# Algebra

1. Multiply. (10x9)(-5x8)

2. Write using positive exponents only. b-19

3. Write 0.0000073 in scientific notation.

4. Add 10y2 + 9y - 2 and 10y2 + 6y - 7.

5. Multiply. (2x - 5y)(3x - y)

6. Multiply. (2m - n)2

7. Divide.

8. The distance from a star to a planet is 5.1  1018 m. How long does it take light, traveling at 1016 m/year, to travel from the star to the planet?

9. Divide.

10. Subtract 2x - 3x2 + 5x3 from 5x3 + 4x - x2.

11. Find the greatest common factor. 21b2, 35b3, 70b10

12. Use the ac test to determine if the following trinomial can be factored. If it can be factored, find the values of m and n.

3x2 + 11x - 4

13. Factor. 12x4y3 + 16x3y3 - 20x3y4

14. If the sides of a square are decreased by 3 cm, the area is decreased by 81 cm2. What were the dimensions of the original square?

15. Factor. x(x - 1) + 9(x - 1)

16. Factor. 9x(x + 6y) - 4(x + 6y)

17. Factor completely. 5x2 + 39x + 28

18. Rewrite the middle term as the sum of two terms and then factor by grouping.

x2 + 11x + 10

19. Rewrite the middle term as the sum of two terms and then factor by grouping.

x2 - 2x - 15

20. Solve. x2 + 8x + 15 = 0

21. If one-half a number is subtracted from five-sixths of the number, the difference is 6. Find the number.

22. Simplify.

23. Add. Express your answer in simplest form.

24. A 6-foot pole casts a shadow of 4 feet. How tall is a tree with a shadow of 18 feet?

25. One number is 3 times another. If the sum of their reciprocals is , find the two numbers.

26. Write in simplest form.

27. Add. Express your answer in simplest form.

28. Subtract. Write your answer in simplest form.

29. Solve.

30. What values for x must be excluded in the following fraction?

31. Evaluate , if possible.

32. Find the length x. Express your answer in simplified radical form.

33. Which two expressions are equivalent?

34. Find the distance between (19, -8) and (7, -3).

35. Evaluate , if possible.

36. Simplify. Assume x represents a positive number.

37. Simplify.

38. Use a calculator to approximate to the nearest hundredth.

39. Graph the quadratic equation after completing the given table of values. y = x2 - 1

x y

-2

-1

0

1

2

40. The length of a rectangle is 3 cm more than 2 times its width. If the area of the rectangle is 89 cm2, find the dimensions of the rectangle to the nearest thousandth.

41. Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry).

y = x2 - 4x

42. Find the x-intercepts.

y = x2 + x - 5

43. Find the x-intercepts.

y = x2 - 4x + 4

44. Graph the quadratic equation after completing the given table of values. y = -x2 - 2x

x y

-3

-2

-1

0

1

45. Find the axis of symmetry.

y = -x2 - 8x + 5

46. The height h in feet of an object after t seconds is given by the function

h = -16t2 + 60t + 9.

How long will it take the object to hit the ground? Round your answer to the nearest thousandth.

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1. Multiply. (10x9)(-5x8) =

Properties of exponential function:

2. Write using positive exponents only. b-19

3. Write 0.0000073 in scientific notation.

The power of 10 should be negative since the number is less than 1.

Place the decimal point after the first non-zero digit.

There are 6 zeros in the number, so the power of 10 is -6.

4. Add 10y2 + 9y - 2 and 10y2 + 6y - 7.

Using the communicative property of addition,

5. Multiply. (2x - 5y)(3x - y)

6. Multiply. (2m - n)2

7. Divide.

8. The distance from a star to a planet is 5.1 ï‚´ 1018 m. How long does it take light, traveling at 1016 m/year, to travel from the star to the planet?

Time = Distance / speed =

9. Divide.

10. Subtract 2x - 3x2 + 5x3 from 5x3 + 4x - x2.

11. Find the greatest common factor. 21b2, 35b3, 70b10

21 = 3 * 7

35 = 5 * 7

70 = 2 * 5 * 7

So the GCF of 21, 35, and 70 is 7.

B2 has factors: 1, b, b2

B3 has factors: 1, b, b2, b3.

B10 has factors: 1, b, b2, b3, b4, ...., b10.

