Free Math Questions Calculator Not Permitted Exam 3

Question 1

If line is translated up 5 units and right 7 units, then what is the slope of the new line?

Accepted Answer

Answer

Choice B is correct. The slope of a line can be determined by finding the difference in the y-coordinates divided by the difference in the x-coordinates for any two points on the line. Using the points indicated, the slope is minus 3 over 2. Translating the line moves all the points on the line the same distance in the same direction, and the image will be a parallel line. Therefore, the slope of the image is minus 3 over 2.

Choice A is not the correct answer. This value may result from a combination of errors. The student may misunderstand how the negative sign affects the fraction and apply the transformation as fraction numerator left parenthesis minus 3 plus 5 right parenthesis over denominator left parenthesis minus 2 plus 7 right parenthesis end fraction.

Choice C is not the correct answer. This value may result from finding the slope of the line and then subtracting 5 from the numerator and 7 from the denominator.

Choice D is not the correct answer. This answer may result from adding 5 over 7 to the slope of the line.

Question 2

The mean number of students per classroom, y, at Central High School can be estimated using the equation y=0.8636 x + 27.227 , where x represents the number of years since 2004 and x less or equal than 10. Which of the following statements is the best interpretation of the number 0.8636 in the context of this problem?

Accepted Answer

The estimated yearly increase in the mean number of students per classroom

Answer

Choice D is correct. When an equation is written in the form y equals m x plus b comma the coefficient of the x-term (in this case 0.8636) is the slope. The slope of a linear equation gives the amount that the mean number of students per classroom (represented by y) changes per year (represented by x).

Choice A is not the correct answer. This answer may result from a misunderstanding of slope and y-intercept. The y-intercept of the equation represents the estimated mean number of students per classroom in 2004.

Choice B is not the correct answer. This answer may result from a misunderstanding of the limitations of the model. Students may see that x less or equal than 10 and erroneously use this statement to determine that the model finds the mean number of students in 2014.

Choice C is not the correct answer. This answer may result from a misunderstanding of slope. The student recognizes that slope models the rate of change, but may think that a slope of less than 1 represents a decreasing function.

Question 3

What is the value of a + 7 ?

Accepted Answer

10

Answer

This question is incomplete as the value of the variable 'a' is not provided. To find the value of the expression 'a + 7', a numerical value for 'a' must be known. If, for example, 'a' were equal to 3, then substituting this value into the expression would result in 3 + 7 = 10, matching the correct answer.

Question 4

What is y in terms of a ?

Accepted Answer

Answer

Choice A is correct. Multiplying both sides of the equation by the denominators of the rational expressions in the equation gives 2 y equals 4 a minus 4. The student should then divide both sides by 2 to isolate the y variable, yielding the equation y equals 2 a minus 2.

Choice B is not the correct answer. This equation may result if a student does not divide both terms by 2 when isolating y in the equation 2 y equals 4 a minus 4.

Choice C is not the correct answer. This equation may result from the student not distributing the 4 when multiplying 4 and open parentheses a minus 1 close parentheses.

Choice D is not the correct answer. This equation may result from solving 2 y equals 4 a minus 4 for a comma yielding a equals 1 half y plus 1. A student who does not understand the meaning of the variables may then switch them to match the answer choice.

Question 5

What is 2y + z in terms of x?

Accepted Answer

Answer

Choice C is correct. Substituting the expressions equivalent to y and z into 2 y plus z results in the expression 2 left parenthesis x cubed plus 2 x plus 5 right parenthesis plus x squared plus 7 x plus 1. The student must apply the distributive property to multiply x cubed plus 2 x plus 5 by 2 and then combine the like terms in the expression.

Choice A is not the correct answer. This answer may result if a student correctly finds 2y in terms of x but does not pay careful attention to exponents when adding to x squared plus 7 x plus 1 and then combines the x cubed and x squared terms.

Choice B is not the correct answer. This answer may result if a student fails to distribute the 2 when multiplying 2 left parenthesis x cubed plus 2 x plus 5 right parenthesis.

Choice D is not the correct answer. This answer may result from a student finding 2 left parenthesis y plus z right parenthesis instead of 2 y plus z.

Math Practice Test

Math Practice Test

Free Math Questions Calculator Not Permitted Exam 3