STEM Entrance Exam Quiz: Can You Pass This STEM Exam?

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  • 1/30 Questions

    What is the value of K if the expression (- 5x3 + 4x2 – 3x + K) is divided by (x-1), and obtains a remainder of 10?

    • 12
    • 14
    • 16
    • 18
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About This Quiz


Are you dreaming of a future in science, technology, engineering, or mathematics? Do you have what it takes to excel in these challenging and rewarding fields? Then put your skills to the test with our comprehensive STEM Entrance Exam Quiz! This quiz covers a wide range of STEM topics, from basic math and science concepts to more advanced problem-solving and See morecritical thinking questions.

We've designed this quiz to help you assess your strengths and weaknesses and identify areas where you might need to focus your studies. This STEM entrance exam reviewer provides a sneak peek into the types of questions you might encounter on the actual exam. We'll challenge you with questions on mathematics, science, and logical reasoning and problem-solving. If you're a high school student preparing for college entrance exams or an adult looking to pursue a career in STEM, this quiz offers a valuable opportunity to assess your readiness and identify areas for improvement.

Stem Entrance Exam Quiz: Can You Pass This Stem Exam? - Quiz

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  • 2. 

    A die is to be thrown and a card is to be drawn in a deck of cards. What is the probability that the card drawn is an ace and an even number will appear on a die?

    • 4/13

    • 5/156

    • 1/13

    • 1/26

    Correct Answer
    A. 1/26
    Explanation
    The probability of drawing an ace from a deck of cards is 4/52, since there are 4 aces in a standard deck of 52 cards. The probability of rolling an even number on a die is 3/6, since there are 3 even numbers (2, 4, and 6) out of 6 possible outcomes. To find the probability of both events occurring, we multiply the probabilities together: (4/52) * (3/6) = 12/312 = 1/26. Therefore, the correct answer is 1/26.

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  • 3. 

    Jace will evaluate a 7th-degree polynomial in m, whose value is 5 through synthetic division. How many coefficients of m shall be written in the first row of the synthetic division procedure?

    • 5

    • 6

    • 7

    • 8 

    Correct Answer
    A. 8 
    Explanation
    In synthetic division, the number of coefficients written in the first row is equal to the degree of the polynomial plus one. Since the polynomial in this question is a 7th-degree polynomial, there will be 8 coefficients written in the first row of the synthetic division procedure.

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  • 4. 

    A committee consisting of 4 males and 3 females is to be formed. In how many ways can the committee be formed if there are 8 females and 6 males available?

    • 840

    • 820

    • 780

    • 760

    Correct Answer
    A. 840
    Explanation
    The committee can be formed by selecting 3 females out of 8 available females and 4 males out of 6 available males. The number of ways to select 3 females out of 8 is given by the combination formula, which is 8C3 = 8! / (3! * (8-3)!) = 8! / (3! * 5!) = (8 * 7 * 6) / (3 * 2 * 1) = 56. Similarly, the number of ways to select 4 males out of 6 is given by the combination formula, which is 6C4 = 6! / (4! * (6-4)!) = 6! / (4! * 2!) = (6 * 5) / (2 * 1) = 15. Therefore, the total number of ways to form the committee is 56 * 15 = 840.

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  • 5. 

    What is the value of P(-2) in the expression: P(x) = 7x4 – 5x3 + 2x2 – 3?

    • 161

    • 159

    • 157

    • 155

    Correct Answer
    A. 157
    Explanation
    To find the value of P(-2), we substitute -2 for x in the expression P(x). Plugging in -2, we get P(-2) = 7(-2)^4 - 5(-2)^3 + 2(-2)^2 - 3. Simplifying this expression, we get P(-2) = 7(16) + 5(8) + 2(4) - 3 = 112 + 40 + 8 - 3 = 157. Therefore, the value of P(-2) is 157.

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  • 6. 

    There are 10 green balls, 8 white balls, and 6 blue balls in a jar.  What is the probability that when a ball is picked from the bag, it is a non-white ball?

    • 1/4

    • 2/3

    • 7/12

    • 1/3

    Correct Answer
    A. 2/3
    Explanation
    The probability of picking a non-white ball can be calculated by dividing the number of non-white balls by the total number of balls. In this case, there are 10 green balls and 6 blue balls, which makes a total of 16 non-white balls. The total number of balls in the jar is 10 + 8 + 6 = 24. Therefore, the probability of picking a non-white ball is 16/24, which simplifies to 2/3.

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  • 7. 

    Which of the following polynomial equation with roots -1, 1, and 4?

