ANNAPOLIS VALLEY REGIONAL SCHOOL BOARD

Transcription

1 ANNAPOLIS VALLEY REGIONAL SCHOOL BOARD Mathematics 10 Cumulative Assessment #1 November 2013 Name: 25 Instructions 1. There are 12 selected response questions. Each question is worth 1 point. 2. Consider the four choices for each question, select the best one, and then fill in the bubble that has the letter that you think is the best answer. It is not necessary to show your work for the selected response questions. 3. You may mark on the diagrams and questions in the booklet, and use any available space as scrap paper. 4. There are 4 constructed response questions. Each question is worth 3 or 4 points. 5. You must show all your work for the constructed response questions. Part values may be given for any correct work shown. 6. If you use a formula, write the formula, and show all of the substitutions you make before working out your answer using the calculator to find the answer. 7. Diagrams are not drawn to scale. AVRSB Page 1

2 Selected Response Consider the four choices for each question, select the best one. Then fill in the bubble that has the letter that you think is the best answer. 1) Arrange the following lengths from smallest to largest. 1m 1in 2 cm 2 ft A 1in, 1m, 2 cm, 2 ft B 1m, 2 ft, 1in, 2 cm C 2 cm, 1in, 1m, 2 ft D 2 cm, 1in, 2 ft, 1m 2) Baseboard trim is sold in 10 lengths for $6.59 each. A rectangular room measures 190 by 148 and has a doorway that is 40 wide. What is the cost of the baseboard, before taxes? A $ B $ C $ D $ ) Two friends live different distances from a skateboard park. Aaron is 2 miles from the park, while Diego is 3050 metres from the park. How much farther does one of the friends have to travel to skateboard at the park? A km B 1.05 km C 1.81 km D 168 km 4) A square based pyramid has a slant height of 13 in. The square base has a side length of 10 in. Find the volume of the pyramid to the nearest in 3. A 100 in 3 B 300 in 3 C 400 in 3 D 433 in 3 5) What is the surface area of a hemisphere which has a diameter of 16 cm? A cm 2 B cm 2 C cm 2 D cm 2 AVRSB Page 2

3 6) Marcia must wrap the box shown below. What is the minimum amount of wrapping paper that will cover all surfaces of the box, to the nearest square inch? A 113 in 2 B 798 in 2 C 1194 in 2 D 2772 in 2 7) A conical paper cup is 15 cm high and it contains 250 cm 3 of liquid when filled to the top. What is its diameter to the nearest tenth of a centimeter? A 4.0 cm B 4.6 cm C 8.0 cm D 12.5 cm 8) Determine the sine ratio for B. A 5 yd C 4 yd B A 0.6 B 0.75 C 0.8 D ) A 12 foot long ladder leans against the wall of a building, forming a 68 angle of inclination with the ground. How far from the base of the building is the foot of the ladder? Round your answer to the nearest inch. A 4 5 B 4 6 C 4 8 D 4 10 AVRSB Page 3

4 10) Determine the size of angle B, to the nearest tenth of a degree, if AD 4 cm, DC 8 cm, BC 5 cm D A 29.2 B 34.0 C 56.0 D ) Given that A 14 determine the length of x. A x 12 km A 3.0 km B 12.4 km C 48.1 km D 49.6 km 12) When the Kim family is moving they decide to set up ramps, at both their front and back doors, in order to make it easier to move large items. - At the front door the ramp is 3 m long and has a rise of 1 m. - At the back door the ramp spans a horizontal distance of 2.5 m and is 3 m long. Which ramp is steeper and how much steeper is it? 3 m 3 m A Front door ;14.1 B Back door ;14.1 C Front door ; 21.4 D Back door ; 21.4 AVRSB Page 4

5 Constructed Response - You must show all your work. - Part values may be given for any correct work shown. - If you use a formula, write the formula, and show any substitutions you make before working out your answer. 13) Robert Pershing Wadlow, also known as the Alton Giant, is the tallest person on record. Wadlow reached 8 11 in height and weighed 439 lb when he died at the age of 22. a) If Wadlow was wearing a top hat that was 4 high would he, without ducking, have been able to walk through a 280 cm high tunnel? Explain. (2 points) b) If Wadlow removed his hat before entering the tunnel how much clearance would he have had when passing through the tunnel? Answer should be to the nearest cm. (1 point) AVRSB Page 5

6 14) Rajah slowly lowers a metal sphere into the top of a cylinder that is filled with water. As he is doing this he notices that water is being forced out by the metal sphere. How much water remains in the cylinder when the sphere sits on the top of the cylinder, so that exactly half of the sphere is visible above the cylinder, as illustrated below? Round your answer to the nearest cm 3. (3 points) - The sphere and the cylinder both have a radius of 5 cm. - The cylinder has a height of 22 cm. 22 cm 5.0 cm AVRSB Page 6

7 15) A 50 foot Christmas tree was sent from Nova Scotia to Boston in Once in Boston the tree was placed vertically in Boston Common and stabilized using two wires that were attached 3 feet from the top of the tree. The wire that was anchored in the ground due north of the tree s location made an angle of 45 with the ground. The second wire was anchored in the ground due east of the tree s location and made an angle of 55 with the ground. How far apart were the two ground supports anchored? Answer should be rounded to the nearest yard. (3 points) East North AVRSB Page 7

8 16) Henri has been asked to paint 30 light poles in a parking lot. All the light poles are the same height and have a 10 cm diameter. He needs to determine the total surface area of the lateral faces of these poles so he can decide the cost of paint in order to submit his cost projections for the job. Henri stands 12 m from the base of one of the 30 identical cylindrical light poles and finds the angle of elevation to the top of the pole to be gallon of paint covers approximately 35 m2 of surface area. What is the minimum amount of paint that Henri should buy to put one coat on the lateral faces of all 30 light poles? (4 points) AVRSB Page 8