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This pre-test is to help me get an understanding of the skills you have acquired from your previous math classes. There is no passing grade for this test, so you should attempt each problem and try your best regardless of whether you think you are right or wrong.
Questions and Answers
1.
What is the product of -10 and 5?
Explanation The product of -10 and 5 is -50. When you multiply a negative number (-10) by a positive number (5), the result is always negative. Therefore, -10 multiplied by 5 equals -50. The second answer choice, - 50, is just another way of representing the same value.
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2.
The bill for your dinner is $45.78. If you want to include a 15% tip, what will be the total for your dinner?
A.
$52.64
B.
$52.65
C.
$6.86
D.
$6.87
Correct Answer B. $52.65
Explanation To calculate the total for the dinner, we need to add the bill amount and the tip amount. The tip is calculated by multiplying the bill amount by the tip percentage (15%). Therefore, the tip amount is 45.78 * 0.15 = 6.867. Rounding up, the tip amount is $6.87. Adding the bill amount and the tip amount, the total for the dinner is $45.78 + $6.87 = $52.65.
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3.
Write an equation of variation for y = 30 when x = 5, where y varies inversly as x.
Correct Answer 30 = k/5 30=k/5
Explanation The equation 30 = k/5 represents the variation of y with respect to x when y varies inversely as x. In this equation, k represents the constant of variation. By multiplying both sides of the equation by 5, we can solve for k and find that k = 150. Therefore, the equation of variation for y = 30 when x = 5 is 30 = 150/5, or simply 30 = k/5.
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4.
Calculate the absolute value of -6 * 2 + - 4 * - 3.
[-6 * 2 + - 4 * - 3] =
Correct Answer 0
Explanation The given expression involves multiplication and addition. According to the order of operations, we need to perform the multiplication first. -6 * 2 equals -12, and -4 * -3 equals 12. Then, we add these two results together: -12 + 12 equals 0. Therefore, the absolute value of -6 * 2 + - 4 * - 3 is 0.
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5.
Which of the followig is a perfect square?
A.
6
B.
12
C.
25
D.
32
Correct Answer C. 25
Explanation A perfect square is a number that can be expressed as the product of two equal integers. In this case, 25 is a perfect square because it can be expressed as 5 * 5, where both factors are equal.
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6.
What is the quotient of -16 and -4?
Correct Answer 4 four
Explanation The quotient of -16 and -4 is 4. When dividing a negative number by a negative number, the result is always positive. Therefore, -16 divided by -4 equals 4. The word "four" is also given as an alternative way to express the quotient.
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7.
Subtract -1 - (-8).
Correct Answer 7 seven
Explanation Subtracting -1 from -8 means adding 1 to -8, which gives us -7. Therefore, the answer is -7. However, it seems that the question is incomplete or not readable as it also provides the option "seven" as an answer. Without further information, it is unclear how "seven" would be a valid answer for a subtraction problem.
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8.
Simplify the following expression: 4x + 5 + 2x
Correct Answer 6x + 5 6x+5 6x +5 6x+ 5
Explanation The given expression can be simplified by combining like terms. The terms 4x and 2x can be added together to give 6x. The constant terms 5 and 0 do not have any variables, so they can be combined to give 5. Therefore, the simplified expression is 6x + 5.
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9.
Simplify the following expression: 10y - (-2y) - 3z - 9z - 6y
Correct Answer 6y-12z 6y - 12z
Explanation The given expression involves combining like terms. By adding the coefficients of the like terms, we can simplify the expression. In this case, we have 10y and -2y, which when combined, give us 8y. Similarly, we have -3z, -9z, and 0z, which combine to give us -12z. Therefore, the simplified expression is 6y - 12z.
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10.
Simplify the following expression: x^{5} * y^{4} * x ^{-7} * y^{10}
*When typing your answer use ^ to represent and exponent (ex: x^2); use * for multiplication; use / for division
Explanation The given expression involves multiplying variables with exponents. To simplify, we can combine the variables by adding their exponents. In this case, we have x^5 * y^4 * x^-7 * y^10. When multiplying variables with the same base, we add their exponents. So, x^5 * x^-7 can be simplified to x^(5-7) which is x^-2. Similarly, y^4 * y^10 can be simplified to y^(4+10) which is y^14. Therefore, the expression simplifies to x^-2 * y^14.
