Designed for the Rising Pre-Calculus studentName ______

Summer Practice 2014

This summer packet emphasizes the key algebra skills required to be successful in Pre-Calculus. You should be able to complete each problem without the aid of a calculator. The calculator is a tool to verify your solution. Use EXACT answers and reduce all fractions to lowest terms. There are helpful websites at the end of the exercises to assist you. This is an optional assignment designed to keep your skills fresh over the summer break. Get a group of students together to work these out – happy computing 

Solve the equation.

2.

Solve the equation for y.


Solve the inequality. Then graph your solution on a number line.

9.

6.

8.

Determine whether the lines are parallel, perpendicular, or neither.

  1. Line 1:

Line 2:

  1. Line 1:

Line 2:

12. Write the equation of the line with the slope of and the y-intercept of -5.

13. Write the equation of the line that passes through the points .

Graph the equation using the most appropriate method. Be sure to include key points. Use the separate graph grids on the last page of this packet for your final answer.

14.15.

16. 17.

18. 19.

20. 21.

Solve each system of equations, and determine the number of solutions for each.

24.

23.

25.

#26 – 28 Evaluate the function for the given value of x.

26. =

27. =

  1. =
  1. Graph the function.

Factor the trinomial. (Be sure to factor completely!)

Use square roots or factoring to solve each equation.

34.

35.

36.

37.

38.

39.

40.

Solve the equation by completing the square. (Must use ‘completing the square’ method!)

41.

42.

43.

Use the quadratic formula to solve the equation. (Must use quadratic formula!)

44.

45.

Write the equation of the quadratic function in standard form .

46. Given the vertex is and passes through the point .

  1. Given the vertex is and passes through the point .

Find the product of the polynomials.


Factor the polynomials completely.

53.

55.

52.

54.

Solve the equation. Check for extraneous solutions.

56.

58.

57.

59.

Perform the indicated operation. Simplify the result completely.

60.

62.

61.

63.

64.

66.

Solve each equation.

68.

70.

65.

67.

69.

Find the value of each variable. Write your answers in simplest radical form.

7172.73.

74. 75. 76.

  1. Perimeter The altitude of an equilateral triangle is 12 centimeters. Find the perimeter of the triangle. Round to the nearest tenth.
/
  1. Area The diagonal of a square is 12 inches. Find the area. Round to the nearest tenth.

  1. Bleachers A fan at a sporting event is sitting at point A in the bleachers. The bleacher seating has an angle of elevation of 30° and abase length of 90 feet. Round to the nearest tenth.
a)Find the height CD of the bleachers.
b)Find the height of the fan sitting at point A from the ground.
c)Find the distance AB that the fan is sitting from the base, point B. /
  1. Canyon A symmetrical canyon is 4850 feet deep. A river runs through the canyon at its deepest point. The angle of depression from each side of the canyon to the river is 60°. Round to the nearest tenth.
a)Find the distance across the canyon.
b)Find the length of the canyon wall from the edge to the river.
c)Is it more or less than a mile across the canyon? (5280 feet = 1 mile)

Here are several websites that may help you: