MAT 1033ATest 4 ReviewandPractice Solutions

• Calculators and calculating devices are strictly prohibited.• Tests may not be made up for any reason other than a mandatory school – sponsored activity for which you must miss class. • If you miss one test for any other reason, your final exam score will be substituted for that test. A second missed test is a zero. No homework bonuses are awarded on a test when the final exam is substituted or you receive a zero on a missed test.

Be sure to complete at least 80% of your pie for Objective 4 to receive the 10 point bonus. Your percentage must be at least 80.0% to receive the bonus.

Topics Notes Chapter Review1: Evaluate principal square roots. 9.1 p. 603: 1 – 3 2: Evaluate principal nth roots. 9.1 p. 603: 4 – 7 3: Find the domain of a radical function 9.1 p. 603: 154: Evaluate expressions with fractional and negative exponents. 9.2 p. 603: 21 – 32 5: Use the rules of exponents to simplify expressions with rational exponents. 9.2 p. 603 – 604:33 – 41 6: Use rational expressions to simplify radicals. 9.2 p. 604: 42 – 44 7: Simplify square roots. 9.3 p. 604: 50 – 62 8: Multiply square roots. 9.3 p. 604: 63 – 68 9: Simplify nth roots. 9.4 p. 604: 71 – 82 10: Add and subtract radicals. 9.5 p. 604: 89 – 95 11: Multiply radicals using polynomial rules 9.5 p. 604: 96 – 102 12: Rationalize denominators (one term). 9.6 p. 604: 103 – 108 13: Rationalize denominators (two terms) 9.6 p. 604: 111, 11214: Solve radical equations. 9.7 p. 604: 115, 116, 119, 12015: Evaluate square roots of negative numbers. 9.8 p. 604: 125, 12616: Add and subtract imaginary numbers. 9.8 p. 604: 129 – 132 17: Multiply and divide imaginary numbers 9.8 p. 605: 133 – 138, 141, 14218: Complete the square. 10.1 p. 697: 11 – 16 19: Solve an equation by completing the square. 10.1 p. 697: 17 – 22 20: Solve quadratic equations using the quadratic formula. 10.2 p. 697: 25 – 32

Topics Remember1: Evaluate principal square roots.2: Evaluate principal nth roots.3: Find the domain of a radical function Set what’s under the square root 4: Evaluate expressions with fractional and negative exponents., 5: Use the rules of exponents to simplify expressions with rational exponents. Make sure you use the rules of exponents:When you multiply you add the exponents.When you divide, you subtract the exponents.6: Use rational expressions to simplify radicals. “raise over root”.7: Simplify square roots. Separate the square root into two parts: the largest perfect square and largest even power, what’s left. Take the square root of the first part and leave the second under the radical.8: Multiply square roots. Multiply and simplify.9: Simplify nth roots. Remember to divide the exponent into 3’s for cube roots, 4’s for fourth roots, and so on.10: Add and subtract radicals. Simplify the square roots completely. Add or subtract like roots only.11: Multiply radicals using polynomial rules Use the rules of polynomials.12: Rationalize denominators (one term). Multiply numerator and denominator by the denominator.13: Rationalize denominators (two terms) Multiply numerator and denominator by the conjugate of the denominator14: Solve radical equations. Isolate the square root. Square both sides. Solve. Check your solutions.15: Evaluate square roots of negative numbers.16: Add and subtract imaginary numbers. Add or subtract the real parts, add or subtract the imaginary parts.17: Multiply and divide imaginary numbers18: Complete the square.19: Solve an equation by completing the square. Complete the square (add the constant to both sides), take the square root (remember ), solve for the variable.20: Solve quadratic equations using the quadratic formula.

Test 4 Practice Test Solutions

(1) Simplify completely.a) b)

(2) Simplify completely.a) b)

(3) Find the domain of the radical function. Write your answer in interval notation.

