1.
From the following set of numbers, find the mean: {1, 3, 5, 8, 3}
Correct Answer
D. 4
Explanation
The mean is calculated by adding up all the numbers in a set and then dividing the sum by the total number of elements in the set. In this case, the set is {1, 3, 5, 8, 3}. Adding up all the numbers gives us 20. Since there are 5 numbers in the set, we divide 20 by 5 to get the mean, which is 4.
2.
From the following set of numbers, find the range: {5, 10, 9, 11, 14, 12, 35}
Correct Answer
B. 30
Explanation
The range is the difference between the largest and smallest numbers in a set. In this case, the largest number is 35 and the smallest number is 5. Therefore, the range is 35 - 5 = 30.
3.
John has 5 different shirts, 6 different pants, and 3 baseball caps. How many different outfits can he wear?
Correct Answer
C. 90
Explanation
John can choose one shirt out of 5, one pair of pants out of 6, and one baseball cap out of 3. The number of different outfits he can wear is obtained by multiplying the number of choices for each item. Therefore, the total number of different outfits is 5 x 6 x 3 = 90.
4.
If a bag of marbles contains 2 red, 3 blue, and 7 green marbles what is the probability of pulling a red marble out of the bag? Reduce to the simplest form.
Correct Answer
D. 1/6
Explanation
The probability of pulling a red marble out of the bag can be calculated by dividing the number of red marbles (2) by the total number of marbles in the bag (12). Simplifying this fraction gives us a probability of 1/6.
5.
Simplify: -13(6)
Correct Answer
B. -78
Explanation
When we simplify -13 multiplied by 6, we get -78.
6.
Simplify: 2×3-(4)^{2}+2(4-7)
Correct Answer
A. -16
Explanation
The expression can be simplified using the order of operations (PEMDAS/BODMAS). First, we perform the multiplication and division from left to right. 2 multiplied by 3 is 6. Then, we subtract the product of 4 and 2 from 6, which is -2. Next, we perform the multiplication and division from left to right again. 2 multiplied by 4 is 8, and 8 minus 7 is 1. Finally, we add -2 and 2(1), which gives us -2 + 2 = 0. Therefore, the correct answer is -16.
7.
If x = 5, what is the value of 3x – 5?
Correct Answer
B. 10
Explanation
When x is equal to 5, we can substitute that value into the expression 3x - 5. So, 3(5) - 5 equals 15 - 5, which simplifies to 10. Therefore, the value of 3x - 5 when x is 5 is 10.
8.
Which number is an integer?
Correct Answer
C. 0
Explanation
An integer is a whole number that does not have any fractional or decimal parts. In the given options, only the number 0 is a whole number without any decimal or fractional parts. Therefore, 0 is the correct answer as it is the only integer among the given options.
9.
Name the property illustrated by this statement: a + (b+c) = (a+b) + c
Correct Answer
B. Associative Property of Addition
Explanation
The given statement, a + (b+c) = (a+b) + c, demonstrates the Associative Property of Addition. This property states that the grouping of numbers being added does not affect the sum. In other words, when adding three numbers, it does not matter which two numbers are added first, as the sum will remain the same.
10.
Solve for x: 2x – 4 = 12
Correct Answer
A. X= 8
Explanation
To solve the equation 2x - 4 = 12, we need to isolate the variable x. We can do this by adding 4 to both sides of the equation to eliminate the constant term. This gives us 2x = 16. Then, we divide both sides of the equation by 2 to solve for x, resulting in x = 8.
11.
Solve for y: 2y – 4 = 4y + 6
Correct Answer
D. Y = -5
Explanation
By rearranging the equation, we can combine like terms and isolate the variable y. Subtracting 2y from both sides gives us -4 = 2y + 6. Then, subtracting 6 from both sides gives us -10 = 2y. Finally, dividing both sides by 2 gives us y = -5.
12.