    • P(x) = x3 – 4x2 – 2x + 4

    • P(x) = x3 – 4x2 – 4x – 4

    • P(x) = x3 – 4x2 + x + 4

    • P(x) = x3 – 4x2 – x + 4

    Correct Answer
    A. P(x) = x3 – 4x2 – x + 4
    Explanation
    The given polynomial equation has roots -1, 1, and 4. To find the correct equation, we need to check which equation gives us these roots when plugged in. By substituting -1, 1, and 4 into each equation, we find that only P(x) = x3 – 4x2 – x + 4 gives us the desired roots. Therefore, P(x) = x3 – 4x2 – x + 4 is the correct equation.

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  • 8. 

    What are the roots of the quadratic equation b2 – 5b – 36 = 0?

    • (9, 4)

    • (9,-4)

    • (-9, -4)

    • (-9,4)

    Correct Answer
    A. (9,-4)
    Explanation
    To find the roots of the quadratic equation b^2 - 5b - 36 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the roots can be found using the formula:
    x = (-b ± √(b^2 - 4ac)) / 2a
    In this case, our equation is b^2 - 5b - 36 = 0. So, we have:
    a = 1 b = -5 c = -36
    Plugging these values into the quadratic formula, we get:
    b = [5 ± √((-5)^2 - 4(1)(-36))] / 2(1) b = [5 ± √(25 + 144)] / 2 b = [5 ± √169] / 2 b = [5 ± 13] / 2
    Now, we have two possible roots:
    b = (5 + 13) / 2 = 18 / 2 = 9
    b = (5 - 13) / 2 = -8 / 2 = -4
    Therefore, the roots of the quadratic equation b^2 - 5b - 36 = 0 are 9 and -4.

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  • 9. 

    A square with a side of 12 cm and a rectangle with a width of 8 cm have the same area. What is the length of the rectangle?

    • 16 CM

    • 17 CM

    • 18 CM

    • 20 CM

    Correct Answer
    A. 18 CM
    Explanation
    The area of a square is calculated by multiplying the length of one side by itself. In this case, the side of the square is given as 12 cm, so the area of the square is 12 cm * 12 cm = 144 cm^2. The area of a rectangle is calculated by multiplying its length by its width. Since the rectangle and the square have the same area, we can set up the equation 144 cm^2 = length of rectangle * 8 cm. Solving for the length of the rectangle, we find that it is 18 cm.

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  • 10. 

    In square FATE, the measure of angle F is 4x + 30.  What is the value of x?

    • 21 degrees

    • 19 degrees

    • 15 degrees

    • 13 degrees 

    Correct Answer
    A. 15 degrees
    Explanation
    The measure of angle F in square FATE is given as 4x + 30. To find the value of x, we can equate this expression to the given answer choices and solve for x. By substituting 15 degrees for x in the expression 4x + 30, we get 4(15) + 30 = 60 + 30 = 90 degrees. Since 90 degrees is not one of the answer choices, we can conclude that the given answer of 15 degrees is incorrect. Therefore, the correct answer cannot be determined from the information provided.

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  • 11. 

    What is the sum of the first 8 terms of an arithmetic sequence whose first term is 37 and the common difference is -4?

    • 180

    • 182

    • 184

    • 186

    Correct Answer
    A. 184
  • 12. 

    The polynomial function P(x) = xn is true when,

    • N is any real number

    • N is an non-negative number

    • N is an integer

    • N is an irrational number

    Correct Answer
    A. N is an integer
  • 13. 

    What is the leading term in a polynomial function P(x) = 5 + 7x4 – 3x + 2x5?

    • 7x4

    • 3x

    • 2x5

    Correct Answer
    A. 2x5
  • 14. 

    The computation for profit in a textile store is presented by the mathematical model P(x) = 3x2 + 6x – 120,000 where x is the number of meters being sold. What is the computed profit if the number of meters being sold is 250?

    • 70,000.00

    • 69000.00

    • 68, 000.00

    • 67,000.00

    Correct Answer
    A. 69000.00
    Explanation
    To find the computed profit when 250 meters are being sold, we can substitute the value of x = 250 into the given mathematical model:
    P(x) = 3x^2 + 6x - 120,000
    So,
    P(250) = 3(250)^2 + 6(250) - 120,000
    Now, let's compute:
    P(250) = 3(62500) + 1500 - 120,000 = 187500 + 1500 - 120,000 = 189000 - 120,000 = 69,000
    Therefore, the computed profit when 250 meters are being sold is $69,000.

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  • 15. 

    Which of the following function will cross the x-axis thrice?

