Geometry Ryken Geometry - Our Lady of Good Counsel High School
Geometry Ryken Geometry - Our Lady of Good Counsel High School
Geometry Ryken Geometry - Our Lady of Good Counsel High School
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Summer 2013<br />
Math Packet for students entering<br />
<strong>Geometry</strong><br />
<strong>Ryken</strong> <strong>Geometry</strong><br />
The problems in this packet are meant to help you review material that you<br />
have learned in previous math courses and will need to understand in order<br />
to be successful in Precalculus. ALL work should be completed to the best <strong>of</strong><br />
your ability.<br />
This packet will be due on the FIRST day <strong>of</strong> class. Any packets<br />
received after that time will incur a 10% grade reduction per<br />
calendar day.<br />
If you cannot remember how to solve some <strong>of</strong> the problems, use the<br />
Internet and notes from previous courses to research the topic so that you<br />
can turn in a completed packet on the first day.<br />
Another excellent review book is the <strong>High</strong> <strong>School</strong> Math Review available<br />
at www.summerskills.com. The answer key contains complete solutions to<br />
all <strong>of</strong> the problems.<br />
Have a great summer. We are looking forward to seeing you this fall.<br />
Student Name _________________________________________<br />
Previous Course Taken __________________________________<br />
Teacher’s Name (<strong>School</strong> if not GC )<br />
________________________________________<br />
*** If you are a freshman, and cannot solve all <strong>of</strong> the problems in this<br />
packet, then you need to contact Dr. Riely, <strong>Good</strong> <strong>Counsel</strong>’s Math Department<br />
Chair or Ms. Stortzum as soon as possible to adjust your schedule for next<br />
year.
Show all work.<br />
I. Determine the slope <strong>of</strong> the line through each pair <strong>of</strong> points. Simplify all<br />
answers. Leave in fraction form where appropriate.<br />
1. (3, 4) and (2, 7) 2. (4, 6) and (-3, 6)<br />
II. Determine the equation for each line using the information given. Write<br />
your equations in slope intercept form. y = mx + b<br />
3. slope <strong>of</strong> 3, passing through the point (4, 10).<br />
4. containing the points <strong>of</strong> (0, 3) and (3, 0)<br />
5. parallel to the line y = -3x + 1 and containing the point (-3, -5)<br />
6. perpendicular to the line y = -3x + 1 and containing the point<br />
(-3, -5).
III.<br />
Solve the following equations, if possible.<br />
7. 5x + 3 = -12 8. (2x -1) – (3x + 5) = -10<br />
9. 3x – 6 – 8x = -2x + 8 10. 4(x – 3) = 10x + 7 – 6x<br />
11. 21<br />
<br />
x<br />
7<br />
12. ½ x – 12 = -2<br />
13. x 2<br />
<br />
3<br />
8<br />
15<br />
14. (3x + 2) – 2(x + 4) = 7<br />
IV: Factor. If you need help with this critical skill, watch these videos:<br />
Simple factoring: http://www.youtube.com/watchv=NzStCbj_kJo<br />
Hard factoring by decomposition: http://www.youtube.com/watchv=a7yenMwLzuU<br />
15. 5x – 10x 3 2<br />
16. x 8x<br />
16<br />
17. x 2 2<br />
49<br />
18. x 10x<br />
24
V: Graphing.<br />
Graph each <strong>of</strong> the following lines or parabolas.<br />
19. y = - ½ x – 1 20. 3x – 2y = 4<br />
VI: Simplify.<br />
21. 2 5<br />
22.<br />
3 6<br />
6<br />
5<br />
4<br />
3<br />
23. (3x 2 y 4 ) 2 24. 4 6 9<br />
x y<br />
2<br />
8x y<br />
25. (4x 3 y 2 )(2xy 8 )<br />
VII: Solve the system <strong>of</strong> equations algebraically.<br />
26. 2x + 3y = 11 27. 5x + 2y = 10<br />
y = -2x + 1 12x - 8y = 24