(4) Simplify completely.b) 81−1/4 c) −361/2

(5) Simplify completely.a) 52/3 ∙ 57/3

b)

(6) Simplify completely.

b)

(7) Simplify completely. Assume all variables represent nonnegative numbers.a)

  b)

(8) Simplify completely. Assume all variables represent nonnegative numbers.

b)

(9) Simplify completely. Assume all variables represent nonnegative numbers.a) b)

(10) Add or subtract as indicated. Simplify completely. Assume all variables represent nonnegative numbers.a)

(11) Multiply. Simplify completely. Assume all variables represent nonnegative numbers.a) b) (9 + ) (9 − ) c) ( + )2

(12) Rationalize the denominator. Simplify completely.

(13) Rationalize the denominator. Simplify completely.

(14) Solve.

{9 }

(15) Simplify completely.a) b) c)

(16) Perform the indicated operation and simplify.a) (7 + 2i) – (3 – 5i)

b)

(17) Perform the indicate operations and simplify.a) (9 + 3i)(2 − 5i) b)

(18) Complete the square for each expression. Indicate the number that goes in the box and factor the trinomial completely.a) The number that goes in the box is 49.The trinomial factors as

b) The number that goes in the box is 100.The trinomial factors as

(19) Solve by completing the square. You must solve by completing the square to receive credit.

(20) Solve by the quadratic formula. You must solve by the quadratic formula to receive credit.

 

Test 4 Extra Practice

1) Simplify completely.a) b)

1) Simplify completely.a) b)

2) Simplify completely.a) b)

2) Simplify completely.a) b)

(3) Find the domain of the radical function. Write your answer in interval notation.

𝑔 (𝑥 )=√4−𝑥

(3) Find the domain of the radical function. Write your answer in interval notation.

4) Simplify completely.b) 64−4/3 c) −251/2

4) Simplify completely.b) 64−4/3 c) −251/2

5) Simplify completely.a) 257/16 ∙ 251/16 b)

5) Simplify completely.a) 257/16 ∙ 251/16

b)

6) Simplify completely.

6) Simplify completely.

7) Simplify completely. Assume all variables represent nonnegative numbers. a)

  b)

7) Simplify completely. Assume all variables represent nonnegative numbers. a)

  b)

8) Simplify completely. Assume all variables represent nonnegative numbers.

b)

8) Simplify completely. Assume all variables represent nonnegative numbers.

b)

9) Simplify completely. Assume all variables represent nonnegative numbers.a) b)

9) Simplify completely. Assume all variables represent nonnegative numbers.a) b)

10) Add or subtract as indicated. Simplify completely. Assume all variables represent nonnegative numbers.

10) Add or subtract as indicated. Simplify completely. Assume all variables represent nonnegative numbers.

11) Multiply. Simplify completely. Assume all variables represent nonnegative numbers.a) b) ( + ) () c) ()2

11) Multiply. Simplify completely. Assume all variables represent nonnegative numbers.a) b) ( + ) () c) ()2

12) Rationalize the denominator. Simplify completely.

12) Rationalize the denominator. Simplify completely.

13) Rationalize the denominator. Simplify completely.

13) Rationalize the denominator. Simplify completely.

14) Solve.

14) Solve.

{2 }

15) Simplify completely.a) b) c)

15) Simplify completely.a) b) c)

16) Perform the indicated operation and simplify.a) b)

16) Perform the indicated operation and simplify.a)

b)

(17) Perform the indicate operations and simplify.a) b)

(17) Perform the indicate operations and simplify.a) b)

18) Complete the square for the expression. Indicate the number that goes in the box and factor the trinomial completely.

18) Complete the square for the expression. Indicate the number that goes in the box and factor the trinomial completely. 25The number that goes in the box is 25.The trinomial factors as

19) Solve by completing the square. You must solve by completing the square to receive credit.

𝑠2+10 𝑠+10=0

19) Solve by completing the square. You must solve by completing the square to receive credit.

20) Solve by the quadratic formula. You must solve by the quadratic formula to receive credit.

20) Solve by the quadratic formula. You must solve by the quadratic formula to receive credit.