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11.
Simplify the following expression: x^{8} / x^{2}
*When typing your answer use ^ to represent and exponent (ex: x^2); use * for multiplication; use / for division
Correct Answer x^6 x ^6
Explanation The expression x^8 / x^2 can be simplified by subtracting the exponents of x. In this case, we subtract 2 from 8, resulting in x^6. Therefore, the simplified expression is x^6.
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12.
Simplify the following expression: (4x)^{3}
*When typing your answer use ^ to represent and exponent (ex: x^2); use * for multiplication; use / for division
Correct Answer 64x^3 4^3*x^3 4^3x^3
Explanation The expression (4x)3 means that we need to multiply the quantity 4x by itself three times. This can be simplified by raising both the 4 and the x to the power of 3. When we do this, we get 4^3 * x^3, which is equal to 64x^3. So the correct answer is 64x^3.
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13.
2^{3} / 4 + 6 * 3 =
Correct Answer 20 twenty
Explanation The given expression follows the order of operations, which states that multiplication and division should be performed before addition and subtraction. Therefore, we first divide 23 by 4, resulting in 5.75. Then, we multiply 6 by 3, giving us 18. Finally, we add 5.75 and 18 together, which equals 23.75. However, since the question only provides two answer options, neither 23.75 nor 20 is a valid choice. Therefore, the correct answer cannot be determined based on the given options.
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14.
Evaluate 4x - 6 when x = 5.
Correct Answer 14 fourteen
Explanation The expression 4x - 6 means to substitute the value of x with 5 and then perform the calculation. Therefore, when x = 5, the expression becomes 4(5) - 6. Simplifying this, we get 20 - 6 which equals 14. So, the correct answer is 14.
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15.
The length of a rectangle is two more than the width. The area is 35. Find the length and the width. (Hint: let x be the width.)
When typing in your answer, list width first and length second. Separate the two with a comma. (Ex: w=?, l=?)
Correct Answer w=5, l=7 w=5,l=7 5, 7 5,7
Explanation The length of the rectangle is two more than the width. Let's assume the width of the rectangle is x. Therefore, the length would be x + 2. The area of the rectangle is given as 35. The formula for the area of a rectangle is length multiplied by width. So, we can set up the equation x(x + 2) = 35. Solving this equation, we find that x = 5. Therefore, the width is 5 and the length is 7.
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16.
What is the slope of the line with the equation: y = 3x - 10
A.
3
B.
-10
C.
10
D.
-3
Correct Answer A. 3
Explanation The slope of a line is the coefficient of the x-term in the equation of the line. In this case, the equation is y = 3x - 10, so the slope is 3.
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17.
Use a trignometric ratio to find x:
Correct Answer tan(30)*15 8.66 cm 8.7 cm 8.66 8.7
Explanation The given question asks to use a trigonometric ratio to find the value of x. The trigonometric ratio used is tan(30), which represents the tangent of 30 degrees. Multiplying this ratio by 15 gives the value of x. The correct answer is 8.66 cm, as it is the result of the calculation tan(30)*15. The other answer choices, 8.7 cm, 8.66, and 8.7, are incorrect as they do not match the calculated value.
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18.
The matrix above is the vertex matrix of a figure. Find the coordinates of the vertices of the figures after the figure has been translated 2 units up, then 1 unit down.
List the new coordinates in order of the original matrix. (i.e - the original matrix would be listed (1,0), (1,1), (4,0), (3, -4)
Explanation The equation x = 6 is already solved for x, so the answer is x = 6. The other options, 6, six, and x = 6, are just alternative ways of representing the same solution.
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20.
Rationalize the denominator of the fraction belwo. What will be the new rationalized fraction?
A.
B.
C.
D.
Correct Answer D.
21.
What is 49 written as a product of prime factors?
A.
49*1
B.
7*7
C.
1*(48+1)
Correct Answer B. 7*7
Explanation The number 49 can be written as a product of prime factors by breaking it down into its prime factors, which are both 7. Therefore, the prime factorization of 49 is 7*7.
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22.
Use the Pythagorean Theorem to find the hypotenuse of a right triangle with legs that measure 3 and 4.
A.
5
B.
25
C.
7
D.
49
Correct Answer A. 5
Explanation The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the lengths of the legs are 3 and 4. By applying the theorem, we can calculate the length of the hypotenuse as the square root of (3^2 + 4^2), which simplifies to the square root of (9 + 16), which further simplifies to the square root of 25. The square root of 25 is 5, so the correct answer is 5.
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23.
What is the greatest common factor of 12 and 28?
Correct Answer 4 four
Explanation The greatest common factor of two numbers is the largest number that divides evenly into both numbers. In this case, we need to find the largest number that can divide both 12 and 28. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 28 are 1, 2, 4, 7, 14, and 28. The largest number that appears in both lists is 4. Therefore, the greatest common factor of 12 and 28 is 4.
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24.
Solve the following equation using the quadratic formula: x^{2}= - 3x+10 (Remember to set the equation equal to 0.)
If there are two solutions type your answer as follows: x=?, x=? (Type a comma between the two answers)
Correct Answer x=-5, x=2 x=2, x=-5 x = -5, x = 2 x = 2, x = -5
Explanation The correct answer is x = -5, x = 2. This is because when we solve the equation x^2 = -3x + 10 by setting it equal to 0, we can rearrange it to x^2 + 3x - 10 = 0. Using the quadratic formula, we have x = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = 3, and c = -10. Plugging in these values, we get x = (-3 ± √(3^2 - 4(1)(-10))) / (2(1)). Simplifying further, we have x = (-3 ± √(9 + 40)) / 2, which becomes x = (-3 ± √49) / 2. Finally, we have x = (-3 ± 7) / 2, giving us the solutions x = -5 and x = 2.
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25.
Check the three properties that are illustrated by the three expressions below. Each one demonstrates a different property.
I. (-1 * 7) + 2 = 2 + (-1 * 7)
II. 9 * 1 = 9
III. 4 (2 + 6) = (4 * 2) + (4* 6)
A.
Identity property of addition
B.
Identity property of multiplication
C.
Distributive Property
D.
Commutative property of addition
E.
Commutative property of multiplication
F.
Associative property of addition
Correct Answer(s) B. Identity property of multiplication C. Distributive Property D. Commutative property of addition
Explanation The first expression, (-1 * 7) + 2 = 2 + (-1 * 7), demonstrates the commutative property of addition. This property states that changing the order of the numbers being added does not change the result.
The second expression, 9 * 1 = 9, illustrates the identity property of multiplication. According to this property, any number multiplied by 1 will result in the same number.
The third expression, 4 (2 + 6) = (4 * 2) + (4 * 6), represents the distributive property. This property states that when a number is multiplied by the sum of two other numbers, it is the same as multiplying the number by each of the two numbers separately and then adding the results together.
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26.
Which of the following shows the associative property?
A.
(5*7) + 2 = 2 + (5*7)
B.
5 + 7 = 7 + 5
C.
(5*7) * 2 = 5 * (7*2)
D.
2 + 7x
Correct Answer C. (5*7) * 2 = 5 * (7*2)
Explanation The given equation, (5*7) * 2 = 5 * (7*2), demonstrates the associative property. This property states that the grouping of numbers in an operation does not affect the result. In this case, the multiplication operation is being grouped differently on both sides of the equation, but the result is still the same. This shows that multiplication is associative, meaning it does not matter how the numbers are grouped when multiplying.
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27.
Evaluate (- x)^{2 }when x = 3
Correct Answer 9 nine
Explanation When evaluating (-x)^2, we first substitute the given value of x, which is 3. So, (-3)^2 is calculated. The negative sign inside the parentheses is squared along with 3, resulting in a positive value. Therefore, (-3)^2 is equal to 9. Additionally, the word "nine" is also a correct representation of the numerical value 9.
