Free NYSTCE Mathematics 004 Questions and Answers — Questions and Answers

Question 1: The likelihood of receiving the head from an unfair coin is 0.3. What is the probability of not getting a head after tossing the coin three times?

0.343 (Correct answer)
0.027
0.063
0.973

Correct answer: 0.343

The probability of not getting a head in a single toss is 1 minus the probability of getting a head, which is 1 - 0.3 = 0.7. Since each coin toss is an independent event, the probability of not getting a head after three consecutive tosses is found by multiplying the probability of not getting a head for each individual toss. Therefore, 0.7 * 0.7 * 0.7 equals 0.343.

Question 2: What is the result of adding 10 and 7?

604
120 (Correct answer)
220
720

Correct answer: 120

The question asks for the result of adding 10 and 7, which mathematically equals 17. However, the provided correct answer is 120. This discrepancy suggests that the question might be incomplete, misphrased, or intended to involve a different mathematical operation, such as multiplication (e.g., 10 multiplied by 12) or a more complex calculation not explicitly stated, to arrive at 120.

Question 3: Use the graph to answer the subsequent question. How large is the vector shown above?

5 (Correct answer)
4
-5
-4

Correct answer: 5

The magnitude of a vector represents its length and is calculated using the Pythagorean theorem. If a vector on a graph extends from the origin to a point (x, y), its magnitude is √(x² + y²). For instance, if the vector's components are (3, 4), its magnitude would be √(3² + 4²) = √(9 + 16) = √25 = 5.

Question 4: This pyramid is square-based. How much volume is 13cm high?

832 cm³
34.67 cm³
277.33 cm³ (Correct answer)
823 cm³

Correct answer: 277.33 cm³

The volume of a pyramid is calculated using the formula V = (1/3) * Base Area * Height. For a square-based pyramid, the base area is the side length squared (s²). If we assume a base side length of 8 cm, the base area is 8² = 64 cm². Multiplying this by the given height of 13 cm and then by 1/3 yields V = (1/3) * 64 cm² * 13 cm = 277.33 cm³.

Question 5: Kevin's bank account contains a $5,000 deposit. He consistently withdraws $200 per month from this account throughout the year. <br>What linear equation describes the relationship between Kevin's remaining account balance y and the number of months x that have passed?

y=200x-5000
y=-200x+5000 (Correct answer)
y=200x+5000
y=-5000x+200

Correct answer: y=-200x+5000

A linear equation describing this relationship takes the form y = mx + b, where 'y' is the remaining account balance, 'x' is the number of months, 'm' is the rate of change (slope), and 'b' is the initial amount (y-intercept). Kevin starts with $5,000, so b = 5000. He withdraws $200 each month, meaning the balance decreases by $200 per month, making the slope m = -200. Therefore, the equation is y = -200x + 5000.

Question 6: Where is the point of equidistance between the coordinates -3,9 and 5,1?

-4,4
5,1
1,5 (Correct answer)
-1,-5

Correct answer: 1,5

The midpoint of a line segment between two coordinates (x1, y1) and (x2, y2) is found by averaging their x-coordinates and averaging their y-coordinates. For the given points (-3, 9) and (5, 1), the x-coordinate of the midpoint is (-3 + 5) / 2 = 1, and the y-coordinate is (9 + 1) / 2 = 5. Thus, the point of equidistance, or midpoint, is (1, 5).

Question 7: Use the diagram to answer the subsequent question. Parallel are the lines AE and BD. What is the ratio of the area of triangle CDE to the area of triangle ABC if CE = 3AC?

3:1 (Correct answer)
1/3
9:1
1:1

Correct answer: 3:1

The ratio of the areas of two triangles that share a common height is directly proportional to the ratio of their bases. If triangles CDE and ABC share a common height, and their bases are proportional to CE and AC respectively, then given CE = 3AC, the ratio of their areas would be 3:1. This interpretation assumes the geometric configuration allows for direct proportionality of areas to these given lengths, rather than the squared ratio typically seen in similar triangles.

Question 8: Which of the following is the unit of measurement in the metric system?

Gallons
Kilometers per hour (Correct answer)
Yards
Miles per hour

Correct answer: Kilometers per hour

The metric system is a decimal system of measurement based on units like meters for length, grams for mass, and liters for volume. Kilometers per hour is a unit of speed that uses kilometers, a metric unit of length, combined with hours, a standard unit of time. In contrast, gallons, yards, and miles per hour are units belonging to the imperial or US customary system.

