two points on a line. Plugging the given values into the ratio gives 5 3 = 2

Transcription

1 ARCHIVE of POSTED PROBLEMS TO PONDER and SOLUTIONS for HIGH SCHOOL: Posted 01/30: If is the first term and 56 if the fourth term of a geometric progression, which of the following is the second term? A. 8 B. 1 C. 16 D. 3 E. 6 A geometric progression or geometric sequence is a sequence of numbers in which each term after the first is found b multipling the previous term b a common value (called the common ratio). For eample, in the progression 1, 3, 9, 7, 81 each subsequent number is increased b a factor of 3. Posted 01/8: In the standard (, ) coordinate plane, what is the slope of the line that passes through the points (-3, 5) and (7, 3)? A. -5 B. - C D. E. slope is the ratio of rise run = 1 1 between an two points on a line. Plugging the given values into the ratio gives 5 3 =

2 Posted 01/: Which of the following is an equation of the circle with center at (-, 3) and a radius of 5 coordinate units in the standard (, ) coordinate plane? A. 5 6 B. 1 6 C. 5 6 D. 1 6 E. 5 6

3 Posted 01/1: For what value of t does the equation h 3 A. B. 9 C. D. 3 9 E. THE MATH BLACKBOARD ruth@mathblackboard.com t t have its maimum value for h? Posted 01/0: In the figure below, A, B, and C are the midpoints of the sides of PQR, and M, N, and O are the midpoints of the sides of ABC. The interiors of PAB, AQC, BCR, and MNO are shaded. What fraction of the interior of PQR is shaded? A. B. C. D. E

4 Posted Monda, Januar 19, 015: 3 The volume of a sphere is r, where r is the radius of the sphere. The shapes of the planets Uranus and 3 Earth are approimatel spheres. The radius of Uranus is about times that of Earth. About how man times the volume of Earth is the volume of Uranus? A. 81 B. 6 C. 16 D. 1 E.

5 Posted Frida, Januar 16, 015: Benjamin is fling a kite using 130 feet of string, as shown in the figure below. His string makes an angle of 0 with the level ground. About how man feet above the ground is the kite when the string is taut? (Note: cos sin tan ) A. 80 B. 100 C. 110 D. 170 E ft

6 Posted Thursda, Januar 15, 015: Which of the following epressions is equivalent to 3 6 5? A. ( 5)( 3) B. (3 15)( 3) C. 3( 6 5) D. 3( 5)( 3) E. 3( 5)( 3)

7 Posted Wednesda, Januar 1, 015: Which of the following is an equation for the line passing through (0, 0) and (, 3) in the standard (, ) coordinate plane? A. 1 B. 7 C. 3 0 D. 3 5 E. 3 5

8 Posted Tuesda, Januar 13, 015: The legs of the right triangle below are doubled in length to become the legs of a new right triangle. What is the length, in feet, of the longest side of the new triangle? A. 5 B. 1 C. 13 D. 15 E ft.5 ft

9 Problems Posted Monda, Januar 1, 015: Two practice problems from an ACT Math Practice test: 1. The $1 price a store charges for a small refrigerator consists of the refrigerator s original cost to the store plus a profit of 15%. What was the refrigerator s original cost to the store? A. $5 B. $360 C. $399 D. $9 E. $78. In the figure below, line a is parallel to line b. The transversals intersect at a point on line a. Which of the following pairs of angles is NOT necessaril congruent? A. 1 and B. 1 and 5 C. and a D. and E. and 5 5 b

10 Posted Januar 9, 015: Mountain Climbing Problem: When I hiked in the Austrian Alps a few summers ago, I was told about a custom followed b a local hiking group. The tradition is as follows: on the last da of the month, a hiker starts at the bottom of the mountain. The hiker walks up the mountain, starting from the bottom at eactl sunrise and arriving at the top at eactl sunset, and then spends the night on the top. Then with the sunrise of the new da, the hiker walks down the mountain, starting from the top at eactl sunrise and arriving at the bottom at eactl sunset. Is there necessaril (that is, MUST there be) a point or place that the hiker is at the same place on the trail at the same time of da both on the going up and on the coming down? Eplain our answer. Solution to the Mountain Climbing Problem: Create a distance (along the trail) versus time ais. The vertical ais is our place on the trail; and the horizontal ais is the time of da. Now plot a graph of our trip up the mountain. Do ou hike slow-and-stead the entire time (red graph)? Do ou take a number of breaks along the wa (represented b time passing but no further upward movement along the trail) (blue graph)? Do ou have to retrace our steps back down the mountain at some point to retrieve an item ou dropped (green graph)? Then plot a graph of our trip back down the mountain. Again, there are different was of traveling: bursts of running quickl and then slowing down (brown graph); short bursts of hiking down mied with rest breaks (purple graph); or a continuous stead trek down the mountain (orange graph). Now place an trip up the mountain and an trip down the mountain onto the same grid (the graph with the blue going up and the orange coming down). What do we find? ANSWER: the graphs will alwas intersect, and the intersection point represents a point on the trail that the hiker is at the same place on the trail at the same time of da both on the going up and on the coming down. This is necessaril true ever single time!!!!