Math Section 1 Multiple Choice
Which of the following statements is true about linear equations of the form ax+b=0? A. The constants a and b must be real numbers with the constant a never equal to zero. B. The constants a and b can never be decimals. C. The constants a and b can never be fractions. D. The constants a and b must be real numbers with the constant a always positive.
A
Which of the following is not a property of inequalities? A. For c<0, if a<b, ac>bc. B. For c<0, if a<b, ac>bc. C. For c<0, if a<b, a−c>b−c. D. For c>0, if a<b, ac<bc.
C
Which of the following statements best defines the term "extraneous solution"? A. An extraneous solution is an approximate solution to an algebraic equation. B. An extraneous solution is an irrational solution to an algebraic equation. C. An extraneous solution is a solution obtained through algebraic manipulations that is not a solution to the original equation. D. An extraneous solution is a solution to a linear equation that contains fractions.
C
Which of the following statements is true? A. A polynomial equation is either a linear equation or a quadratic equation. B. Every quadratic equation is also a linear equation. C. All linear equations and all quadratic equations are polynomial equations. D. Every linear equation is also a quadratic equation.
C
Suppose that you are solving a quadratic equation and realize that the discriminant is equal to 7. Which of the following statements best describes the solutions to this quadratic equation? A. There must be exactly one real solution. B. There will be no solutions to this quadratic equation. C. There must be two nonreal solutions. D. There must be two real solutions.
D
Which of the following best describes the zero product property? A. If the product of two factors is equal to zero, then both factors must be equal to zero. B. The product of zero and another factor is always zero. C. If two nonzero factors are multiplied together, then the product must also be nonzero. D. If two factors multiplied together are equal to zero, then at least one of the factors must be zero.
D
Which of the following statements describes the absolute value of a number a? A. Given a, a is always positive. B. The positive value of a negative number a can be represented by the absolute value of a number a. C. The opposite value of a number a can be represented by the absolute value of a number a. D. The distance from the number a to 0 on a number line can be represented by the absolute value of a number a.
D
If u is an algebraic expression and c is a real number such that c>0, then the inequality u>c is equivalent to A. u<−c or u>c. B. u<−c or u<c. C. −c<u<c. D. u>−c or u>c.
A
Which of the following statements is true about rational equations? A. It is important to check the solutions to a rational equation because it is possible to encounter extraneous solutions. B. Rational equations always have no solution. C. When solving a rational equation, it is never a good idea to multiply both sides of the equation by the least common denominator. D. A rational equation can never lead to a linear equation.
A.
If u is an algebraic expression and c is a real number such that c>0, then the equation u=c is equivalent to A. −u=c. B. u=−c or u=c. C. u=−c. D. −c<u<c.
B
If u is an algebraic expression and c is a real number such that c>0, then the inequality u<c is equivalent to A. −c>u>c. B. −c<u<c. C. u<−c and u<c. D. u<−c or u>c.
B
Which of the following is not a valid strategy when solving a polynomial equation of the form ax3+bx2=cx? A. Subtract ax3 and bx2 from both sides. B. Divide the equation by x. C. Subtract cx from both sides. D. Set the equation equal to zero and factor out an x.
B
Which of the following statements is not true concerning the equation x2-c=0 for c>0? A. A quadratic equation in this form can always be solved using the square root property. B. This equation is not considered to be a quadratic equation because it is not of the form ax2+bx+c=0. C. The left-hand side of this equation is called a difference of two squares. D. A quadratic equation in this form can always be solved by factoring.
B
Which of the following statements is true? A. Every absolute value equation has two solutions. B. It is possible for an absolute value equation to have no solution. C. The solution to an absolute value equation is always positive. D. The solution to an absolute value equation must always be greater than or equal to zero.
B
