Free NWEA Math Questions and Answers — Questions and Answers

Question 1: Value of α:

70°
85° (Correct answer)
65°
75°

Correct answer: 85°

The sum of the interior angles in any triangle is always 180 degrees. Given two angles of 65° and 30°, their sum is 65° + 30° = 95°. To find the third angle, α, subtract this sum from 180°: α = 180° - 95° = 85°. Thus, the value of α is 85°.

Question 2: 6398 ÷ 14 is what?

362
457 (Correct answer)
467
452

Correct answer: 457

To find the result of 6398 divided by 14, perform long division. 14 goes into 63 four times (4 * 14 = 56), leaving a remainder of 7. Bring down the 9 to make 79. 14 goes into 79 five times (5 * 14 = 70), leaving a remainder of 9. Bring down the 8 to make 98. 14 goes into 98 exactly seven times (7 * 14 = 98), with no remainder. Therefore, 6398 ÷ 14 equals 457.

Question 3: At 48 years old, Roj's father is four times older than Roj. By the next year, what age will Roj be?

13 (Correct answer)
12
10
9

Correct answer: 13

First, calculate Roj's current age. If Roj's father is 48 years old and is four times older than Roj, then Roj's current age is 48 ÷ 4 = 12 years old. The question asks for Roj's age 'by the next year.' Adding one year to Roj's current age, Roj will be 12 + 1 = 13 years old.

Question 4: What is the perimeter of Triangle a (on the left) based on the information provided by the images?

34 (Correct answer)
35
36
32

Correct answer: 34

The perimeter of a triangle is calculated by adding the lengths of all three of its sides. For Triangle 'a', the provided image shows side lengths of 10, 12, and 12. Summing these values gives 10 + 12 + 12 = 34. The information from Triangle 'b', which is identical and explicitly states its perimeter as 34, further confirms this calculation.

Question 5: Which of these coordinates best describes the system of equations' solution? X+3Y=6 2X+Y=7

(1,3)
(2,3)
(0,2)
(3, 1) (Correct answer)

Correct answer: (3, 1)

To find the solution to the system of equations, we can use substitution. From the first equation, X + 3Y = 6, we can express X as X = 6 - 3Y. Substitute this expression for X into the second equation, 2X + Y = 7, which yields 2(6 - 3Y) + Y = 7. Simplifying gives 12 - 6Y + Y = 7, leading to 12 - 5Y = 7. Subtracting 12 from both sides results in -5Y = -5, so Y = 1. Finally, substitute Y = 1 back into X = 6 - 3Y to find X = 6 - 3(1) = 3. Thus, the solution is (3, 1).

Question 6: Sam receives a 2,000 dollar salary each month for selling automobiles, plus a 1% commission on all sales. In addition, he must pay 15% income tax on his entire salary. Which equation, based on Sam's sales (s), depicts his monthly income after taxes (I)?

I=2000+0.01s-0.15x2000
I=2000+0.01-0.15(2000+0.01)
I=0.85(2000+0.1s)
I=0.85(2000+0.01s) (Correct answer)

Correct answer: I=0.85(2000+0.01s)

Sam's total gross income before taxes consists of his base salary ($2000) plus a 1% commission on sales (s), which is 0.01s. So, his gross income is (2000 + 0.01s). Since he pays 15% income tax on his *entire* salary, he retains 100% - 15% = 85% of his gross income. Therefore, his monthly income after taxes (I) is calculated by multiplying his gross income by 0.85, resulting in the equation I = 0.85(2000 + 0.01s).

Question 7: Ten balls in various colors—three yellow, five green, and two red—are contained within a box. Without a substitute, three balls are chosen at random from the box. How likely is it that none of them are yellow?

14÷72
7÷24 (Correct answer)
7÷10
343÷1000

Correct answer: 7÷24

There are 10 balls in total (3 yellow, 5 green, 2 red). To choose three balls with none of them being yellow, we must select from the 7 non-yellow balls (5 green + 2 red). The probability of the first ball not being yellow is 7/10. For the second, it's 6/9 (since one non-yellow ball is removed). For the third, it's 5/8. Multiplying these probabilities: (7/10) * (6/9) * (5/8) = 210/720. Simplifying this fraction by dividing the numerator and denominator by their greatest common divisor (30) gives 7/24.

Question 8: Which of these will yield the least amount of data?

10x (1÷9) (Correct answer)
10x (1÷6)
10x1.6
10x14

Correct answer: 10x (1÷9)

To determine which option yields the least amount, we need to calculate the value of each expression. Option A: 10 * (1/9) = 10/9 ≈ 1.11. Option B: 10 * (1/6) = 10/6 ≈ 1.67. Option C: 10 * 1.6 = 16. Option D: 10 * 14 = 140. Comparing these results, 10/9 (approximately 1.11) is the smallest value, thus yielding the least amount.

Question 9: Which of the following time measures should be in the highest value before the lowest?

250 minutes, 6000 seconds, 3.5 hours, 1/6th a day
1/6th a day, 3.5 hours, 250 minutes, 6000 seconds
6000 seconds, 3.5 hours, 250 minutes, 1/6th a day
6000 seconds, 3.5 hours, 1/6th a day, 250 minutes (Correct answer)

Correct answer: 6000 seconds, 3.5 hours, 1/6th a day, 250 minutes

To order the time measures from lowest to highest, convert them all to a common unit, such as minutes. 6000 seconds is 100 minutes (6000/60). 3.5 hours is 210 minutes (3.5 * 60). 1/6th of a day is 4 hours (24/6), which is 240 minutes (4 * 60). 250 minutes remains 250 minutes. Arranging these from lowest to highest gives: 100 minutes (6000 seconds), 210 minutes (3.5 hours), 240 minutes (1/6th a day), and 250 minutes. This sequence matches option D, assuming the question intended to ask for an ascending order despite stating 'highest value before the lowest'.

Question 10: Select the pairs that have comparable triangles.

Pair (b)
Pairs (a) and (b) (Correct answer)
Pair (a)
Pair (c)

Correct answer: Pairs (a) and (b)

Comparable triangles, also known as similar triangles, are those that have the same shape, meaning their corresponding angles are equal. In Pair (a), both triangles have angles of 90°, 30°, and 60°, making them similar. In Pair (b), both triangles have angles of 70°, 50°, and 60°, also making them similar. However, in Pair (c), the angles (80°, 40°, 60° vs. 80°, 50°, 50°) are not all equal, so they are not similar. Therefore, only pairs (a) and (b) contain comparable triangles.

Question 11: A six-hour marathon runner was involved. Choose every measurement that adds up to six hours.

21,600 Seconds (Correct answer)
300 Minutes
360 Minutes (Correct answer)
21,000 Seconds
10,300 Seconds

Correct answer: 21,600 Seconds

To find the measurements that add up to six hours, convert six hours into minutes and seconds. Six hours is equal to 6 * 60 = 360 minutes. To convert minutes to seconds, multiply by 60: 360 minutes * 60 seconds/minute = 21,600 seconds. Therefore, both 21,600 Seconds and 360 Minutes are equivalent to six hours.

Free NWEA Math Questions and Answers

Value of α: