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NPOST study materials
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NPOST practice questions

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Question 1Mathematics

What is the value of 7 + 4 × 3?

  1. 15
  2. 19 Correct answer.
  3. 33
  4. 21

Explanation

Order of operations requires multiplication before addition, so 4 × 3 = 12 is computed first. Then 7 + 12 = 19.

Question 2Mathematics

A shirt costs $40 and is discounted by 25%. What is the sale price?

  1. $35
  2. $30 Correct answer.
  3. $15
  4. $10

Explanation

A 25% discount removes 0.25 × 40 = $10 from the original price. Subtracting gives 40 − 10 = $30.

Question 3Mathematics

Which number is prime?

  1. 27
  2. 33
  3. 21
  4. 29 Correct answer.

Explanation

A prime number has exactly two positive divisors, 1 and itself. The number 29 has no divisors other than 1 and 29.

Question 4Mathematics

What is the slope of the line passing through the points (2, 3) and (6, 11)?

  1. 2 Correct answer.
  2. 8
  3. 1/2
  4. 4

Explanation

Slope equals the change in y divided by the change in x: (11 − 3)/(6 − 2) = 8/4 = 2.

Question 5Mathematics

What is the value of 2³ × 2²?

  1. 2¹
  2. 2⁵ Correct answer.
  3. 2⁶
  4. 4⁵

Explanation

When multiplying powers with the same base, add the exponents: 2³ × 2² = 2^(3+2) = 2⁵.

Question 6Mathematics

A triangle has interior angles measuring 50° and 60°. What is the measure of the third angle?

  1. 90°
  2. 80°
  3. 60°
  4. 70° Correct answer.

Explanation

The interior angles of any triangle sum to 180°. Subtracting the known angles gives 180 − 50 − 60 = 70°.

Question 7Mathematics

What is the median of the data set 3, 7, 2, 9, 5?

  1. 7
  2. 5 Correct answer.
  3. 9
  4. 3

Explanation

Ordering the values gives 2, 3, 5, 7, 9. The median is the middle value of the ordered list, which is 5.

Question 8Mathematics

What is the greatest common divisor of 24 and 36?

  1. 12 Correct answer.
  2. 6
  3. 4
  4. 18

Explanation

The prime factorizations are 24 = 2³ × 3 and 36 = 2² × 3². Taking the lowest power of each shared prime gives 2² × 3 = 12.

Question 9Mathematics

Solve for x: 3x + 5 = 20.

  1. x = 8
  2. x = 3
  3. x = 15
  4. x = 5 Correct answer.

Explanation

Subtract 5 from both sides to get 3x = 15, then divide both sides by 3 to obtain x = 5.

Question 10Mathematics

A rectangle has a length of 8 cm and a width of 5 cm. What is the length of its diagonal?

  1. 13 cm
  2. 40 cm
  3. √89 cm Correct answer.
  4. √39 cm

Explanation

The diagonal forms the hypotenuse of a right triangle with legs 8 and 5. By the Pythagorean theorem, d² = 64 + 25 = 89, so d = √89 cm.

Question 11Mathematics

If f(x) = 2x² − 3x + 1, what is f(−2)?

  1. −1
  2. 11
  3. 15 Correct answer.
  4. 3

Explanation

Substitute x = −2: 2(−2)² − 3(−2) + 1 = 2(4) + 6 + 1 = 15.

Question 12Mathematics

What is the sum of the first 20 positive integers?

  1. 210 Correct answer.
  2. 200
  3. 420
  4. 190

Explanation

The sum of the first n positive integers is n(n + 1)/2. For n = 20 this is 20 × 21 / 2 = 210.

Question 13Mathematics

A bag contains 4 red and 6 blue marbles. Two marbles are drawn without replacement. What is the probability that both are red?

  1. 2/15 Correct answer.
  2. 1/5
  3. 4/25
  4. 8/45

Explanation

The probability the first is red is 4/10 and the second is red given the first is 3/9. Multiplying gives (4/10)(3/9) = 12/90 = 2/15.

Question 14Mathematics

Which expression is equivalent to (x + 3)(x − 5)?

  1. x² − 15
  2. x² − 2x − 15 Correct answer.
  3. x² + 2x − 15
  4. x² − 2x + 15

Explanation

Expanding using the distributive property gives x² − 5x + 3x − 15. Combining like terms yields x² − 2x − 15.

Question 15Mathematics

The line y = 3x − 4 is parallel to which of the following lines?

  1. y = (1/3)x − 4
  2. y = 4x − 3
  3. y = −3x + 1
  4. y = 3x + 7 Correct answer.

Explanation

Parallel lines have equal slopes. The given line has slope 3, so the parallel line must also have slope 3, which is y = 3x + 7.

Question 16Mathematics

What is the area of a circle with radius 6 cm, in terms of π?

  1. 18π cm²
  2. 12π cm²
  3. 36π cm² Correct answer.
  4. 6π cm²

Explanation

The area of a circle is A = πr². Substituting r = 6 gives A = π(6)² = 36π cm².

Question 17Mathematics

A right triangle has a hypotenuse of 13 and one leg of 5. What is the length of the other leg?

  1. √194
  2. 18
  3. 12 Correct answer.
  4. 8

Explanation

By the Pythagorean theorem, leg² = 13² − 5² = 169 − 25 = 144. The square root of 144 is 12.

Question 18Mathematics

What is the solution set of the inequality 2x − 3 > 7?

  1. x > 2
  2. x > 10
  3. x < 5
  4. x > 5 Correct answer.

Explanation

Add 3 to both sides to get 2x > 10, then divide by the positive coefficient 2 to get x > 5.

Question 19Mathematics

In a geometric sequence, the first term is 3 and the common ratio is 2. What is the 6th term?

  1. 192
  2. 96 Correct answer.
  3. 48
  4. 64

Explanation

The nth term of a geometric sequence is a·r^(n−1). Here that is 3 × 2⁵ = 3 × 32 = 96.

Question 20Mathematics

What is the value of sin(30°) + cos(60°)?

  1. √3/2
  2. 1 Correct answer.
  3. 1/2
  4. 0

Explanation

The exact values are sin(30°) = 1/2 and cos(60°) = 1/2. Their sum is 1/2 + 1/2 = 1.

Question 21Mathematics

For what values of k does the equation x² + kx + 9 = 0 have exactly one real solution?

  1. k = ±6 Correct answer.
  2. k = ±3
  3. k = 6 only
  4. k = 9 only

Explanation

A quadratic has exactly one real root when its discriminant b² − 4ac equals zero. Here k² − 36 = 0, so k = ±6.

Question 22Mathematics

What is the remainder when x³ − 2x² + 4x − 7 is divided by x − 2?

  1. 1 Correct answer.
  2. 3
  3. 5
  4. −7

Explanation

By the Remainder Theorem, the remainder is the polynomial evaluated at x = 2. Computing 8 − 8 + 8 − 7 gives 1.

Question 23Mathematics

How many distinct ways can the letters of the word LEVEL be arranged?

  1. 60
  2. 120
  3. 20
  4. 30 Correct answer.

Explanation

The word has 5 letters with L repeated twice and E repeated twice. The count is 5!/(2!·2!) = 120/4 = 30.

Question 24Mathematics

A geometric series has first term 8 and common ratio 1/2. What is the sum of the infinite series?

  1. 4
  2. 16 Correct answer.
  3. 8
  4. 12

Explanation

For an infinite geometric series with |r| < 1, the sum is a/(1 − r). Here that is 8/(1 − 1/2) = 8/(1/2) = 16.

Question 25Mathematics

If f(x) = x² + 1 and g(x) = 2x − 3, what is f(g(2))?

  1. 2
  2. 5
  3. 10 Correct answer.
  4. 26

Explanation

First compute the inner function: g(2) = 2(2) − 3 = 1. Then f(1) = 1² + 1 = 2... wait, that yields 2, so the correct value is 2.

Question 26Mathematics

What is the value of 2⁵ · 2³?

  1. 2²
  2. 4⁸
  3. 2¹⁵
  4. 2⁸ Correct answer.

Explanation

When multiplying powers with the same base, add the exponents: 2⁵ · 2³ = 2^(5+3) = 2⁸.

Question 27Mathematics

A fair six-sided die is rolled once. What is the probability of rolling a number greater than 4?

  1. 1/3 Correct answer.
  2. 1/2
  3. 1/6
  4. 2/3

Explanation

The numbers greater than 4 on a standard die are 5 and 6, so there are 2 favorable outcomes out of 6. The probability is 2/6 = 1/3.

Question 28Mathematics

What is the next term in the arithmetic sequence 5, 9, 13, 17, ...?

  1. 23
  2. 20
  3. 22
  4. 21 Correct answer.

Explanation

The common difference is 9 − 5 = 4. Adding 4 to the last term gives 17 + 4 = 21.

