Linear Equations and Rational Equations; Models and Applications; Complex Numbers and Quadratic Equations

Linear Equations and Rational Equations; Models and Applications; Complex Numbers...

Review for Exam 1

Section 1.2. Linear Equations and Rational Equations

1. Find the value of the variable that satisfies the equation. Check your solution.

8x 14 = 58

2. Solve and check the following linear equation.

7x (2x 10) = 50

3. Solve and check the following equation.

8x 5 = 4 + 7x

4. Solve the linear equation.

8x + 5 = 6x + 33

5. Solve and check the linear equation.

3(x 4) + 10 = 2(x + 3)

6. Solve and check the linear equation.

3(x 4) 4(x 3) = x + 3 (x 5)

7. Solve and check the following linear equation.

5 = 3(x 4) (x 9)

8. Solve and check the following linear equation.

42 [3 + 5y 2(y + 4)] = 5(4y 4) [7(y 1) 20y + 16]

9. Solve and check the equation.

10. Solve and check the linear equation.

11. Solve and check the equation.

12. Solve.

13. Solve and check the linear equation.

14. Solve and check the linear equation.

15. Solve the equation.

16. The following rational equation has denominators that contain variables.

For this equation,

a. Write the value or values of the variable that make a denominator zero. These are the restrictions on the variable.

b. Keeping the restrictions in mind, solve the equation:

17.

a.

b.

18.

a.

b.

19.

a.

b.

20.

a.

b.

21.

a.

b.

22

a.

b.

23.

a.

b.

24.

a.

b.

25.

a.

b.

Section 1.3. Models and Applications

1. Solve the formula for the specified variable.

P = ay for a

2. Solve the following formula for the specified variable.

A = e . n for e

3. Solve the following formula for the specified variable.

K = Tgy for T

4. Solve the following formula for the specified variable.

V = 5πt for t

5. Solve the formula for the specified variable.

for n

6. Solve the following formula for the specified variable

7. Solve the formula for q.

S = Z + qm

8. Solve the following formula for the specified variable.

B = f (s + z) for s

9. Solve the following formula for t.

B = G + Grt

10. Solve the formula for u.

j =

11. Solve M = 2HA + 2HT for H.

12. Solve the formula for c.

Section 1.4. Complex Numbers

1. Write the expression in the standard form a + bi.

(9 8i) + (3 + 3i)

2. Write the expression in the standard form a + bi.

(3 + 6i) (7 6i)

3. Subtract.

8 (4 + 8i) (7 i)

4. Subtract.

3i (13 9i)

5. Multiply.

7i (5 4i)

6. Find the following product and write the result in standard form a + bi.

(2 + 4i) (8 + i)

7. Find the product.

(4 6i) (5 8i)

8. Multiply.

(8 + 2i) (8 2i)

9. Find the following product and write the result in standard form, a + bi.

(2 + i) (2 i)

10. Multiply.

11. Divide and express the result in standard form.

12. Divide and simplify to the form a + bi.

13. Divide and express the result in standard form.

14. Divide the following complex numbers and express the result in standard form a + bi, where a and b are fractions in lowest terms.

15. Perform the indicated operations and write the result in standard form, a + bi.

+

16. Perform the indicated operations and write the result in standard form, a + bi.

+

Section 1.5. Quadratic Equations

1. Use factoring to solve the quadratic equation. Check by substitution or by using a graphing utility and identifying x-intercepts.

2. Solve the equation by factoring.

3. Solve the equation by factoring.

4. Use factoring to solve the quadratic equation Check by substitution or by using a graphing utility and identifying x-intercepts.

5. Use factoring.

6. Solve the equation by factoring.

7. Solve the quadratic equation by the square root property.

8. Solve the equation by the square root property.

9. Solve the following equation using the square root property.

10. Solve the equation by square root property

11. Solve the equation by the square root property.

12. Solve the quadratic equation using the square root property.

13. Solve the quadratic equation using the square root property.

14. Solve the quadratic equation by the square root property.

15. Solve the following equation by the square root property.

16. Solve the quadratic equation by completing the square.

17. Solve the quadratic equation by completing the square.

18. Solve the quadratic equation by completing the square.

19. Solve the quadratic equation by completing the square.

20. Solve the equation by completing the square.

21. Solve the quadratic equation by completing the square.

22. Solve the quadratic equation by completing the square.

23. Solve the following equation by completing the square.

24. Solve the quadratic equation by completing the square.

25. Solve the equation using the quadratic formula.

26. Solve the equation using the quadratic formula.

27. Solve the equation using the quadratic formula.

28. Solve the equation using the quadratic formula.

29. Solve the equation using the quadratic formula.

30. Solve the equation using the quadratic formula.

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