Eureka: January 2014

Wednesday, January 29, 2014

Watch a short presetation on the 30-60-90 triangle properties. CLICK HERE

SEE BELOW:

Since COMBINATIONS occur frequently,
you may want to practice using the n C r KEY on the TI-83

Please DOUBLE click on video to enlarge!

MEAN MEDIAN MODE

RULES FOR DIVISIBILITY:

A NUMBER IS DIVISIBLE BY_____, IF ______
2 The last digit is even (0,2,4,6,8)
128 is 129 is not
3 The sum of the digits is divisible by 3
381 (3+8+1=12, and 12÷3 = 4) Yes
217 (2+1+7=10, and 10÷3 = 3 1/3) No
4 The last 2 digits are divisible by 4
1312 is (12÷4=3) 7019 is not
5 The last digit is 0 or 5
175 is 809 is not
6 The number is divisible by both 2 and 3
114 (it is even, and 1+1+4=6 and 6÷3 = 2) Yes
308 (it is even, but 3+0+8=11 and 11÷3 = 3 2/3) No
7 If you double the last digit and subtract it from the rest of the number and the answer is: 0, or divisible by 7 (Note: you can apply this rule to that answer again if you want)
672 (Double 2 is 4, 67-4=63, and 63÷7=9) Yes
905 (Double 5 is 10, 90-10=80, and 80÷7=11 3/7) No
8 The last three digits are divisible by 8
109816 (816÷8=102) Yes 216302 (302÷8=37 3/4) No
9 The sum of the digits is divisible by 9
(Note: you can apply this rule to that answer again if you want)
1629 (1+6+2+9=18, and again, 1+8=9) Yes
2013 (2+0+1+3=6) No
10 The number ends in 0
11 If you sum every second digit and then subtract all other digits and the answer is: 0, or divisible by 11
1364 ((3+4) - (1+6) = 0) Yes
3729 ((7+9) - (3+2) = 11) Yes
25176 ((5+7) - (2+1+6) = 3) No
12 The number is divisible by both 3 and 4
648 (By 3? 6+4+8=18 and 18÷3=6 Yes.
By 4? 48÷4=12 Yes) Yes
524 (By 3? 5+2+4=11, 11÷3= 3 2/3 No.
Don't need to check by 4.) No

Monday, January 27, 2014

Geometry Questions

Team 2015 - EQUILATERAL TRIANGLE AREAS

1. (Team) The ratio of the height of a triangle ABC to the height of a triangle MNP is 2/9. If the two triangles are similar, what is the ratio of the area of the triangle ABC to the area of the triangle MNP? Give your answer as a common fraction.

2. (Sprint) How many square units are in the area of the largest triangle that can be inscribed in a circle whose area is 159 Pi? Round your answer to the nearest integer.

3. (Countdown) How many degrees are in the measure of the smaller angle that is formed by the hands of a clock when it is 4 o'clock?

4. (Sprint) The base of an isosceles triangle is 48 cm long. If the area of the triangle cannot exceed 1080 square centimeters, What is the maximum number of centimeters in the perimeter of the triangle?

5. Let ABCD be square with edge length of 5 cm. We draw a circle of center A and radius 5 cm. and a circle of center C and radius 5 cm.. What percent of the square is the area inside the square that is not inside the intersection of the two circles? Express your answer to the nearest whole number.

6. (Sprint) Let ABC be right triangle in C . Suppose that points D, E are on the side AB such that AC = CD = DE = EB . Suppose also that AE = 13 sqrt(3) in. What is the number of inches in DE ?

8. (Sprint) Let C be a circle of center O . Let A be a point on the circle. Let P be a point on the radius AO such that AP=9 cm, and PO=8 cm. From the point P we draw a perpendicular to the radius AO . This perpendicular intersects the circle on a point B . Find the length of BP .

9. (Target) A huge right pyramid whose square base measures 575 feet along each edge is sitting on its base on the ground. An ant is crawling on the pyramid along the shortest path from the ground to the vertex. When she reaches the vertex she is 421 feet above the base. To the nearest tenth of a foot, what is the positive difference she crawled and the height of the pyramid?

10. (Team) Find the number of degrees in the positive difference between the sum of the of the measures of the 14 interior angles having blue vertices and the sum of the of the measures of the 7 exterior angles having red vertices of the given polygon.