Math 11AW Unit 4: Slopes and Rates
Math 11AW Unit 4: Slopes and Rates. Name: _________________ Date: _____________ Block: ______
Lesson Notes 4.3: Vertical and Horizontal Lines and Solving Slope Problems..
Try these:
[pic]
Vicki is planning to build an above-ground pool. The pool needs to be on level, or horizontal, land. Where should Vicki build the pool?
[pic]
a) What is the slope of each area of land in Vicki's cross-section plan of her yard?
[pic]
b) Vicki should build in area ___ . It has a slope of ____.
Example 1) This is a plan for Jean's new gazebo. How can she check whether the posts will be plumb? Plumb means exactly vertical.
A. What is the slope of the supporting posts for the roof?
B. Are the supporting posts for the roof plumb? Explain.
Try these.
[pic]
Rowell is installing a pipe. The minimum grade must be 4%. The vertical drop must be [pic] in. What does the horizontal run need to be?
a) What is the grade 4% as a slope ratio?
b) How can you use the slope to calculate the run?
The horizontal run needs to be ________ in.
Example 2) Penny knows that the slope of a ski run is [pic]. The coordinates of the top and bottom of the ski run on a cross-section plan are (2 m, 0 m) and (1250 m, y). What is the missing coordinate?
Example 3) This topographic map uses contour lines to show hills and valleys. The lines show points of equal elevation. Omar is using the map to calculate the grade of the mountain. What is the grade of Mount Green along the line drawn on the map?
Math 11AW Unit 4: Slopes and Rates. Name: _________________ Date: _____________ Block: ______
Assignment 4.3: Vertical and Horizontal Lines.
1. a) Which line looks as if it has a slope of 0? Which line looks as if it has an undefined slope?
Slope: _____________ Slope: _____________
[pic]
b) Use the slope formula to verify the slope of each line above.
2. Is the line joining each pair of points vertical, horizontal, or neither? Justify your answers.
a) (34.5, 2.6) and (45.0, 2.6) c) (68, 1 0) and (52, 12)
b) (40, 1 00) and (40, 200) d) (31, 5) and (62, 12)
3. Order the slopes in Question 2 from flattest to steepest.
4. This mountain road passes through the West Gate Canyon in Kootenay National Park. The centre of the road is the origin.
• The top of one section of canyon wall is (7.5 m, 28.5 m).
• The base of this section of canyon wall is (7.5 m, 19.0 m).
What is the slope of this section of canyon wall?
5. A line connecting the points (x, 5) and (4, 8) has slope –0.6.
a) What is the missing coordinate, x?
b) Plot both points on the grid. Connect the points. Count squares to verify that the slope is correct.
6. Nathan designs dirt bike ramps. He wants the slope of a ramp to be [pic]. He needs the ramp to be 8 m high.
a) How long should the base of the ramp be?
b) How long should the ramp be, to the nearest tenth of a metre?
7. Simon owns a logging company. He will use helicopter logging for any hill with a grade greater than 10%. Will Simon use helicopter logging for the terrain on the right?
8. What is the pitch of the roof of an A-frame building if its height is 3.6 m and its width is 5.4 m?
9. How wide is the shed in the diagram below if the pitch of the left side is 3:4 and the pitch of the right side is 8:9?
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