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28.
Solve the following system of equations: x + y = 9
x - y = 7
A.
X=16, y = -7
B.
X=8, y=1
C.
X=2, y= -9
D.
X=5, y=4
Correct Answer B. X=8, y=1
Explanation The given system of equations can be solved by using the method of substitution or elimination. In this case, the correct answer x=8, y=1 satisfies both equations. By substituting x=8 and y=1 into the first equation, we get 8 + 1 = 9, which is true. Similarly, by substituting x=8 and y=1 into the second equation, we get 8 - 1 = 7, which is also true. Therefore, x=8 and y=1 is the correct solution to the system of equations.
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29.
What percent of 20 = 8?
Correct Answer 40% 40 40 percent forty percent
Explanation The correct answer is 40%. This is because the question is asking for the percentage of 20 that equals 8. In other words, what percent of 20 is 8? To find this, we divide 8 by 20 and multiply by 100 to get the percentage. Therefore, 8/20 * 100 = 40%.
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30.
A local radio station sponsors a T-shirt toss and floppy hat drop during home pro basketball games. The T-shirts cost the radio station $8 each and the hats cost $12 each. The promotional cost C for the radio station depends on the number of shirts s and hats, h given away at the game. Write a rule expressing C as a function of s and h.
Do not put spaces when you type your function/equation/answer.
Explanation The promotional cost C for the radio station depends on the number of shirts s and hats h given away at the game. The cost of each shirt is $8 and the cost of each hat is $12. To find the total cost, we multiply the number of shirts by the cost per shirt and add it to the product of the number of hats and the cost per hat. Therefore, the rule expressing C as a function of s and h is C = 8s + 12h.
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31.
Factor the following polynomial: x^{2} - 3x - 18
Do not put spaces when you type your answer. Put parentheses around the two expressions: (???)(???)
Correct Answer (x-6)(x+3) (x+3)(x-6)
Explanation The given polynomial x^2 - 3x - 18 can be factored as (x-6)(x+3) or (x+3)(x-6). Both expressions are equivalent and represent the correct factored form of the polynomial.
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32.
What is the size of the following matrix? Type your answer as follows: ___x___ separate the two numbers with an x and do not use spaces.
Correct Answer 3x2 3 x 2 3 by 2
Explanation The size of the matrix is 3x2, which means it has 3 rows and 2 columns.
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33.
When you add the following matrices, what will the resulting matrix be?
A.
B.
C.
D.
Correct Answer D.
34.
The number of miles you drive your tractor, d, in t hours is given by the function d =13t. Is this an example of direct variation, inverse variation, or neither?
Correct Answer direct Direct direct variation Direct variation
Explanation The given function d = 13t represents a direct variation because the number of miles driven (d) is directly proportional to the number of hours driven (t). This means that as the number of hours driven increases, the number of miles driven also increases at a constant rate of 13 miles per hour.
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35.
Find the distance between the two points: (-5, 8) and (0, -4).
d= ?
Correct Answer d=13 13
Explanation The distance between two points can be found using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is equal to the square root of the sum of the squares of the differences between their x-coordinates and y-coordinates. In this case, the x-coordinates are -5 and 0, and the y-coordinates are 8 and -4. Plugging these values into the distance formula, we get: d = √((-5-0)^2 + (8-(-4))^2) = √(25 + 144) = √169 = 13. Therefore, the distance between the two points is 13.
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36.
Given that y varies direct as x, write an equation relating x and y when x = 6 and y = 1.
(Do not put spaces as you type your answer.)
Correct Answer 1=6k 1=k*6 k*6=1 6k=1
Explanation The equation relating x and y when x = 6 and y = 1 is 1 = 6k. This equation represents the direct variation between x and y, where k is the constant of variation. Since y varies directly as x, we can write the equation as y = kx. Substituting the given values, we get 1 = 6k. This means that the constant of variation, k, is equal to 1/6. Therefore, the equation relating x and y is y = (1/6)x.
