STEM Entrance Exam Quiz: Can You Pass This STEM Exam?
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Gear up to tackle the challenges of our STEM Entrance Exam Quiz. It is designed by experts in the fields of science, technology, engineering, and mathematics, this quiz covers a wide range of topics essential for success in the exam. From fundamental concepts to advanced theories, our quiz ensures that you are thoroughly prepared to tackle any question that comes your way.
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STEM Entrance Exam Questions and Answers
1.
If the set of numbers 3, -12, 48, -192 form a geometric sequence, what is the common ratio between any two consecutive terms?
A.
â€“ 12
B.
â€“ 8
C.
-6
D.
-4
Correct Answer D. -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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2.
What is the next term in the arithmetic sequence: 2, 13/4, 9/2, 23/4
A.
7
B.
29/4
C.
15/2
D.
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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3.
Which of the following is NOT an example of a harmonic sequence?
A.
1/6, 1/7, 1/8, 1/9,...
B.
4, 0, -4, -2
C.
1/4, 1/12, 1/36,1/108,...
D.
1/3, 1/12, 1/21, 1/30,...
Correct Answer B. 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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4.
What is the sum of all even integers from 21 to 51?
A.
540
B.
596
C.
600
D.
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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5.
What quotient shall be obtained when (x+9) divides (x^{2} – 81)?
A.
X+9
B.
X-9
C.
9X+1
D.
9X-1
Correct Answer B. 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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6.
What is the remainder of the expression ( 5b^{2}+ 15b – 35) is divided by (b + 5)?
A.
15
B.
20
C.
25
D.
30
Correct Answer A. 15
7.
Which of the following is (3a + 1) a factor of?
A.
3a^{2} + 3a + 1
B.
3a^{2} + 5a + 1
C.
6a^{2} + 5a + 1
D.
6a^{2} + 5a + 3
Correct Answer C. 6a^{2} + 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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8.
What is the value of K if the expression (- 5x^{3} + 4x^{2} – 3x + K) is divided by (x-1), and obtains a remainder of 10?
A.
12
B.
14
C.
16
D.
18
Correct Answer B. 14
Explanation .
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9.
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?
A.
5
B.
6
C.
7
D.
8
Correct Answer D. 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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10.
What is the value of P(-2) in the expression: P(x) = 7x^{4} – 5x^{3} + 2x^{2} – 3?
A.
161
B.
159
C.
157
D.
155
Correct Answer C. 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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11.
Which of the following polynomial equation with roots -1, 1, and 4?
A.
P(x) = x^{3} â€“ 4x^{2} â€“ 2x + 4
B.
P(x) = x^{3} â€“ 4x^{2} â€“ 4x â€“ 4
C.
P(x) = x^{3} – 4x^{2} + x + 4
D.
P(x) = x^{3} – 4x^{2} – x + 4
Correct Answer D. P(x) = x^{3} – 4x^{2} – 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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12.
What are the roots of the quadratic equation b^{2} – 5b – 36 = 0?
A.
(9, 4)
B.
(9,-4)
C.
(-9, -4)
D.
(-9,4)
Correct Answer B. (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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13.
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?
A.
16 CM
B.
17 CM
C.
18 CM
D.
20 CM
Correct Answer C. 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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14.
In square FATE, the measure of angle F is 4x + 30. What is the value of x?
A.
21 degrees
B.
19 degrees
C.
15 degrees
D.
13 degrees
Correct Answer C. 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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15.
What is the sum of the first 8 terms of an arithmetic sequence whose first term is 37 and the common difference is -4?
A.
180
B.
182
C.
184
D.
186
Correct Answer C. 184
16.
The polynomial function P(x) = x^{n} is true when,
A.
N is any real number
B.
N is an non-negative number
C.
N is an integer
D.
N is an irrational number
Correct Answer B. N is an non-negative number
Explanation The given polynomial function P(x) = xn is true when N is a non-negative number because the exponent, represented by N, must be a non-negative integer or zero. This is because raising a number to a negative exponent or a non-integer exponent would result in a non-polynomial function. Therefore, the given polynomial function is only true when N is a non-negative number.
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17.
What is the leading term in a polynomial function P(x) = 5 + 7x^{4} – 3x + 2x^{5}?
A.
7x^{4}
B.
3x
C.
2x^{5}
Correct Answer C. 2x^{5}
18.
The computation for profit in a textile store is presented by the mathematical model
P(x) = 3x^{2} + 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?
A.
70,000.00
B.
69000.00
C.
68, 000.00
D.
67,000.00
Correct Answer B. 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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19.
Which of the following function will cross the x-axis thrice?
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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20.
Which of the following mathematical models is used to determine the distance between two points whose coordinates are (x_{1}, y_{1}) and (x_{2}, y_{2})?
A.
A.
B.
B.
C.
D.
Correct Answer C. 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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21.
What is the expansion of (2x – 3)^{3}?
A.
8x^{3} – 27
B.
8x^{3} – 36x^{2} + 54x – 27
C.
8x^{3} + 54x â€“ 27
D.
8x^{3} + 36x^{2} – 54x – 27
Correct Answer B. 8x^{3} – 36x^{2} + 54x – 27
22.
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?
A.
243 ways
B.
225 ways
C.
15 ways
D.
3 ways
Correct Answer A. 243 ways
23.
What is the value of the expression C (8, 6)? (C=Combination)
A.
56
B.
48
C.
28
D.
14
Correct Answer C. 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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24.
What is the value of expression 10!/(4!7!)
A.
90
B.
60
C.
40
D.
30
Correct Answer D. 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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25.
What is the equation of the circle whose center is at the point (3,2), and the point (9,10) is on the circle?
A.
(x + 3)^{2} + (y + 2)^{2} = 10
B.
(x – 3)^{2} + (y – 2)^{2} = 100
C.
(x – 2)^{2} + (y – 3)^{2} = 100
Correct Answer B. (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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26.
What is the value of P(8, 5)? (P = Permutation)
A.
2580
B.
1120
C.
860
D.
6720
Correct Answer D. 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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27.
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?
A.
4/13
B.
5/156
C.
1/13
D.
1/26
Correct Answer D. 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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28.
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?
A.
840
B.
820
C.
780
D.
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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29.
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?
A.
1/4
B.
2/3
C.
7/12
D.
1/3
Correct Answer B. 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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