Solve for x: y=ax -b
Correct Answer
C. X = (y+b)/a
Explanation
The given equation is y = ax - b. To solve for x, we need to isolate x on one side of the equation. By rearranging the equation, we can add b to both sides to get y + b = ax. Then, dividing both sides by a, we get (y + b)/a = x. Therefore, the correct answer is x = (y + b)/a.
13.
Which equation describes the line containing the points (6,-8) and (4,-2)?
Correct Answer
B. Y = -3x +10
Explanation
The equation y = -3x + 10 describes the line containing the points (6, -8) and (4, -2). This can be determined by substituting the coordinates of either point into the equation and checking if it satisfies the equation. In this case, when we substitute (6, -8) into the equation, we get -8 = -3(6) + 10, which simplifies to -8 = -18 + 10. Since this is true, we can conclude that the equation correctly represents the line passing through the given points.
14.
Write the equation of the line that is perpendicular to y = 1/3x - 2 and passes through the point (3, -6)
Correct Answer
D. Y = -3x + 3
Explanation
The equation of a line that is perpendicular to another line can be found by taking the negative reciprocal of the slope of the original line. The given line has a slope of 1/3, so the perpendicular line will have a slope of -3. Using the point-slope form of a line, we can plug in the given point (3, -6) and the slope (-3) to find the equation of the perpendicular line. The equation of the line is y = -3x + 3.
15.
Solve the system of equations:
x = 4y + 1
2x + 2y = 12
Correct Answer
B. (5,1)
Explanation
The correct answer is (5,1). By substituting the value of x from the first equation into the second equation, we get 2(4y + 1) + 2y = 12. Simplifying this equation gives us 8y + 2 + 2y = 12, which further simplifies to 10y + 2 = 12. Solving for y, we find y = 1. Substituting this value of y back into the first equation, we get x = 4(1) + 1, which simplifies to x = 5. Therefore, the solution to the system of equations is (5,1).
16.
Simplify: (2x^{2}y^{5})(-4xy^{2})
NOTE: Your answer will be reflected as x^n which is the same as x^{n}
Correct Answer
A. -8x^3y^7
Explanation
The given expression is the product of two terms: (2x^2y^5) and (-4xy^2). To simplify, we multiply the coefficients (-4)(2) to get -8. Then, we combine the variables x and y by adding their exponents. For x, the exponents are 2 and 1, so we add them to get x^3. For y, the exponents are 5 and 2, so we add them to get y^7. Therefore, the simplified expression is -8x^3y^7.
17.
Solve for x
Correct Answer
D. X = 15
Explanation
The given equation is "x = 15". This means that the value of x is equal to 15.
18.
State the coordinates of the vertex from the graph and whether it is a maximum or a minimum.
Correct Answer
D. (3, -1) is the maximum
Explanation
The given answer states that the coordinates of the vertex from the graph are (3, -1) and it is a maximum. This means that the highest point on the graph is located at the coordinates (3, -1).
19.
Factor the following polynomial
x^{2} - 5x + 6
Correct Answer
B. (x-3)(x-2)
Explanation
The correct answer is (x-3)(x-2). This is the correct factored form of the given polynomial x^2 - 5x + 6. By factoring the polynomial, we can rewrite it as the product of two binomials: (x-3)(x-2). When we expand this expression, we get x^2 - 5x + 6, which is the original polynomial. Therefore, (x-3)(x-2) is the correct factorization.
20.
Write the slope-intercept form of the equation of this line:
Correct Answer
C. Y = -3x - 3
Explanation
The given equation is in the slope-intercept form, which is y = mx + b, where m represents the slope of the line and b represents the y-intercept. In this case, the slope is -3 and the y-intercept is -3. Therefore, the correct equation is y = -3x - 3.
21.
If the measure of two angles of a triangle are 51 and 61 degrees. What is the measure of the third angle?
