Geometry Ryken Geometry - Our Lady of Good Counsel High School

Summer 2013
Math Packet for students entering
Geometry
Ryken Geometry
The problems in this packet are meant to help you review material that you
have learned in previous math courses and will need to understand in order
to be successful in Precalculus. ALL work should be completed to the best of
your ability.
This packet will be due on the FIRST day of class. Any packets
received after that time will incur a 10% grade reduction per
calendar day.
If you cannot remember how to solve some of the problems, use the
Internet and notes from previous courses to research the topic so that you
can turn in a completed packet on the first day.
Another excellent review book is the High School Math Review available
at www.summerskills.com. The answer key contains complete solutions to
all of the problems.
Have a great summer. We are looking forward to seeing you this fall.
Student Name _________________________________________
Previous Course Taken __________________________________
Teacher’s Name (School if not GC )
________________________________________
*** If you are a freshman, and cannot solve all of the problems in this
packet, then you need to contact Dr. Riely, Good Counsel’s Math Department
Chair or Ms. Stortzum as soon as possible to adjust your schedule for next
year.

Show all work.
I. Determine the slope of the line through each pair of points. Simplify all
answers. Leave in fraction form where appropriate.
1. (3, 4) and (2, 7) 2. (4, 6) and (-3, 6)
II. Determine the equation for each line using the information given. Write
your equations in slope intercept form. y = mx + b
3. slope of 3, passing through the point (4, 10).
4. containing the points of (0, 3) and (3, 0)
5. parallel to the line y = -3x + 1 and containing the point (-3, -5)
6. perpendicular to the line y = -3x + 1 and containing the point
(-3, -5).

III.
Solve the following equations, if possible.
7. 5x + 3 = -12 8. (2x -1) – (3x + 5) = -10
9. 3x – 6 – 8x = -2x + 8 10. 4(x – 3) = 10x + 7 – 6x
11. 21
x
7
12. ½ x – 12 = -2
13. x 2
3
8
15
14. (3x + 2) – 2(x + 4) = 7
IV: Factor. If you need help with this critical skill, watch these videos:
Simple factoring: http://www.youtube.com/watchv=NzStCbj_kJo
Hard factoring by decomposition: http://www.youtube.com/watchv=a7yenMwLzuU
15. 5x – 10x 3 2
16. x 8x
16
17. x 2 2
49
18. x 10x
24

V: Graphing.
Graph each of the following lines or parabolas.
19. y = - ½ x – 1 20. 3x – 2y = 4
VI: Simplify.
21. 2 5
22.
3 6
6
5
4
3
23. (3x 2 y 4 ) 2 24. 4 6 9
x y
2
8x y
25. (4x 3 y 2 )(2xy 8 )
VII: Solve the system of equations algebraically.
26. 2x + 3y = 11 27. 5x + 2y = 10
y = -2x + 1 12x - 8y = 24