Precalculus Honors - Kingswood Oxford School

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Honors Precalculus Kingswood Oxford School

Honors Precalculus Preseason Practice

Directions: On separate paper complete all problems, beginning by copying the original problem (you do not need to copy word problems). Be sure to show work, justifying your solutions mathematically.

When “solving,” you are expected to find solutions algebraically, but you are encouraged to check your solutions with a graphing calculator. Work in a neat, organized manner.

1. Find the distance between the points algebraically. a.

2. Solve algebraically, no calculators. a. 5

2

x

10

x

b.

1

2

1

3

p

4

3 c.

x

1

3

x

2

5

7 d.

2

3

3

4

7 

5

9

3. Solve. Find all solutions.

x

2

9

x

0 a.

c.

8

12

0 e.

4

x x

3

2

x

3

3

 g.

8

x

3

12

x

2

2

x

0

4. Find the real solutions of each equation. b. d. f.

2

x

2

5

x

2

x

2

15

0

x

5

x

11

x

11

x

6

3 a.

y

5 b.

x

c

.

2

12 2

x

x

1

Honors Precalculus Kingswood Oxford School

5. Solve each equation. a.

2

x

3 5

6. Find an equation for the line with the given properties. a.

Parallel to the line

y

2

x

7

; containing the point

3, 2

. b.

Perpendicular to the line 2

x

2 ; containing the point

3,0

.

7. The formula for the area

A

of a trapezoid is

A

1

2

1

b

2

. Solve this equation for

b

1

.

8. The graph below represents the cost of hiring a taxi versus the number of miles ridden. a.

b.

c.

Find an equation of the line through the two points.

How much does the meter read as soon as you get in the cab (before it even begins to move)?

What does the slope mean?

9. Simplify. Assume that each radical represents a real number. a.

15

35

42 b.

75

32

a b

6

3 c.

13 5

 

4 5

 d.

 

2

Honors Precalculus Kingswood Oxford School e.

36

4 g.

4

10. Sketch the graph of each equation. a.

y

x

3

2

11. Simplify. a.

x

3

y

2

1

x

2

y

2 c.

12. Solve. a.

y

i

i y

7

13. Simplify. f. b.

20

125

45

x

2

18

x

2

2

x

8

x

2

12

x

6

3

x

9

x

4 a.

80 b. 24

3

2

14. Simplify completely and write your answer using only positive exponents. Assume all variables are positive numbers. a.

2

4

xy

2

1

3

2 b.

a

1

b

1 c.

 

1

3

Honors Precalculus Kingswood Oxford School

15. Solve the system.

3

x

4

x

4

y

10

y

14

11

16. Orchid problem: In order to collect a rare orchid in Brazil, the botanist must purchase a license.

Since the botanist can sell the orchid she collects, she can use the proceeds to pay for all or part of the license. If she collects only 3 orchids, she is still in debt by $2050. If she collects seven orchids, she makes a profit of $1550. The Brazilian Oncidium Board allows a limit of 10 orchids per collector.

Assume that profit and number of orchids collected are related by a linear function. a) Which variable should be independent? b) Write a suitable domain for the independent variable. c) Plot the graph of the function d) Find the particular equation for this function. e) Find the x- and y- intercepts. What do these numbers represent in the real world?

17. Show that the line containing the points

 

and

 

,

a

b

, is perpendicular to the line

Also show that the midpoint of

 

and

 

lies on the line

y

x

.

y

x

.

18. Show that in any triangle (see figure below), the line segment joining the midpoints of two sides is parallel to the third side and half as long.

4

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