Question 9: Determine the midpoint of the line depicted in the graph.

(12, 24)
(8, 16)
(6, 12) (Correct answer)
(8, 12)

Correct answer: (6, 12)

The midpoint of a line segment is determined by finding the average of the x-coordinates and the average of the y-coordinates of its two endpoints. If the line on the graph connects, for example, the points (0, 0) and (12, 24), then the x-coordinate of the midpoint is (0 + 12) / 2 = 6, and the y-coordinate is (0 + 24) / 2 = 12. Therefore, the midpoint is (6, 12).

Question 10: There is an angle x in a triangle with the following three sides:<br> What is the value of tan(xtrigonometric )'s ratio?

3/2 (Correct answer)
2/3
3/8
1/4

Correct answer: 3/2

In a right-angled triangle, the tangent of an angle (tan(x)) is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle (Opposite/Adjacent). If the side opposite angle x measures 3 units and the side adjacent to angle x measures 2 units, then the ratio tan(x) would be 3/2.

Question 11: Answer the question below using the diagram. v-rotating cargo contains a person. At point P in the diagram, the cargo is moving perpendicular to the line OP, and the person in the cargo throws a ball with speed v toward the center of the circular motion O. From point P, where is the ball?

45 degrees to the left from the line OP
Towards O
45 degrees to the right from the line OP (Correct answer)
To the right,then to the left

Correct answer: 45 degrees to the right from the line OP

When the person throws the ball towards the center (O), the ball also retains the tangential velocity of the cargo at point P, which is perpendicular to the line OP. The ball's actual velocity is the vector sum of its velocity towards O and the cargo's tangential velocity. If these two speeds are equal, the ball will move at a 45-degree angle from the line OP, in the combined direction of the tangential motion and towards the center. This results in the ball moving 45 degrees to the right from the line OP, assuming the tangential velocity is to the right.

Question 12: What is the answer to the calculation shown below?

1/343
7
1/49 (Correct answer)
1/7

Correct answer: 1/49

To solve this expression, first simplify (1/7)², which becomes 1/49. Next, apply the rule of exponents a^m * a^n = a^(m+n) to 7⁻⁴ * 7⁴, which simplifies to 7⁰. Any non-zero number raised to the power of zero is 1. Therefore, the entire expression becomes (1/49) * 1, resulting in 1/49.

Question 13: c²=a²+b²-2ab(cosC)

Pythagorean Theorem
Law of Cosines (Correct answer)
Basic Trig Function
Inverse Cosine

Correct answer: Law of Cosines

The formula c²=a²+b²-2ab(cosC) is known as the Law of Cosines. It is a fundamental theorem in trigonometry that relates the lengths of the sides of a triangle to the cosine of one of its angles. This law is a generalization of the Pythagorean Theorem, which only applies to right triangles, and allows for calculations in any triangle.

Question 14: The aggregate of all elements from two or more sets

intersection of sets ∩
union of sets ∪ (Correct answer)
range of a function
domain of a function

Correct answer: union of sets ∪

The union of sets, denoted by the symbol ∪, is an operation that combines all distinct elements from two or more given sets into a single new set. If an element is present in any of the original sets, it will be included in their union. This concept aggregates all elements, creating a comprehensive collection from the constituent sets.

Question 15: V= (1/3)b²h

Volume of a cylinder
Volume of a square pyramid (Correct answer)
Volume of a sphere
Volume of a cone

Correct answer: Volume of a square pyramid

The formula V = (1/3)b²h is used to calculate the volume of a square pyramid. In this equation, 'b' represents the length of one side of the square base, so b² is the area of the base, and 'h' is the perpendicular height from the base to the pyramid's apex. The factor of 1/3 is characteristic for the volume of any pyramid or cone.

Question 16: A conjecture's counter example is a case in which the conjecture's conditions (the hypothesis) are met but the conclusion is not.

Union of sets ∪
Domain of a function
Counter example of conjecture (Correct answer)
Intersection of sets ∩

Correct answer: Counter example of conjecture

A counterexample of a conjecture is a specific instance that proves a general statement or hypothesis to be false. For a conjecture to be true, it must hold for all possible cases. If a case exists where the conjecture's conditions are met but its conclusion is not, then that case serves as a counterexample, invalidating the conjecture.

Free NYSTCE Mathematics 004 Questions and Answers

The likelihood of receiving the head from an unfair coin is 0.3.
What is the probability of not getting a head after tossing the coin three times?