Math 10 Ch 6 Exam Review

Math 10 Ch 6 Exam Review

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Which line segment has slope ?

i) / ii)
iii) / iv)
a. / iv / c. / iii
b. / i / d. / ii

____ 2. Determine the slope of the line that passes through G(3, –3) and H(–5, 9).

a. / c.
b. / d.

____ 3. Is the slope of this line segment positive, negative, zero, or not defined?

a. / negative / c. / positive
b. / zero / d. / not defined

____ 4. Is the slope of this line segment positive, negative, zero, or not defined?

a. / positive / c. / zero
b. / negative / d. / not defined

____ 5. Is the slope of this line segment positive, negative, zero, or not defined?

a. / negative / c. / positive
b. / not defined / d. / zero

____ 6. A road rises 9 m for every 60 m measured horizontally. Determine the slope of the road.

a. / c.
b. / d.

____ 7. A line has x-intercept 2 and y-intercept 6? Determine the slope of the line.

a. / c.
b. / d.

____ 8. Which of these line segments are parallel?

a. / CD and EF / c. / EF and GH
b. / AB and EF / d. / AB and CD

____ 9. Determine the slope of the line that is parallel to this line segment.

a. / c. / –
b. / d. / –

____ 10. The slope of a line is . What is the slope of a line that is parallel to this line?

a. / – / c.
b. / / d.

____ 11. The slope of a line is . What is the slope of a line that is perpendicular to this line?

a. / – / c. /
b. / d. / –

____ 12. A line has x-intercept –5 and y-intercept 1. Determine the slope of a line parallel to this line.

a. / – / c.
b. / – / d.

____ 13. A line has x-intercept 4 and y-intercept –5. Determine the slope of a line perpendicular to this line.

a. / c.
b. / d.

____ 14. The slope of a line is . What is the slope of a line that is perpendicular to this line?

a. / / c.
b. / d. /

____ 15. A line passes through D(–5, 3) and N(12, –4). Determine the coordinates of two points on a line parallel to DN.

a. / (–10, 6) and (–8, 24) / c. / (–10, 6) and (24, –8)
b. / (6, –10) and (24, –8) / d. / (–10, 24) and (6, –8)

____ 16. A line passes through R(8, 1) and F(–5, –4). Determine the coordinates of two points on a line perpendicular to RF.

a. / (16, 2) and (21, –11) / c. / (16, 2) and (–11, 21)
b. / (16, –11) and (21, 2) / d. / (2, 16) and (21, –11)

____ 17. Write an equation for the graph of a linear function that has slope and y-intercept –3.

a. / / c. /
b. / / d. /

____ 18. Which graph represents the equation ?

a. / c.
b. / d.

____ 19. For a service call, a plumber charges a $95 initial fee, plus $45 for each hour he works. Write an equation to represent the total cost, C dollars, for t hours of work.

a. / / c. /
b. / / d. /

____ 20. To join a tennis club, Josephine pays a start-up fee of $130, plus a monthly fee of $24. Write an equation to represent the total cost, C dollars, for t months of membership.

a. / / c. /
b. / / d. /

____ 21. Which graph has slope 1 and y-intercept 0?

a. / c.
b. / d.

____ 22. Write an equation for the graph of a linear function that has slope 1 and y-intercept 8.

a. / / c. /
b. / / d. /

____ 23. Use the equation to calculate the value of y when .

a. / 31 / c. / –74
b. / –31 / d. / –39

____ 24. Determine the slope and y-intercept of this graph.

a. / slope: ; y-intercept: 1.5 / c. / slope: ; y-intercept: 1.5
b. / slope: ; y-intercept: –1.5 / d. / slope: ; y-intercept: –1.5

____ 25. Describe the graph of the linear function with this equation:

a. / The graph is a line through (–2, 3) with slope .
b. / The graph is a line through (2, ) with slope .
c. / The graph is a line through (2, ) with slope .
d. / The graph is a line through (–2, 3) with slope .

____ 26. Write an equation for the graph of a linear function that has slope 8 and passes through R(4, ).

a. /
b. /
c. /
d. /

____ 27. Describe the graph of the linear function with this equation:

a. / The graph is a line through (8, –7) with slope 5.
b. / The graph is a line through (, 7) with slope .
c. / The graph is a line through (, 7) with slope 5.
d. / The graph is a line through (8, –7) with slope .

____ 28. Which graph represents the equation ?

a. / c.
b. / d.

____ 29. Determine the y-intercept of the graph of this equation:

a. / 23 / c. /
b. / 3 / d. /

____ 30. In which form is the equation written?

a. / Slope-intercept form / c. / General form
b. / Slope-point form / d. / Standard form

____ 31. Which equation is written in general form?

a. / / c. /
b. / / d. /

____ 32. Which graph represents the equation ?

a. / c.
b. / d.

____ 33. Which graph represents the equation ?

a. / c.
b. / d.