    • P(x) = (x2-1)(x2 – 5x + 6)

    • P(x) = (2x2 – 5x + 2) (x+3)

    • Both A and B

    • Neither A Nor B

    Correct Answer
    A. P(x) = (2x2 – 5x + 2) (x+3)
    Explanation
    The function P(x) = (2x^2 - 5x + 2) (x+3) will cross the x-axis thrice because it is a quadratic function with a leading coefficient of 2, which means it opens upwards. The quadratic factor (2x^2 - 5x + 2) will have two x-intercepts, and the linear factor (x+3) will have one x-intercept. When multiplied together, these factors will result in a function that crosses the x-axis three times.

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  • 16. 

    Which of the following mathematical models is used to determine the distance between two points whose coordinates are (x1, y1) and (x2, y2)?

    Correct Answer
    A. D. 
    Explanation
    The correct answer is D. The distance between two points whose coordinates are (x1, y1) and (x2, y2) can be determined using the mathematical model known as the distance formula. This formula is derived from the Pythagorean theorem and states that the distance between two points in a Cartesian plane is equal to the square root of the sum of the squares of the differences between their x-coordinates and y-coordinates.

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  • 17. 

    If the set of numbers 3, -12, 48, -192 form a geometric sequence, what is the common ratio between any two consecutive terms?

    • – 12

    • – 8

    • -6

    • -4

    Correct Answer
    A. -4
    Explanation
    The common ratio between any two consecutive terms in a geometric sequence is found by dividing one term by the previous term. In this case, dividing -12 by 3 gives us -4. Therefore, -4 is the common ratio between any two consecutive terms in the given sequence.

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  • 18. 

    What is the next term in the arithmetic sequence:  2, 13/4, 9/2, 23/4

    • 7

    • 29/4

    • 15/2

    • 31/4

    Correct Answer
    A. 7
    Explanation
    The given arithmetic sequence starts with 2 and increases by 5/4 each time. To find the next term, we add 5/4 to the previous term 23/4, which gives us 28/4 or 7. Therefore, the next term in the sequence is 7.

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  • 19. 

    Which of the following is NOT an example of a harmonic sequence?

    • 1/6, 1/7, 1/8, 1/9,...

    • 4, 0, -4, -2

    • 1/4, 1/12, 1/36,1/108,...

    • 1/3, 1/12, 1/21, 1/30,...

    Correct Answer
    A. 4, 0, -4, -2
    Explanation
    1/4, undefined (since the reciprocal of 0 is not defined), -1/4, -1/8,... This does not form an arithmetic sequence, and the presence of 0 makes it impossible to properly form a reciprocal sequence. Therefore, this is not a harmonic sequence.

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  • 20. 

    What is the sum of all even integers from 21 to 51?

    • 540

    • 596

    • 600

    • 640

    Correct Answer
    A. 540
    Explanation
    The sum of all even integers from 21 to 51 can be calculated by finding the average of the first and last even numbers in the range (22 and 50) and multiplying it by the number of terms. Calculating the number of terms = [(50 - 22) / 2] + 1 = 15. The average of 22 and 50 is 36, so multiplying it by 15 gives us a sum of 540.

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  • 21. 

    What quotient shall be obtained when (x+9) divides (x2 – 81)?

    • X+9

    • X-9

    • 9X+1

    • 9X-1

    Correct Answer
    A. X-9
    Explanation
    When (x+9) divides (x^2 - 81), it means that (x^2 - 81) can be expressed as a product of (x+9) and another factor. To find this factor, we can use the method of polynomial long division. By dividing (x^2 - 81) by (x+9), we get a quotient of (x-9). Therefore, the correct answer is X-9.

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  • 22. 

    What is the remainder of the expression ( 5b2+ 15b – 35) is divided by (b + 5)?

    • 15

    • 20

    • 25

    • 30

    Correct Answer
    A. 15
  • 23. 

    What is the expansion of (2x – 3)3?

    • 8x3 – 27

    • 8x3 – 36x2 + 54x – 27

    • 8x3 + 54x – 27

    • 8x3 + 36x2 – 54x – 27

    Correct Answer
    A. 8x3 – 36x2 + 54x – 27
  • 24. 

    Mr.Torres has to travel going to his workplace during weekdays (Monday to Friday). He has three ways to travel – by train, car, or jeep. In how many ways can Mr. Torres report for work during the said days?

    • 243 ways

    • 225 ways

    • 15 ways

    • 3 ways

    Correct Answer
    A. 243 ways
  • 25. 

    What is the value of the expression C (8, 6)? (C=Combination)

    • 56

    • 48

    • 28

    • 14

    Correct Answer
    A. 28
    Explanation
    To calculate C(8, 6), we use the combination formula:

    C(n, k) = n! / (k!(n - k)!)

