Level I

18 February 2009

Practice:  Solve for x if .

1.  A line with slope = -4 and a line with slope = 7 intersect at the point (-40, 70).  What is the distance between the x-intercepts of these lines?

The distance is -22.5 - -50 = 27.5.

2.  A man begins a 4-mile walk at 2:00 in the afternoon.  If he walks at a constant speed of 5 ft/sec, at what time h:mm:ss does he finish?

Answer.  So it takes 70 minutes, 24 seconds to complete the walk and the answer is 3:10:24.

3.  Find the angle CDE if ABD is a right triangle, angle ABD is 34 degrees, angle DFG is 81 degrees, and angle FGD is 57 degrees.

Answer.  So angle BDA is 180 – 90 – 34 = 56 degrees and angle FDG is 180 – 81 – 57 = 42 degrees.  So the answer is

180 – 56 – 42 = 82 degrees.

4.  Solve for x if .

5.  How many square inches are in a rectangle which is 5.6 feet long and 2.5 feet high?

6.  What is the y-intercept of the line which passes through the points (6,17) and (10,33)?

Answer.  We see the slope is .  So the answer is 17 – 6(4) = -7.

7.  One basketball season Phillip made 80% of his free throws while Cosmo made 64% of his free throws.  Together they made 148 of 200 free throws.  How many free throws did Phillip attempt?

Answer.  Let this number be x.

8.  What is the area of the triangle enclosed by the lines and the x-axis?

9.  Simplify as much as possible: .

10.  A model used to predict the time y (in minutes) for a runner to run a marathon given that he can run a 10k race in x minutes is

y = 5.48x – 28.  What time x did a runner do in a 10k race if the model predicts he will run the marathon in 2:43:48 (or 163.8 minutes)?

11.  Given that AB is perpendicular to BD, BD = 9, AD = 15, and AC = 37, what is the length of DC?

Answer.  You should recognize ABC as three times a 3-4-5 right triangle, so AB = 12.  (It is also .)  Then BC equals , so the answer is 26.

12.  These concentric circles are of radius 1, 2, 3, and 4.  If a dart is thrown at random (but does hit the target) what is the probability it lands in the smallest circle or in the annulus between the second and third circle?  Answer  with common factors cancelled.

13.  A right triangle has sides of lengths 5 and 12.  What are the two possible lengths of the third side?

14.  Find the area of the parallelogram (solid lines).