Download Review for June Exam #2

Math 9
June Exam Review #2
Semester 2
1. Calculate the slope of each line.
a) The rise is 4 and the run is 5.
b) y  8 when x  2
c) The change in x is 6 and the change in y is 10
d) The line passes through points (2,7) and (6,-1)
2. Determine two more ordered pairs that lie on each line.
a) The rise is 3, the run is 4, and (2,-5) is on the line.
2
b) The slope is
and the y-intercept is (0,5).
3
3
c) The slope is  and the x-intercept is (3,0).
5
d) y  5 , x  2 , and (-1,1) is on the line.
3. a) Graph y =
2
x4
3
b) Graph 3x – 6y = 12
4. Identify the slope and y-intercept for each line.
a) y = 3x + 4
b) y = -1.11 + 9.7x
2
c) y = - x  6.8
5
d) y = 3
5. Determine the slope and y-intercept for each of these lines.
a) 3x – 4y + 9 = 0
b) 2x + 6y = 32
c) 5x – y = 12
d) 8x + 2y – 4 = 0
6. Calculate the slopes of the lines that pass through each of the following pairs of
points.
a) A(8,2) and B(1,9)
b) E(-1,5) and F(3,2)
c) C(-1,2) and D(3, -8)
7. Determine the equations of the lines described below.
a) passing through the point M(6,9) with slope = 
b) passing through the points P(3,-11) and Q(0,5).
c) passing through the points D(2,9) and E(1,13)
d) passing through the points A(5,2) and B(5,-3)
3
4
8. Determine whether the points A(2,-6) and B(-3,10) lie on the line y= -4x +2.
9. Which choice best describes the line defined by the equation y = -4x + 27?
a) rising to the right
b) falling to the right c) horizontal d) vertical
10. Which of the following equation s represents the same line as described by 12x –
3y + 21 = 0?
a) y =
1
x7
4
b) y = 4x + 7
c) y = -4x + 21
11. A line passes through the point ( 1, - 4) and has a slope of
d) y =
1
x  63
4
5
. Which of the
2
following points would also be on this line?
a) (6, -2)
b) (3, 1)
c) ( 3, 1)
d) (3, -9)
12. Points M(14, 6) and N(-7, k) lie on a line that has a slope of
3
. Determine the
7
value of k.
13. Determine the equation of the line that passes through the points (-5,7) and (5,15).
14. Solve each equation.
a) 3x + 6 = 12
b) 5 – 2x = 11
c) 4x – 8 = 12
15. Determine the x – intercept of each of the following.
a) y = -5x + 20
b) 2x – y + 10
16. Solve each equation.
a) 9x + 2 = 11x – 10
c) -3(x + 1) -2 = 4x – 5(x – 3)
4
2
3
x  1 x  2
5
3
4

x  6  6
4  x
4
d)
3
2
b) 
17. Is x = 3 the solution to: 5(3x – 2) = 4 – 10(x + 1)
d) -6x + 8 = -10
18. Rearrange the formula for the variable indicated.
a) P = 2l + 2w, solve for l
b) V = r 2 h ; solve for h
c) A = P + Prt; solve for P
d) Ax + By = C; solve for y
19. The formula C =
5
( F  32) is used to convert Fahrenhiet temperatures to
9
Celsius.
a) Determine the Celsius temperature when F = 90.
b) Solver for F in terms of C.
c) Determine the Fahrenheit temperature when C = 25.
20. Solve for y in terms of x.
a) 8x – 4y = 12
b) 5x = 10y – 20
c) 3x – 3y – 9 = 0
d)
x y
 2
4 8
21. Josh has $32.00 in loonies and toonies.
a) Write a linear relation expressing the total amount of money in terms of the
number of loonies and toonies.
b) Write an equation to express the number of toonies in terms of the number of
loonies.
c) Is it possible that Josh has 13 toonies and 5 loonies? Explain.
22. Calculate the missing length.
23. A path is being constructed between the corners of the school
playground, as shown. Determine the length of the path.
24. Determine the length of the hypotenuse.
25. Determine the lengths of the boom and the
forestay to one decimal place.
26. The outside play area of a daycare centre is
shown. Show how you can use the
Pythagorean theorem to ensure that the
fence corners are at right angles.
27. A Pythagorean triple is a group of three whole numbers that can represent the
lengths of the sides of a right triangle. The smallest Pythagorean triple is 3,4,5.
Which of the following are Pythagorean triples?
a) 7, 24, 25
b) 3, 6, 8
c) 9, 21, 23
d) 31, 35, 38
28. Calculate the area and perimeter of each regular polygon.
29. Find the length of x accurate to the nearest tenth.
30. A school field has the dimensions shown.
a) Calculate the length of one lap of the track.
b) If Amanda ran 625 m, how many laps did she run?
c) Calculate the area of the field.
31. A right triangle’s legs are 20 cm and 48 cm. What is the area of the square whose
side length is equal to the hypotenuse?
32. Determine the surface area of a square-based pyramidal candle with a base side
length of 8 cm and a slant height of 10 cm.
33. Calculate the volume and surface area of each figure.
34. A solid figure is said to be truncated when a portion of the
bottom is cut and removed. The cut line must be parallel to
the base. Many paper cups, such as the one shown here, are
truncated cones. Calculate the volume of this paper cup.
35. Calculate the volume and surface area of this sphere.