Short Answer

34. Determine the slope of this line segment.

35. A school plans to build a wheelchair ramp from the sidewalk to the front entrance of the school. The slope of the ramp must be . The entrance to the school is 75 cm above the ground. What is the horizontal distance needed for the ramp?

36. The slopes of two lines are and . Are the two lines parallel, perpendicular, or neither?

37. The coordinates of the endpoints of segments are given below. Are the two line segments parallel, perpendicular, or neither?

a) R(–2, 8), S(–12, –4) and T(3, –1), U(9, 4)

b) F(–7, –8), G(–4, 1) and V(–4, 10), W(14, 4)

38. Graph the line with y-intercept 3 and slope –2.

39. Write an equation in slope-point form for this line.

40. Write this equation in slope-intercept form:

41. Write this equation in general form:

42. Determine the slope of the line of this equation:

Problem

43. a) Determine the rise, run, and slope of this line segment.

b) Draw a line segment whose slope is:

i) zero

ii) not defined

iii) the same as the slope of the line segment in part a

44. Construction workers are paving a road. The road must drop 4 cm for every 650 cm measured horizontally.

a) What is the slope of the road?

b) Suppose a section of the road drops 24.5 cm. How long is this section of the road measured horizontally?

45. A line passes through R(6, 9) and K(–6, 15).

a) What is the slope of line RK?

b) Line VB is parallel to RK. What is the slope of VB? Explain your answer.

c) Line WX is perpendicular to RK. What is the slope of WX? Explain your answer.

46. Reggie says FGHJ is a parallelogram. Ann says FGHJ is a rectangle. Who is correct? Justify your answer.

47. Line segment OT has endpoints O(6, –9) and T(–15, 9).

Line segment VL has endpoints V(9, 12) and L(–9, –9).

a) Are these two line segments parallel, perpendicular, or neither? Justify your answer.

b) Sketch the line segments to verify your answer to part a.

48. For the equation :

a) Explain how to change the equation so the line has a greater slope, then a lesser slope.

b) Explain how to change the equation so the line has a greater y-intercept, then a lesser y-intercept.

c) Rewrite the equation so the new line has a y-intercept that is one less than the given y-intercept, and a slope that is one more than the given slope.

49. Write an equation to describe this function. Verify the equation.

50. An equation of a line is . Determine the value of m when the line passes through the point J(–5, 2).

51. a) Write an equation in slope-point form for this line.

b) Write the equation in part a in slope-intercept form. What is the y-intercept of this line?

52. In Canada, the number of girls playing organized ice hockey from January 1990 to January 2010 increased by approximately 4162 girls per year. In January 2000, there were approximately 45 400 girls playing organized ice hockey.

a) Write an equation in slope-point form to represent the number of girls, n, playing organized ice hockey as a function of the number of years, t, after 1990.

b) Use the equation in part a to estimate the number of girls playing organized ice hockey in January 2009.

53. Students at Tahayghen Secondary School sell punch during the school carnival. The number of cups sold, n, is a linear function of the temperature in degrees Celsius, t. The students sold 458 cups when the temperature was 25°C. They sold 534 cups when the temperature was 29°C.

a) Write an equation in slope-point form to represent this function.

b) Use the equation in part a to determine the approximate temperature when the students sell 325 cups of punch.

54. Determine the slope of a line that is perpendicular to the line with this equation:

55. Determine the value of k when the equations and represent lines that are:

a) parallel

b) perpendicular

Math 10 Ch 6 Exam Review

Answer Section

MULTIPLE CHOICE

1. ANS: B PTS: 1 DIF: Easy REF: 6.1 Slope of a Line

LOC: 10.RF5 TOP: Relations and Functions KEY: Procedural Knowledge

2. ANS: C PTS: 1 DIF: Easy REF: 6.1 Slope of a Line

LOC: 10.RF5 TOP: Relations and Functions KEY: Procedural Knowledge

3. ANS: D PTS: 1 DIF: Easy REF: 6.1 Slope of a Line

LOC: 10.RF5 TOP: Relations and Functions KEY: Conceptual Understanding

4. ANS: C PTS: 1 DIF: Easy REF: 6.1 Slope of a Line

LOC: 10.RF5 TOP: Relations and Functions KEY: Conceptual Understanding

5. ANS: A PTS: 1 DIF: Easy REF: 6.1 Slope of a Line

LOC: 10.RF5 TOP: Relations and Functions KEY: Conceptual Understanding

6. ANS: D PTS: 1 DIF: Easy REF: 6.1 Slope of a Line

LOC: 10.RF5 TOP: Relations and Functions KEY: Procedural Knowledge

7. ANS: C PTS: 1 DIF: Moderate REF: 6.1 Slope of a Line

LOC: 10.RF5 TOP: Relations and Functions KEY: Procedural Knowledge

8. ANS: B PTS: 1 DIF: Easy