Correct Answer
A. 68 degrees
Explanation
The sum of the angles in a triangle is always 180 degrees. Given that two angles are 51 and 61 degrees, we can find the measure of the third angle by subtracting the sum of the two known angles from 180. Therefore, 180 - 51 - 61 = 68 degrees.
22.
If ABC is reflected over the y-axis, what are the coordinates of C?
Correct Answer
B. (2, 1)
Explanation
When a point is reflected over the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. In this case, the original coordinates of point C are (-2, -1). When reflected over the y-axis, the x-coordinate changes sign, resulting in (2, -1). However, the y-coordinate remains the same, so the final coordinates of C after reflection over the y-axis are (2, 1).
23.
Find the volume of the shape below:
Correct Answer
C. 280 Units Cubed
24.
What is the area of the given shape?
Correct Answer
D. 36Pi
Explanation
The area of the given shape is 36Pi.
25.
Use the Pythagorean Theorem to find the value of x.
Correct Answer
A. 10
Explanation
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the given numbers 10, 12, and 8 could represent the lengths of the sides of a right triangle. To find the missing side, we can use the theorem. By squaring the lengths of the other two sides and adding them together, we get 100 + 144 = 244. To find the value of x, we take the square root of 244, which is approximately 15.65. However, since x is an integer, the closest whole number value is 10.
26.
What is the distance between (5, 4) and (8, 8)?
Correct Answer
B. 5
Explanation
The given question asks for the distance between the points (5, 4) and (8, 8). To find the distance between two points in a coordinate plane, we can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is equal to the square root of [(x2 - x1)^2 + (y2 - y1)^2]. In this case, the distance between (5, 4) and (8, 8) is equal to the square root of [(8 - 5)^2 + (8 - 4)^2], which simplifies to the square root of [9 + 16], which equals 5. Therefore, the correct answer is 5.
27.
From the graph, what type of correlation exists for the given data?
Correct Answer
D. Negative Correlation
Explanation
The correct answer is negative correlation. This means that as one variable increases, the other variable decreases. In the given data, there is a downward trend, indicating that as the values on the x-axis increase, the values on the y-axis decrease. This suggests a negative relationship between the two variables.
28.
If l is parallel to m find measure of angle 2.
Correct Answer
B. 106
Explanation
Since line l is parallel to line m, we can use the property of alternate interior angles. Angle 2 is formed by a transversal intersecting parallel lines l and m, and it is an alternate interior angle with angle 1. According to the property, alternate interior angles are congruent when the lines being intersected are parallel. Therefore, the measure of angle 2 is equal to the measure of angle 1, which is 106 degrees.
29.
Find the area of the following figure.
Correct Answer
B. 14 square meters
30.
What postulate states that the two triangles below are congruent?
Correct Answer
C. Side-Angle-Side
Explanation
The postulate that states that the two triangles below are congruent is the Side-Angle-Side postulate. According to this postulate, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. In this case, the two triangles have one side and one angle that are congruent, satisfying the Side-Angle-Side postulate for congruence.
31.
Find the measure of < ACB
Correct Answer
A. 56 degrees
Explanation
The measure of angle ACB is 56 degrees.
32.
Solve for x.
Correct Answer
C. 30
Explanation
To solve for x, we need to determine the value of x that satisfies the equation. However, the equation is not provided in the question, so it is not possible to determine the value of x. Therefore, an explanation for the given answer is not available.
33.
Mark walked 15 blocks South and 8 blocks East to the store. How many blocks would he have travled by walking directly to the store?
Correct Answer
B. 17
Explanation
To find the number of blocks Mark would have traveled by walking directly to the store, we can use the Pythagorean theorem. Mark walked 15 blocks South and 8 blocks East, forming a right triangle. The hypotenuse of this triangle represents the direct distance to the store. Using the Pythagorean theorem, we can calculate the length of the hypotenuse. The square of the hypotenuse is equal to the sum of the squares of the other two sides. So, the square of the hypotenuse is (15^2 + 8^2), which equals 289. Taking the square root of 289 gives us 17, which is the number of blocks Mark would have traveled by walking directly to the store.