The GCF of b2, b3, and b10 is then b2.

Therefore, the GCF is 7b2

12. Use the ac test to determine if the following trinomial can be factored. If it can be factored, find the values of m and n.

3x2 + 11x - 4

b = 11

ac = 3 * (-4) = -12

so we need to find two integers m and n

m + n = 11

and mn = -12

we know -12 = 12(-1), and 12 + (-1) = 11

so m = 12 and n = -1.

13. Factor. 12x4y3 + 16x3y3 - 20x3y4

Extract the GCF

14. If the sides of a square are decreased by 3 cm, the area is decreased by 81 cm2. What were the dimensions of the original square?

Original sides: x cm, original area: x2

New sides: (x - 3) cm, new area: (x-3)2

So the side of the square is 15 cm.

15. Factor. x(x - 1) + 9(x - 1) = by extracting out the common factor (x -1)

16. Factor. 9x(x + 6y) - 4(x + 6y)

17. Factor completely. 5x2 + 39x + 28

Using the ac test:

b = 39, ac = 5 * 28 = 140

now we need to find m and n such that

m + n = 39

and mn = 140

140 = 35 * 4

And 35 + 4 = 39

So m = 35 and n = 4

Then replace 39x with 35x + 4x, by grouping

18. Rewrite the middle term as the sum of two terms and then factor by grouping.

x2 + 11x + 10

19. Rewrite the middle term as the sum of two terms and then factor by grouping.

x2 - 2x - 15

20. Solve. x2 + 8x + 15 = 0

By factoring,

Two solutions: x = - 3 and x = -5

21. If one-half a number is subtracted from five-sixths of the number, the difference is 6. Find the number.

22. Simplify.

23. Add. Express your answer in simplest form.

The concept is factor the denominator of the first fraction, then extract the common factors in the two fractions.

24. A 6-foot pole casts a shadow of 4 feet. How tall is a tree with a shadow of 18 feet?

In the above diagram, EF is the pole, EF = 6

AF = 4 is the shadow.

For the tree shadow AC = 18, we need to find AC

25. One number is 3 times another. If the sum of their reciprocals is , find the two numbers.

The two numbers are x and 3x

26. Write in simplest form.

27. Add. Express your answer in simplest form.

28. Subtract. Write your answer in simplest form.

First write the fractions using the LCD, and evaluate the numerators.

29. Solve.

The numerators have to be equal for the above equation, so

30. What values for x must be excluded in the following fraction?

The denominator cannot be zero, so

So 2 and 7 should be excluded.

31. Evaluate , if possible.

32. Find the length x. Express your answer in simplified radical form.

Using the Pythagorean theorem,

33. Which two expressions are equivalent?

34. Find the distance between A(19, -8) and B(7, -3).

35. Evaluate , if possible.

36. Simplify. Assume x represents a positive number.

37. Simplify.

38. Use a calculator to approximate to the nearest hundredth.

39. Graph the quadratic equation after completing the given table of values. y = x2 - 1

x y

-2 3

-1 0

0 -1

1 0

2 3

40. The length of a rectangle is 3 cm more than 2 times its width. If the area of the rectangle is 89 cm2, find the dimensions of the rectangle to the nearest thousandth.

Let the width be x, then the length is 3 + 2x

The area is

Using the quadratic formula,

The length is

The length is 13.926 cm, the width is 5.963 cm.

41. Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry).

y = x2 - 4x

the axis of symmetry:

x y

-1 5

0 0

1 -3

2 -4

3 -3

4 0

5 5

42. Find the x-intercepts.

y = x2 + x - 5

So the two x-intercepts are:

43. Find the x-intercepts.

y = x2 - 4x + 4

The only x-intercept is (2, 0)

44. Graph the quadratic equation after completing the given table of values. y = -x2 - 2x

x y

-3 -3

-2 0

-1 1

0 0

1 -3

45. Find the axis of symmetry.

y = -x2 - 8x + 5

The line of symmetry is x = 4.

46. The height h in feet of an object after t seconds is given by the function

h = -16t2 + 60t + 9.

How long will it take the object to hit the ground? Round your answer to the nearest thousandth.

When hitting the ground, h = 0

So it takes 3.894 seconds to hit the ground.

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