Practice Set 6
- Problem #1: In right triangle ABC, line segment AP is the altitude from point A to hypotenuse BC. The length of segment BP is 18, and the length of segment CP is 8. What is the length of segment AP?
- Problem #2: It takes you 2 hours to shovel the snow for your driveway. It takes your little brother 3 hours to complete the same job. How long does it take for the two of you to complete the job working together? Express your answer in minutes.
- Problem #3: ABCD is a square with side length 20 ft. P is a point on side AB. What is the area of the triangle PCD? Express your answer in square feet.
- Problem #4: Three circles with radii 2, 3, and 10 are externally tangent. If you connect the centers of the circles, you will form a triangle. What is the area of this triangle?
- Problem #5: Two secant lines are drawn from point A to the circle shown, one intersecting the circle at points B and D, the other intersecting the circle at points C and E. Chords BE and CD intersect at point F. Suppose that AD=AE, angle DAE measures 25 degrees, and angle ADC measures 20 degrees. What is the degree measure of BFD?
- Problem #6: What is the probability that two consecutive positive integers less or equal than 225 have a product less than or equal to 225? Express your answer as a common fraction.
- Problem #7: How many 1x1 stickers can you fit on the outside surface of a 3x3x3 Rubik's cube? You may not overlap stickers over one another.
- Problem #8: A certain ninja has three swords. He can arrange the swords so that their ends are touching, forming a triangle; the length of each sword is a side length of the triangle. His first sword is 25 inches long; his second sword is 39 inches; his third sword is x inches long. If x is an integer, what is the maximum possible value of x?
- Problem #9: How many positive factors does 699 (6 to the 99th power) have?
- Problem #10: The arithmetic mean of the set {1, 2, 8, 10} is increased by .75 when the number x is added to the set. What is the value of x?
Solutions