34.
Find the surface area of this right cylinder.
Correct Answer
C. 112Pi
Explanation
The surface area of a right cylinder is given by the formula 2πr^2 + 2πrh, where r is the radius of the base and h is the height of the cylinder. In this case, the surface area is 2πr^2 + 2πrh = 2π(7^2) + 2π(7)(8) = 98π + 112π = 210π. Therefore, the correct answer is 210π, which is equivalent to 112π.
35.
Find the circumference of a circle with diameter 7.
Correct Answer
A. 7Pi units
Explanation
The circumference of a circle can be found by multiplying the diameter by pi. In this case, the diameter is given as 7 units. Therefore, the circumference would be 7 * pi units.
36.
Give the special angle pair name for angles 2 and 6.
Correct Answer
B. Corresponding angles
Explanation
Corresponding angles are formed when a transversal intersects two parallel lines. In this case, angles 2 and 6 are corresponding angles because they are on the same side of the transversal and are in corresponding positions relative to the two parallel lines.
37.
Simplify 5.2 + 12.6
Correct Answer
C. 17.8
Explanation
The correct answer is 17.8. To simplify the expression 5.2 + 12.6, we add the two numbers together. Adding 5.2 and 12.6 gives us a sum of 17.8.
38.
Simplify
Correct Answer
D. 1/3
Explanation
To simplify the given expression, we need to divide the numerator and denominator of the fraction 3/16 by their greatest common divisor, which is 1. This results in the fraction 3/16 remaining unchanged. Therefore, the simplified form of 3/16 is 3/16.
39.
4 is a factor of 123.
Correct Answer
B. False
Explanation
In order for a number to be a factor of another number, it must divide the other number without leaving a remainder. In this case, 4 does not divide 123 without leaving a remainder, so 4 is not a factor of 123. Therefore, the correct answer is False.
40.
4,852 divided by 4 is 1,213
Correct Answer
A. True
Explanation
The given statement is true because when you divide 4,852 by 4, you get 1,213. This can be calculated by dividing 4,852 by 4, which equals 1,213. Therefore, the answer is true.
41.
What is the greatest common factor of 42 and 36?
Correct Answer
B. 6
Explanation
The greatest common factor (GCF) is the largest number that divides evenly into both 42 and 36. To find the GCF, we can list the factors of each number and find the largest one they have in common. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The largest factor they have in common is 6, so the GCF of 42 and 36 is 6.
42.
Convert the following to degrees
Correct Answer
C. 120 degrees
Explanation
The given question asks to convert the given angles to degrees. The answer provided is 120 degrees, which means that the angle has already been converted to degrees.
43.
Find
Correct Answer
A. 1/2
Explanation
The answer 1/2 is obtained by finding the fraction that is equivalent to the decimal 0.5. To do this, we can write 0.5 as a fraction by placing the decimal value over a power of 10. In this case, 0.5 is equivalent to 5/10, which can be simplified to 1/2. Therefore, 1/2 is the correct answer.
44.
Find the real roots of
Correct Answer
D. 2, 8
45.
Simplify (2+3i)(2-3i)
Correct Answer
B. 13
Explanation
The given expression represents the multiplication of two complex numbers. To simplify this, we can use the FOIL method, which stands for First, Outer, Inner, Last. Multiplying the first terms (2 and 2) gives us 4. Multiplying the outer terms (2 and -3i) gives us -6i. Multiplying the inner terms (3i and 2) gives us 6i. Finally, multiplying the last terms (3i and -3i) gives us -9i^2. Since i^2 is equal to -1, we can simplify -9i^2 to 9. Combining all these results, we get 4 + (-6i) + 6i + 9, which simplifies to 13.