Express As a Single Power
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Name:Date:
MPM 1D
Unit 4: Review
1.Write the equation for each line defined below:
a) perpendicular to the line , passing through the point .
b) perpendicular to the line , passing through the point .
2.Given the equation , state the slope and the obvious point on the graph.
3.Given the equation , state the slope and the obvious point on the graph
4.Which of the following equations are non-linear?
a) b) c) d) e)
5.Given the line below, write the equation of the line in
a) slope-intercept form b) point-slope formc) standard form.
6.State the x- and y-intercepts for each line below.
a) b)
c) d)
7.Solve for x.
a)
b)
8.Use the grids provided below to solve the following linear systems.
a) b)
9.Write the equation of the line thathas an x-intercept -9 and y-intercept -6.
10.Write the equation of the line that has an x-intercept 7 and y-intercept -10.
11.Write the following equations in standard form: a) b)
12.Find the equation of the line perpendicular to the line and same x-intercept as.
13.Find the equation of the line parallel to the line and same y-intercept as.
14.Calculate the surface area and volume for a square-based pyramid with a slant
height of 12 m and base length 6 m.
15.Calculate the surface area and volume for a square-based pyramid with a height of
8 cm and base length 15 cm.
16.Consider the line , state a) the slope of the line. b) the equation of the
perpendicular line passing through .
17.Consider the line , state a) the slope of the line b) the equation of the perpendicular line passing through .
18.Determine the equation of the line passing through the points and .
19.Determine the equation of the line parallel to passing through . Write your final answer in standard form.
20.Determine the equation of the line perpendicular to passing through . Write your final answer in standard form.
21.Find the value of each unknown.
a) b) c)
22.Determine the measure of eachinterior and exterior angle of a regular 19-a-gon.
23.Determine the number of sides of a polygon whose interior angles total 3780°
24.The sum of the interior angles of a polygon is 2160°. Find the number of sides of thepolygon.
25.Determine the number of sides of a regular polygon based on the following criteria:
a) with interior angles of 157.5 °b) with exterior angles of 12°.
26.Amanda works in a store that sells sports equipment. Hockey gloves sell for $65 a pair and helmets cost $95 each. One shift she sells 219 items. Her receipts total $ 18,195. How many gloves did Amanda sell?
27.A small store sells used CDs and DVDs. The CDs sell for $5 each and the DVDs sell for $7 each. James sold 38 items and collected $ 236. The store owner wants to know how many CDs and how many DVDs were sold.
28.The amount Jenny earned babysitting on New Year's Eve $5 less than three-quarters of the amount than Lilly earned. The difference in their earnings is $14. Find the amount each person earned.
29.Calculate the surface area and volume for the cone with a diameter of 14 cm and a slant height of 21 cm.
30.Calculate the surface area and volume of a cone with a radius of 40 m and a height of 18 cm and no bottom.
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Solutions: 1a) b) 2. , 3., 4.a and d 5a) b) or c) 6a) x-int: 16, y-int: 12 b) x-int: 18, y-int: -4c) x-int: , y-int: -13
d) x-int: -13, y-int: 7a) b) 8a) b) 9. 10.
11a) b) 12. 13. 14. , 15. , 16a) undefined b) 17a) zero b) 18. or or 19. 20. 21a) b) , , c) 22. interior angles ; exterior angles 23. 23 sides 24. 14 sides 25a) 16 sides b) 30 sides 26. 87 gloves 27. 15 CDs and 23 DVDs 28. Lilly earned $36 and Jenny earned $22
29. , 30. ,