Complete Solutions to Practice Test -17-

1.What are the solutions to the quadratic equation  A. 3, 6  B. 6, 6  C. 3, 12  D. 4, 9  E. -4, -9 Factor. You need two numbers that will multiply to 36 and add to -15. × = Now use the zero factor property. Answer C

2.If for all x and y,, then  A.  B.  C.  D.  E. undefined Solve for b. Add b to both sides. Answer A

3. For all  A.  B.  C.  D.  E. Factor. Cancel. Answer B

4. What is the value of the expression when  A.  B.  C.  D.  E. Substitute and simplify. Answer A

5. If then  A. 0  B. 4  C. 9  D. 25  E. no solution Radical Equation First isolate the radical. Subtract 4 from both sides. Square both sides to get rid of the radical. Subtract 5 from both sides. Divide by 5. Answer B

6. For all  A.  B.  C.  D.  E. Find the square root of x 9. Each pair of (xx) inside represents one x outside. Choice D is the only answer that matches this result.

7. If the ratio of 4 to b is 5 to 7 then b = ?  A. 3  B.  C.  D. 16  E. Write the proportion as two equal fractions. Cross multiply. Divide by 5. Answer B

8. Simplify  A.  B.  C.  D.  E. When raising a power to a power multiply the exponents. Answer B

9. Simplify  A.  B.  C. 6  D.  E. Simplify the radicals. The common denominator is 3 Answer B

10. Which equation best describes this graph?  A.  B.  C.  D.  E. The y-intercept of the graph is (0, 3). This eliminates choices A and E. The point (0, 3) works in B, C, and D.

10. Which equation best describes this graph?  A.  B.  C.  D.  E. Try the point (-1, 4) in B. Try the point (-1, 4) in D. This eliminates choice B. This eliminates choice D.

10. Which equation best describes this graph?  A.  B.  C.  D.  E. Try the point (-1, 4) in C. Answer C

11. For all B and C and A ≠ 0, if then  A.  B.  C.  D.  E. Solve for x Subtract B Divide by A Answer D

12. Simplify  A.  B.  C.  D.  E. Simplify the radicals The common denominator is 15 Answer D

13. If 25 is subtracted from the square of a certain number b the result is 11. Which of the following equations determines the correct value of b?  A.  B.  C.  D.  E. Since the result is 11 we can expect the equation to = 11. Eliminate choices A, B, and C. The word “from” indicates that the equation will start with b 2. Answer E or B

14. For all x,  A.  B.  C.  D.  E. Distribute the negative through the second parenthesis. Make sure you change all the signs. Combine like terms. Answer A

15. If the reciprocal of a certain number x is added to the result is 2. What is x?  A. 1  B. 2  C. 3  D. -2  E. -3 If x is the number then the reciprocal of x is… Multiply by 3x to clear the denominators. Answer C

16. Find the value of when  A. 12  B. 24  C. 36  D. 48  E. 60 Substitute x = 2 Answer C

17. Which equation best describes this graph?  A.  B.  C.  D.  E. The point (0, 5) does not work in choices C, D, or E. Try the point (3, -4) in choice B. Verify choice A, try the point (3, -4). Answer A

18 In the standard rectangular coordinate plane find the distance between (-3, 4) and (2, -8).  A. 12  B. 13  C. 25  D. 144  E. 169 Use the distance formula. Answer B

19 For all x,  A.  B.  C.  D.  E. Answer E

20. For all  A.  B.  C.  D.  E. Answer E

21. For all  A.  B.  C.  D.  E. Answer C

22. If x = -2 and y = 5, what is the value of the expression 2x 3 – 3xy ?  A.14  B.46  C.54  D.-46  E.-54 2x 3 – 3xy 2(-2) 3 – 3(-2)(5) 2(-8) – 3(-10) -16 – = 14

23. What are the solutions to the quadratic equation x 2 – 2x = 48?  A. -12, -4  B. -8, -6  C. 6, 8  D. -6, 8  E. -8, 6 Set the equation equal to zero. x 2 – 2x = 48 x 2 – 2x – 48 = 0 Factor (x + 6)(x – 8) = 0 Write a solution set. x = {-6, 8}

24.For all x  ±3,  A.  B.  C.  D.  E.

24.For all x  ±3, Rational Expression Factor Cancel This is a match for D

25.Which is the complete factorization of 5y 3 – 125y Factor out the common 5y 5y(y 2 – 25) Difference of squares 5y(y + 5)(y – 5)  A.  B.  C.  D.  E.