    Plug in the values:

    C(8, 6) = 8! / (6!(8 - 6)!)

    Calculate the factorials:

    8! = 8 * 7 * 6!
    6! = 6 * 5 * 4 * 3 * 2 * 1

    Now calculate:

    C(8, 6) = (8 * 7 * 6!) / (6! * 2!)

    Simplify:

    C(8, 6) = (8 * 7) / (2 * 1)

    C(8, 6) = 56 / 2

    C(8, 6) = 28

    So, the answer is:

    C) C(8, 6) = 28

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  • 26. 

    What is the value of expression 10!/(4!7!)

    • 90

    • 60

    • 40

    • 30 

    Correct Answer
    A. 30 
    Explanation
    The expression 10!/(4!7!) can be simplified as follows:
    10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 4! = 4 × 3 × 2 × 1 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1
    Substituting these values into the expression:
    10!/(4!7!) = (10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / [(4 × 3 × 2 × 1) × (7 × 6 × 5 × 4 × 3 × 2 × 1)]
    Many terms cancel out in the numerator and the denominator:
    (10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / [(4 × 3 × 2 × 1) × (7 × 6 × 5 × 4 × 3 × 2 × 1)] = (10 × 9 × 8) / (4 × 3 × 2) = (720) / (24) = 30
    So, the value of the expression 10!/(4!7!) is 30.

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  • 27. 

    What is the equation of the circle whose center is at the point (3,2), and the point (9,10) is on the circle?

    • (x + 3)2 + (y + 2)2 = 10

    • (x – 3)2 + (y – 2)2 = 100

    • (x – 2)2 + (y – 3)2 = 100

    Correct Answer
    A. (x – 3)2 + (y – 2)2 = 100
    Explanation
    The equation of a circle with center (h, k) and radius r is given by (x - h)^2 + (y - k)^2 = r^2. In this question, the center of the circle is given as (3, 2) and a point on the circle is (9, 10). By substituting these values into the equation, we get (x - 3)^2 + (y - 2)^2 = 100, which matches the given answer.

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  • 28. 

    Which of the following is (3a + 1) a factor of?

    • 3a2 + 3a + 1

    • 3a2 + 5a + 1

    • 6a2 + 5a + 1

    • 6a2 + 5a + 3

    Correct Answer
    A. 6a2 + 5a + 1
    Explanation
    (6a^2 + 5a + 1) is divisible by (3a + 1), because when we divide it by (3a + 1), we get no remainder:
    (6a^2 + 5a + 1) ÷ (3a + 1) 2(3a^2 + 3a) + 1 = (2 * 3a^2) + (2 * 3a) + 1
    When we divide the first two terms, we get a quotient of (2 * 3a^2) + (2 * 3a), which is the same as (3a^2 + 3a) multiplied by 2. Therefore, (3a + 1) is a factor of (6a^2 + 5a + 1).

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  • 29. 

    What is the value of P(8, 5)? (P = Permutation)

    • 2580

    • 1120

    • 860

    • 6720

    Correct Answer
    A. 6720
    Explanation
    The value of P(8, 5) represents a permutation of 8 items taken 5 at a time. In permutation, the order of selection matters. The formula for calculating permutations is:
    P(n, r) = n! / (n - r)!
    Where:
    P(n, r) represents the number of permutations of n items taken r at a time.
    n! (read as "n factorial") represents the product of all positive integers from 1 to n.
    In this case, for P(8, 5):
    P(8, 5) = 8! / (8 - 5)! P(8, 5) = 8! / 3!
    Now, calculate the factorials:
    8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40,320 3! = 3 × 2 × 1 = 6
    Now, divide 8! by 3!:
    P(8, 5) = 40,320 / 6 = 6,720
    So, P(8, 5) = 6,720.

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  • 30. 

    A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If two marbles are drawn at random without replacement, what is the probability that both marbles are blue? 

    • 3/10 

    • 9/100 

    • 1/15 

    • 3/50

    Correct Answer
    A. 1/15 
    Explanation
    To find the probability of drawing two blue marbles without replacement, we need to consider the probability of each draw separately.
    First draw: The probability of drawing a blue marble is 3 (number of blue marbles) / 10 (total number of marbles).
    Second draw: After taking out one blue marble, there are only 2 blue marbles left and 9 total marbles. So, the probability of drawing another blue marble is 2/9.
    To get the probability of both events happening, we multiply the individual probabilities: (3/10) * (2/9) = 6/90 = 1/15.

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  • Current Version
  • Jan 02, 2025
    Quiz Edited by
    ProProfs Editorial Team
  • Apr 14, 2019
    Quiz Created by
    Jude Sodusta

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