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37.
If r = 5 and s = 8, what is the value of r^{2} - 2s?
Correct Answer 9 nine
Explanation The value of r^2 - 2s can be calculated by substituting the given values of r and s into the expression. Since r = 5 and s = 8, we can substitute these values to get 5^2 - 2(8). Simplifying this expression gives us 25 - 16, which equals 9. Therefore, the value of r^2 - 2s is 9.
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38.
Suppose that you are asked to collect information about the colors of cars that drive by school during the day and you record the following:
What is the probability that a car is green?
A.
1/6
B.
80/180
C.
20/180
Correct Answer A. 1/6
Explanation The probability that a car is green is 1/6. This can be determined by dividing the number of green cars (1) by the total number of cars (6).
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39.
Suppose that you are asked to collect information about the colors of cars that drive by school during the day and you record the following:
What is the probability that a car is red or blue?
A.
40/180
B.
60/180
C.
5/9
D.
100
Correct Answer C. 5/9
Explanation The probability that a car is red or blue can be calculated by adding the probabilities of the car being red and the car being blue. From the given information, the probability of a car being red is 40/180 and the probability of a car being blue is 60/180. Adding these probabilities together gives us 100/180, which simplifies to 5/9. Therefore, the probability that a car is red or blue is 5/9.
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40.
Suppose that you are asked to collect information about the colors of cars that drive by school during the day and you record the following:
What is the probability that a car is not blue?
A.
60/180
B.
1/3
C.
50/180
D.
2/3
Correct Answer D. 2/3
Explanation The probability that a car is not blue can be calculated by subtracting the probability of a car being blue from 1. Since the total number of cars recorded is 180 and 60 of them are blue, the probability of a car being blue is 60/180. Therefore, the probability of a car not being blue is 1 - 60/180 = 120/180 = 2/3.
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41.
What is the total area of the following figure?
A.
192 sq units
B.
156 sq units
C.
128 sq units
D.
126 sq units
Correct Answer B. 156 sq units
42.
Find the midpoint of the line segment that connects the points (6,5) and (12, 9). Type your answer with no spaces and make sure you put parentheses around the answer.
ex: (?,?)
Correct Answer (9,7) (9, 7) 9,7
Explanation The midpoint of a line segment is found by taking the average of the x-coordinates and the average of the y-coordinates of the two given points. In this case, the x-coordinate average is (6+12)/2 = 9, and the y-coordinate average is (5+9)/2 = 7. Therefore, the midpoint is (9,7).
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43.
What type of correlation does the following scatterplot show?
A.
Low positive correlation
B.
Low negative correlation
C.
Strong negative correlation
D.
Strong positive correlation
Correct Answer D. Strong positive correlation
Explanation The scatterplot shows a strong positive correlation. This means that as one variable increases, the other variable also tends to increase. The data points in the scatterplot are closely clustered together in an upward sloping pattern, indicating a strong positive relationship between the variables.
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44.
The following chart shows the pattern of a function for the x and y values. Answer the following question about this chart/pattern.
What number is being added each time?
Correct Answer 4 four
Explanation The number being added each time is 4. This can be determined by observing the pattern in the chart and noticing that the value of y increases by 4 each time the value of x increases by 1. The word "four" in the answer is likely just a clarification or alternative way of expressing the number 4.
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45.
The following chart shows the pattern of a function for the x and y values. Answer the following question about this chart/pattern.
What function/equation would represent the rule being demonstrated that allows you to detrmine y from the value of x?
Hint: y = ___*x + ____
Write the entire equation in your answer (y=?*x+?). Do not use spaces in your answer.
Correct Answer y=4*x+13 y=4x+13 y=4*x + 13
Explanation The equation that represents the rule being demonstrated is y = 4*x + 13.
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46.
The following chart shows the pattern of a function for the x and y values. Answer the following question about this chart/pattern.
What is y when x = 95? (Figure out the equation, then use it to solve for y.)
Correct Answer y=393 393 y = 393
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