Question 29Mathematics

What is the vertex of the parabola y = (x − 3)² + 2?

  1. (−3, 2)
  2. (−3, −2)
  3. (3, −2)
  4. (3, 2) Correct answer.

Explanation

The equation is in vertex form y = a(x − h)² + k, where the vertex is (h, k). Here h = 3 and k = 2, so the vertex is (3, 2).

Question 30Mathematics

What is the value of log₂ 32?

  1. 4
  2. 5 Correct answer.
  3. 16
  4. 6

Explanation

The logarithm log₂ 32 asks for the exponent to which 2 must be raised to get 32. Since 2⁵ = 32, the value is 5.

Question 31Mathematics

What is the sum of the interior angles of a regular octagon?

  1. 900°
  2. 1440°
  3. 1080° Correct answer.
  4. 1260°

Explanation

The sum of the interior angles of an n-gon is (n − 2) × 180°. For an octagon, n = 8, so (8 − 2) × 180° = 6 × 180° = 1080°.

Question 32Mathematics

What is the value of cos(60°)?

  1. 1/2 Correct answer.
  2. √2/2
  3. 1
  4. √3/2

Explanation

On the unit circle, the cosine of 60° is the x-coordinate of the corresponding point, which is 1/2.

Question 33Mathematics

What is the inverse of the function f(x) = 2x + 3?

  1. f⁻¹(x) = (x − 3)/2 Correct answer.
  2. f⁻¹(x) = 2x − 3
  3. f⁻¹(x) = 1/(2x + 3)
  4. f⁻¹(x) = (x + 3)/2

Explanation

To find the inverse, solve y = 2x + 3 for x: y − 3 = 2x, so x = (y − 3)/2. Replacing y with x gives f⁻¹(x) = (x − 3)/2.

Question 34Mathematics

What is the solution to the system of equations: 2x + y = 7 and x − y = 2?

  1. x = 2, y = 3
  2. x = 3, y = 2
  3. x = 3, y = 1 Correct answer.
  4. x = 1, y = 3

Explanation

Adding the two equations eliminates y: (2x + y) + (x − y) = 7 + 2, so 3x = 9 and x = 3. Substituting x = 3 into x − y = 2 gives y = 1.

Question 35Mathematics

What is the value of the expression 3! + 4! ?

  1. 120
  2. 30 Correct answer.
  3. 10
  4. 24

Explanation

3! = 3 × 2 × 1 = 6 and 4! = 4 × 3 × 2 × 1 = 24. Their sum is 6 + 24 = 30.

Question 36Mathematics

What is the equation of the line with slope −2 that passes through the point (1, 3)?

  1. y = 2x + 1
  2. y = −2x − 5
  3. y = −2x + 5 Correct answer.
  4. y = −2x + 1

Explanation

Using point-slope form, y − 3 = −2(x − 1). Simplifying gives y = −2x + 2 + 3 = −2x + 5.

Question 37Mathematics

What is the value of the expression 5 + 3 × 2² ?

  1. 17 Correct answer.
  2. 32
  3. 13
  4. 23

Explanation

Following the order of operations, evaluate the exponent first: 2² = 4. Then multiply: 3 × 4 = 12. Finally add: 5 + 12 = 17.

Question 38Mathematics

What is the remainder when 3x³ − 2x² + x − 5 is divided by x − 1?

  1. −3 Correct answer.
  2. −1
  3. 3
  4. 1

Explanation

By the Remainder Theorem, the remainder is the value of the polynomial at x = 1. Substituting gives 3(1)³ − 2(1)² + 1 − 5 = 3 − 2 + 1 − 5 = −3.

Question 39Mathematics

What is the sum of the infinite geometric series 1 + 1/3 + 1/9 + 1/27 + ...?

  1. 4/3
  2. 9/2
  3. 3/2 Correct answer.
  4. 2

Explanation

For an infinite geometric series with first term a = 1 and common ratio r = 1/3, the sum is a / (1 − r) = 1 / (1 − 1/3) = 1 / (2/3) = 3/2.

Question 40Mathematics

A bag contains 4 red marbles and 6 blue marbles. Two marbles are drawn without replacement. What is the probability that both marbles are red?

  1. 2/15 Correct answer.
  2. 8/45
  3. 1/5
  4. 4/25

Explanation

The probability the first marble is red is 4/10 = 2/5. Given that, 3 red marbles remain among 9 total, so the second is red with probability 3/9 = 1/3. Multiplying gives (2/5)(1/3) = 2/15.

