 + $2,250 = $17,250.00.

Question 36: 36. A recent study showed that an increase in body weight by 10 kilograms resulted in a 0.15% increase in heart disease. What fraction is equal to 0.15%?

3/2000 (Correct answer)
2/750
7/4000
5/3462
1/500

Correct answer: 3/2000

To convert a percentage to a fraction, first divide the percentage by 100. So, 0.15% becomes 0.15 / 100 = 0.0015. Next, convert the decimal to a fraction: 0.0015 is equivalent to 15/10000. Finally, simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, 5, resulting in 3/2000.

Question 37: 37. 6.334 x 10<sup>4 </sup>= </strong>

0.0006334
0.06334
6334
63340 (Correct answer)
633400

Correct answer: 63340

Multiplying a number by 10 raised to a positive power means moving the decimal point to the right by the number of places indicated by the exponent. In this case, 10^4 means moving the decimal point 4 places to the right. Starting with 6.334, moving the decimal 4 places to the right results in 63340.

Question 38: 38. If 3x + 5x = -8, then x + 1 =

-2
-1
0 (Correct answer)
1
2

Correct answer: 0

First, solve the equation 3x + 5x = -8 for x. Combine the like terms on the left side: 8x = -8. Divide both sides by 8 to find x = -1. The question asks for the value of x + 1. Substitute x = -1 into the expression: -1 + 1 = 0.

Question 39: 39. Two angle in a triangle equal 120°. What is the measure of the third angle?

60° (Correct answer)
70°
80°
90°
120°

Correct answer: 60°

The sum of the interior angles in any triangle is always 180 degrees. If two angles sum to 120 degrees, you subtract this sum from 180 degrees to find the measure of the third angle. Therefore, 180° - 120° = 60°.

Question 40: 40. Which of the following would be an appropriate unit to measure sugar for a cookie recipe?

liters
cups (Correct answer)
quarts
kilograms
pounds

Correct answer: cups

When measuring ingredients for a cookie recipe, especially dry ingredients like sugar, 'cups' is the standard unit of volume used in most household kitchens. Liters and quarts are typically for larger liquid volumes, while kilograms and pounds are units of mass or weight, not volume, and are less common for small recipe measurements.

PARCC Mathematics Practice Questions 1

1.
An instrument store gives a 10% discount to all students off the original cost of an instrument.
During a back to school sale an additional 15% is taken off the discounted price.
Julie, a student at the local high school, purchases a flute for $306.
How much did it originally cost?