The Standardized College Admissions Test in the United States.
For this section, solve each problem and decide which is the best of the choices given. Fill in the corresponding oval on the answer sheet. You may use any available space for scratch work. (CALCULATOR NOT PERMITTED)
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Question 1 of 10
Question 2 of 10
Which of the following expressions is equivalent to the expression shown above?Correct
Question 3 of 10
Which of the following represents the function shown?Correct
Question 4 of 10
If line L shown above is reflected over the x-axis, what is the slope of the new line?Correct
Question 5 of 10
The mean number of students per classroom, y, at Central High School can be estimated using the equation where x represents the number of years since 2004 and Which of the following statements is the best interpretation of the number 0.8636 in the context of this problem?Correct
Choice D is correct. When an equation is written in the form 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).
Question 6 of 10
If where and what is in terms ofCorrect
Choice A is correct. Multiplying both sides of the equation by the denominators of the rational expressions in the equation gives The student should then divide both sides by 2 to isolate the variable, yielding the equation
Question 7 of 10
If and what is in terms of x?Correct
Choice C is correct. Substituting the expressions equivalent to y and z into results in the expression The student must apply the distributive property to multiply by 2 and then combine the like terms in the expression.
Question 8 of 10
Which of the following is equal to
Choice D is correct. Applying the distributive property to multiply the binomials yields the expression The note in the stem of the question reminds students that therefore Substituting this value into the expression gives the student and combining like terms results in
Question 9 of 10
In the equation above, what is the value of k?Correct
Choice B is correct. Simplifying the numerators yields and cross-multiplication gives Solving for k yields
Question 10 of 10
In the system of linear equations above, is a constant. If the system has no solution, what is the value ofCorrect
Choice C is correct. If the system of equations has no solution, the graphs of the equations in the xy-plane are parallel lines. To be parallel, the lines must have the same slope, and this will be true if the expression is a multiple of the expression Since the expression would have to be 12 times the expression This means so The resulting system is and which is equivalent to and which has no solution