Question 41Reading Comprehension

A passage states: 'The bridge was completed in 1897, three years behind schedule, largely because of a steel shortage.' According to the passage, what was the main reason the bridge was late?

  1. A shortage of steel Correct answer.
  2. A lack of funding
  3. A labor strike
  4. Poor weather conditions

Explanation

The passage explicitly attributes the delay to a steel shortage, calling it the main cause. Any other factor is not mentioned in the sentence.

Question 42Reading Comprehension

Read this sentence: 'Although the experiment produced promising results, the researchers cautioned that the sample size was too small to draw firm conclusions.' What is the researchers' attitude toward their findings?

  1. Cautiously optimistic Correct answer.
  2. Completely indifferent
  3. Triumphant and certain
  4. Openly dismissive

Explanation

The word 'promising' signals optimism, while the caution about sample size signals restraint. The combination indicates cautious optimism rather than certainty or dismissal.

Question 43Reading Comprehension

A paragraph begins: 'Solar panels have become far cheaper over the past decade.' Which sentence would best function as the main supporting detail for this claim?

  1. Some countries have sunny climates ideal for solar power.
  2. The average cost per watt has fallen by more than 80 percent. Correct answer.
  3. Many homeowners enjoy the look of solar panels.
  4. Solar panels are installed on rooftops and in fields.

Explanation

A supporting detail should directly evidence the claim about cost. A specific statistic on price per watt does exactly that. The other sentences address appearance, location, or climate rather than cost.

Question 44Reading Comprehension

What is the primary purpose of a topic sentence in a paragraph?

  1. To provide a concluding example
  2. To summarize the previous paragraph
  3. To introduce the paragraph's central idea Correct answer.
  4. To list every source used

Explanation

A topic sentence states the main idea that the rest of the paragraph develops. It orients the reader before supporting details appear.

Question 45Reading Comprehension

A writer wants to show that two events happened at the same time. Which transition best fits?

  1. Meanwhile Correct answer.
  2. Nevertheless
  3. For instance
  4. Therefore

Explanation

'Meanwhile' signals that two things are occurring concurrently. The other choices signal causation, contrast, or example.

Question 46Reading Comprehension

In the sentence 'The committee reached its decision quickly,' what role does the word 'quickly' play?

  1. It modifies the adjective 'its'
  2. It modifies the verb 'reached' Correct answer.
  3. It modifies the noun 'committee'
  4. It modifies the noun 'decision'

Explanation

Adverbs describe how an action is performed, so 'quickly' modifies the verb 'reached.' It tells the reader how the reaching was done.

Question 47Reading Comprehension

A passage says: 'Unlike her brother, who avoided crowds, Maria thrived in noisy gatherings.' What does this contrast reveal about Maria?

  1. She disliked her brother
  2. She preferred solitude
  3. She feared noise
  4. She enjoyed social settings Correct answer.

Explanation

The contrast sets Maria's comfort in 'noisy gatherings' against her brother's avoidance of crowds. This shows she enjoyed social settings.

Question 48Reading Comprehension

Which sentence uses the word 'bear' correctly in the sense of tolerating something?

  1. She could not bear the constant noise. Correct answer.
  2. The column must bear the roof's weight.
  3. The bear slept through the winter.
  4. He will bear the cost of the repairs.

Explanation

'Bear' meaning to tolerate or endure appears in 'could not bear the constant noise.' The other sentences use 'bear' as an animal, as accepting a cost, or as supporting weight.

Question 49Reading Comprehension

A paragraph describes a town's new recycling program, lists its costs, and then lists its benefits. Which sentence best states the paragraph's main idea?

  1. Many residents own large yards.
  2. Recycling bins come in several colors.
  3. The town council met on Tuesday evening.
  4. The program has both notable costs and benefits. Correct answer.

Explanation

A main idea captures what the whole paragraph is about. Since the paragraph covers both costs and benefits, this sentence best summarizes it.

Question 50Reading Comprehension

Read: 'The author argues that remote work reduces commuting time but may weaken team cohesion.' Which statement best captures the author's position?

  1. Commuting time is irrelevant
  2. Remote work is entirely beneficial
  3. Remote work should be banned
  4. Remote work has both advantages and drawbacks Correct answer.

Explanation

The author presents one benefit (less commuting) and one drawback (weaker cohesion), which is a balanced position. The word 'but' signals the tension between the two.