Name: Test 1 Preview Math 306 September 21, 2011 Pythagoras and Number Sets

Transcription

1 Name: Test 1 Preview Math 306 September 21, 2011 Pythagoras and Number Sets. Multiple choice: Circle the letter representing the best answer. 1. Which of the following groups of numbers represents lengths of sides of a right triangle? a) 4 cm, 5 cm, 6 cm b) 4 m, 7.5 m, 8.5 m c) 9 mm, 20 mm, 21 mm d) 3.5 dm, 4.5 dm, 5.5 dm 2. The perimeter of the triangle shown at the right is: a) 53 m b) 62 m c) 84 m d) 56 m 7m 24 m x m 3. Three students are passing the football around in a field. To the nearest tenth of a metre, how far is Peter from Marty? Peter a) 10.0 m b) 22.4 m Marty 30 m c) 20.0 m d) 36.1 m 20 m Kaitlin 4. The diagonal of a square: a) is equal to half the area of the square. b) is equal to twice the side length. c) forms a right angle with a side. d) is a hypotenuse of a triangle. 5. Jafar runs from point to point E, and then to point D as shown in the diagram. BCD is a rectangle. Rounded to the nearest metre, how far does he run? 15 m D a) 53 m b) 40 m c) 49 m d) 56 m B 12 m E 26 m C

2 B. Short answer: Show steps where required, and answer using the proper units. 6. Circle the Irrational numbers in the list below. 4 π The right triangle shown has side measures r, m and d. Determine whether each of the following statements is true (T) or false (F). m r a) rea = T F 2 b) m + r = d T F c) r 2 = d 2 m 2 T F d) r is the hypotenuse T F e) d is the longest side T F 4 9 r 2 3 d m 8. Circle T (true) or F (false) for each of the following. a) c) = T F b) π = T F = T F d) = 9 25 T F e) 3. 9 = 4 T F f) 21 = T F Indicate whether each statement is TRUE or FLSE. a) Every integer is a rational number. b) non- terminating decimal number is an irrational number. c) There is no rational number between 2.53 and d) The sum of two rational numbers can be an integer. e) N is included in Z f) -5 IN g) 5.16 < h) 3.56 Q i) Every IReal number is either rational or irrational. 10. Write each of the following using periodic notation. a) b) c) d) 9 11 e) 1 24 f) 3 7 1

3 11. Write each of the following terminating decimals as reduced, pure (not mixed) fractions. a) b) c) Write the following periodic decimals as reduced, pure fractions. Show all steps used. a) 0.36 b) 1.08 c) C. Full Workout: Show all work, and answer with appropriate units in a complete sentence. 13. baseball diamond is really a square with perimeter 110 m. When the catcher throws the ball from home plate to second base, how far does the ball travel? 2nd base home plate 14. Find the perimeter of the trapezoid shown at the right. Round your answer to the nearest tenth of a unit. 15. Determine the distances between the following pairs of points by forming right triangles. Round your answer to the nearest tenth of a unit. a) to B b) B to C C c) to C B

4 16. Determine the perimeter of an equilateral triangle with height 10 cm. (the 2x s are there to help you) 2x 2x 10 cm 2x 17. Calculate the value of x in the right triangle shown at the right. 5x 3x 36 cm 18. The figure below is a cube with edge 10 cm. What is the perimeter of triangle BC? 19. ladder is placed against a wall as shown. t present, the foot of the ladder is 2.5 meters from the base of the building and the top of the ladder is touching the building meters above the ground. The foot of the ladder is moved so that it is now 3.2 meters from the base of the building. How high is the top of the ladder above the ground now?

5 20. Determine the measure of segment in the following figure below m 12 m 21. Show the following in graphic notation, interval notation and set-builder notation : ll Real numbers that are greater or equal to 4 and less than or equal to 9. Interval notation Set-builder 22. Show the following in graphic notation and in interval notation : R >5 Interval notation 23. Show the following in graphic notation, interval notation and set builder notation : ll Real numbers less than or equal to 0. Interval notation Set builder 24. Show the following in graphic notation and in interval notation : R -3 <5 Interval notation

6 25. Show the following in graphic notation and then list the values in its solution set: Z -4< <3 Solution Set 26. Show the following solution set in graphic notation and in set-builder notation: S = 10,11,12,13,. Set-builder 27. Show the following in graphic notation and in set-builder notation: ] -, 2.7 [ Set-builder Bonus: Determine the measure of DC in the triangle by first determining the area and the height BD. B 15 cm 25 cm D C