Thursday, April 30, 2009

Don't Miss The Easy Ones

Did you know that 35% of all math errors are due to reading? Think about it. You know they use tricky wording. Sometimes we think we know what they want AND we don't really answer the right question. So, hey, don't ever miss the easy ones!!! There are enough easy ones on the EOCT to really boost your score. You can score higher on this test than you usually do on your teacher's tests! My students always score higher on the EOCT than they do if I design the test.

1. Read the problem, then read it again.
2. Make sure the answer you give is exactly what the question asks for.
3. Use the proper units.
4. Watch out for the "gotcha" answer. Those are there for people who go too fast.
5. What are they asking you for?
6. Label your drawing.
7. Read it and read it again.

Tuesday, April 28, 2009

EOCT "Must Knows" In A Nutshell

1. Central angle = intercepted arc
2. Inscribed angle = 1/2 intercepted arc
3. If two sides of a triangle are 3 and 7, the third side must be greater than 4 and less than 10.
4. The midsegment of a triangle connects the midponts of any two sides of a triangle.
5. The midsegment is parallel to the 3rd side.
6. The midsegment = 1/2 of the 3rd side.
7. The midsegment forms 2 triangles that are similar.
8. In an equilateral triangle, the median, altitude, angle bisector, and perp bisector are all the same segment.
9. Triangles contain 180 degrees. Quads contain 360 degrees. Pentagons contain 540 degrees. Hexagons contain 720 degrees. Circles contain 360 degrees.
10. Number of degrees in convex polygon is (n-2)180.
11. Number of degrees in exterior angles of convex polygon is 360.
11. Acute triangle---each angle is less than 90.
12. Supplementary angles add to 180. Complementary angles add to 90.
13. Triangles are congruent by SAS, SSS, ASA, AAS, HL, and LL.
14. Triangles are similar by SSS~, AA~, SAS~
15. Similar triangles means corresponding sides are proportional and corr angles are congruent.
16. Similar triangles have a scale factor.
17. Scale factor is side/side. Use corresponding sides.

Sunday, April 26, 2009

Problems #20-24

20. A building that is 50 feet tall casts a shadow 30 feet long. Nearby, a tree casts a 75 foot long shadow. How tall is the tree? (Hint: Use similar triangle ratios) Read it twice. Wording is tricky.

a. 95 ft
b. 110 ft
c. 125 ft
d. 140 ft

Answers: 50/30 =x/75 so x = 125

21. Which unit is correct for describing the surface area of a hexagonal pyramid?
a. cm
b. cm squared
c. cm cubed

Answer: (b) Area is always "units squared".

22. If r>0 and s <0, in which quadrant of the xy-plane does the point (r,s) lie?
a. Quadrant I
b. Quadrant II
c. Quadrant III
d. Quadrant IV

Answer: d. (+, -) in Quadrant IV

23. Which set of points is equidistant from the rays that form an angle? (Hint: Draw it)
a. Perpendicular bisector
b. Skew Line
c. Angle Bisector
d. Central Angle

Answer: C. Angle Bisector

24. Which unit is used to measure the amount of liquid needed to fill a cylindrical container?
a. inches
b. square inches
c. cubic inches

Answer: C. Filling a container is volume. Volume is always cubic units.

Silly Math Jokes

I failed every subject except for algebra.How did you keep from failing that ?I didn't take algebra !
Teacher: Are you good at math ?Pupil: Yes and noTeacher: What do you mean ?Pupil: Yes, I'm no good at math !

Dad, can you help me find the lowest common denominator in this problem please ?Don't tell me that they haven't found it yet, I remember looking for it when I was a boy !
Teacher: Did you parents help you with these homework problems ?Pupil: No I got them all wrong by myself !

Teacher, I can't solve this problem.Any five year old should be able to solve this one.No wonder I can't do it then, I'm nearly ten !

Teacher: If 1+1=2 and 2+2=4, what is 4+4 ? Pupil: That's not fair you answer the easy ones and leave us with the hard one !

Teacher: How much is half of 8? Pupil: Up and down or across ? Teacher: What do you mean ? Pupil: Well,up and down makes a 3 or across the middle leaves a 0

Teacher: Now class, whatever I ask, I want you to all answer at once. How much is six plus 4 ?Class: At once !

If there are ten cats in a boat and one jumps out, how many are left ?None, they were all copycats !

Friday, April 17, 2009

Great Link for Free Geometry Help

This site has free math help, lots of it! The short videos on all topics are good. There are also lessons written out that really explain a lot. If you have been absent or just need to review, go visit this site. They even have a forum that will work problems for you!

#19 Regular Hexagon

19. If a regular hexagon has sides equal to 12, what is the area? (this problem comes up over and over again in different ways. make sure you can work it!)

Answer: 62.4 sq. units. You can find this using the formula for the area of a regular polygon, (1/2 x apothem x perimeter). You can also find the area of one equilateral triangle with side 12, and multiplying that by 6.

20. Given a pentagonal prism.
a. How many total vertices? 10
b. How many lateral faces? 5
c. How many total faces? 7
d. How many bases? 2

F+V=e+2 Total Faces + Vertices = edges + 2

21. Find the area of an equilateral triangle with perimeter 18.
If perimeter is 18, then each side is 6. Area: 15.6 sq. units

22. If a circle has diameter 20, find: (so radius is 10)
a. area of the circle 100 pi or 314.2 sq. units
b. circumference of the circle 62.8
c. volume of a sphere with the same diameter 4188.8 cu. un.
d. area of a sphere with the same diameter 1256.5 sq.un.
e. area of semi-circle 50 pi sq. un. or 157.1 sq. un.

Thursday, April 16, 2009

Prob #18 Similar Polygons

Given 2 similar triangles. The ratio of their sides is 2:3.

a. What is the ratio of the perimeters of the triangles? 2:3

b. What is the ratio of the altitudes of the triangles? 2:3

c. What is the ratio of the medians of the triangles? 2:3

d. What is the ratio of the angle bisectors of the triangles? 2:3

e. What is the ratio of the areas of the triangles? 4:9

f. What is the scale factor of the triangles? 2:3

Answer: ALL corresponding linear parts are in the same ratio as the sides. The ratio of the areas is the ratio of the sides squared. The ratio of the volumes is the ratio of the sides cubed.

Tuesday, April 14, 2009

Pythagorean Triples

You will see these right triangle triples on your End Of Course Test, your PSAT, and your SAT. It's worth knowing them by heart because it will save you time and build your confidence. There are many sets of triples that work for right triangles but here are the ones you need to know.

( 3, 4, 5) ( 5, 12, 13) ( 7, 24, 25) ( 8, 15, 17) ( 9, 40, 41)

You and a friend work on these together until you both know them by heart.

Monday, April 6, 2009

Where Are The Answers?

I have decided to keep the answers a secret for awhile. New folks are joining us everyday, people are on Spring Break at different times, sooooooo go ahead and work the problems and I'll post the answers at a later date. Continue to email me your answers and I will answer you back, so YOU can get the answers you need.

The Mathster

Geometry #13

Answer is c: 156 degrees

Friday, April 3, 2009

End of Week I Geometry EOCT

Hi Guys!

This is the end of our first week. Thanks for coming along and working with me this week. We had a great start! I've decided to wait awhile to post answers as many students are still coming on and getting started. Just email me your answers when you can....until I post them. LOL. Hope this practice time "helps you remember". Check back daily for more problems. I promise to throw in some really easy ones too.

Enjoy Spring Break!

Geometry Practice Problems for Thursday

Good Morning! Today is the last school day before Spring Break for some people. Woo hoo! Enjoy!

Today's problems are very basic and are just to help you remember the basics. All answers for this week will be posted on Saturday. If you would like personal feedback, email me at

9. The perimeter of a square is 68 meters. If one side is 3x+2, what is the value of x?
Answer: x = 5 meters

10. A right triangle has legs of 24 inches and 18 inches. Find the length of the hypotenuse.
Answer: The hypotenuse = 30. The answer is found using the Pythagorian Thm. It is in the 3-4-5 family.

11. Two angles are supplementary. One is 68 degrees. Find the other angle.
Answer: 112 degrees. Supplementary angles are two angles that add up to 180.

12. If the radius of a circle is 5, find the:

Area: 25 pi sq. units or 78.54 sq. units

Circumference: 10 pi units or 31.4 units

(on a multiple choice test answers may be left in terms of pi or may be written as a decimal. Be able to recognize the answer in either form.

Have a great break....or just a great weekend. See you Monday!

Thursday, April 2, 2009

Geometry EOCT Problems 5-8

Welcome back! Send me you answers! If you have not started these problems yet, go back to #1 on yesterday's post and get started. Keep a notebook with all of your problems worked out.

5. If a=b and b=c, than a=c illustrates which property?
a. Reflexive b. Commutative c. Transitive d. Distributive
Answer: c. Transitive

6. Given A = (6,3) and B = (8, -2). Find AB. (AB means the distance from A to B).
The formula you need for this problem is on the formula sheet. Just make sure you know how and when to use it.
Answer: AB = 5.4

7. Given: "If a, then b." Write the:
Inverse: "If not a, then not b." Could be written: "If ~a, then ~b."

: "If not b, then not a." Could be written: "If~b, then ~a."

8. Draw a triangle that has two angles which each measure 43 degrees.
a. Is the triangle isosceles, equilateral, or scalene?
b. What is the measure of the 3rd angle?
c. Is the triangle right, acute, or obtuse?

Answer: The triangle is isosceles because 2 sides are congruent. The 3rd angle measures 94 degrees, so the triangle is obtuse.

Enjoy the rest of the day! See you tomorrow!

The Mathster

Wednesday, April 1, 2009

Geometry EOCT Problems 1-4

First Day!!!

Good idea to keep all of these problems worked in a notebook. That way you can review it all right before the test...and you can share it with your teacher.

This set of problems is to help you "remember" way back to beginning of the year.

1. What is the "converse" of the following statement? What is the hypothesis? What is the conclusion?

If Jenny goes to the ballgame, then she will wear her red jacket.

a. Converse: If Jenny wears her red jacket, then she will go to the ballgame.
b. Hypothesis: If Jenny goes to the ballgame
c. Conclusion: Then she will wear her red jacket.

2. Which word describes a triangle whose angles measure 23, 38, and 119 degrees?
a. isosceles b. acute c. right d. obtuse
d. Obtuse

3. Find the midpoint of a segment with endpoints (3, 7) and (5, -1).
Midpoint is (4 , 3)

4. What is the area of a circle with radius = 4 cm? Leave pi in your answer.
Area is 16 pi sq. cm. or 50.27 sq. cm.

Email your answers to Put EOCT as the subject. If you want me to communicate with your teacher, send me that information too.

Congratulations for getting started! Come back tomorrow.

Feel free to leave a comment but DON'T leave the answers here! LOL.