APPENDIX D

ACHIEVEMENT TEST (LINEAR FUNCTIONS)

 

            The purpose of this test is to explore your knowledge on linear equations and related concepts, in terms of their different representations: table, graph, algebraic and verbal.  Show all your work, in the exercises that can require it.

 

Use the following figure to answer items 1 and 2.

 

1.      The coordinates of point C are: __________

 

2.      In what quadrant is point A located? __________

 

Refer to the following figure to answer items 3 and 4.

 

3.      If point P is moved from a quadrant to other in the Cartesian plane and its new coordinate is by the form (-x, y), in what quadrant is point P now located?

 

 

 

 

4.      If point P is now located in the x positive axis, then, what form has the coordinate of point P?

 

 

 

Refer to the illustration below to answer item 5.

 

                                                                                        

  1. The straight line joining the points (2, 3) and (2, 7) cuts the straight line joining the points (1, 4) and (6, 4) at the point:

 

    1. (4, 2)
    2. (1, 4)
    3. (1, 3)
    4. (2, 3)
    5. (2, 4)

 

Refer to the information below to answer items 6 and 7:

 

The table below compares the height from which a ball is dropped (d) and the height to which it bounces (b).

 

d

50

80

100

150

b

25

40

50

75

 

 

  1. Do you think that the trend between d and b is linear? Why yes or no? Explain briefly your answer.

 

 

 

 

 

 

  1. If so, state the equation that best describes the relationship between d and b.

 

 

 

 

 

 

Refer to the following table to answer item 8.

 

m

-1

1

2

4

n

-1

3

5

9

 

  1. The equation that better relate the variables m and n for the table shown above is:

 

    1. n = m
    2. n = 3m
    3. n = -m2 + 1
    4. n = m2 + 1
    5. n = 2m + 1

 

 

  1. In the Cartesian coordinate system, what is the equation of the straight line passing through the point (0, -5) and parallel to the straight line whose equation is y = 2x + 3?

 

    1. x + 2y + 5 = 0
    2. 2xy – 5 = 0
    3. 2x – 5y + 3 = 0
    4. 2x + y + 5 = 0

 

 

  1. Which is the slope of these two linear equations?

 

 

 

 

 

 

  1. Which is the relationship, if any, between the slopes of these two linear equations?

 

 

 

 

 

 

 

 

 

 

 

 

Refer to the following graph to answer item 12.

 

  1. The equation of  line l is y = 4x – 5.  The equation of line m is y = 2x + 2. What is the solution of the simultaneous equations:
    1. the coordinates of P1
    2. the coordinates of P2
    3. the coordinates of P3
    4. the x value at P2 and the y value at P3
    5. the y value at P2 and the x value at P3

 

  1. What is the interpretation of the solution of these two linear equations? Explain.

 

 

 

 

Use the following graph to answer items 14-17.

 

 

 

 

14.  The graph shows the distance traveled by a tractor during a period of four (4) hours. How fast is the tractor moving?

 

 

 

 

15.  How far the tractor is in 1 hour?

 

16.  In 3 hours?

 

17.  In 10 hours?

 

15.

 

 

16.

17.

18.  Suppose now that after the four (4) hours, the same tractor returns to its original starting point to stop working.  Using as reference the graph showed above, draw a new graph describing this situation.

 

9

 

 

 

 

 

 

 

 

 

 

 

8

 

 

 

 

 

 

 

 

 

 

 

7

 

 

 

 

 

 

 

 

 

 

 

6

 

 

 

 

 

 

 

 

 

 

 

5

 

 

 

 

 

 

 

 

 

 

 

4

 

 

 

 

 

 

 

 

 

 

 

3

 

 

 

 

 

 

 

 

 

 

 

2

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

0

1

2

3

4

5

6

7

8

9

 

 

Use the following graph to answer item 19.

 

 

  1. How much longer does it take for Car B to go 50 kilometers than it does for Car A to go to 50 kilometers?

 

 

 

 

Use the following graph to answer items 20 and 21.

 

 

  1. Three hours after starting, Car A is how many kilometers ahead of Car B?

 

 

 

 

 

 

  1. Which slope of the straight lines is bigger? The slope of the straight line of Car A or Car B? Explain briefly your answer.

 

 

 

 

 

Use the following information to answer item 22.

 

            David plans to study how well sunflowers grow in different size pots. The graphs below show four possible outcomes of this experiment.

 

            Which graph does the following statement best describe?

 

  1. As the pot size increases, the plant height decreases. _______________________

23.  Lisa jogs 2 miles everyday.  One day after running, she measures her pulse every two minutes.  These are the results.  Her pulse rate was 140 beats per minute 2 minutes after running.  It was 115 beats per minute after 4 minutes.  It was 105 beats per minute after 6 minutes.  It was 90 beats per minute after 8 minutes.  It was 75 beats per minute after 10 minutes. Which of these graphs best shows her results?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

24.  Juan left his flashlight burn for 14 straight hours. He measured the amount of light given off (in lumens) at various times. He collected these data.

 

Time

(hours)

Light Given Off

(lumens)

0

9.5

2

8.5

3

8.5

5

6.0

8

4.2

14

0.6

 

Which graph best shows his results?

 

 

 

 

 

 

  1. Lisa measured the height a ball bounced when it was dropped.  When dropped 50 cm the ball bounced 40 cm. A 10 cm drop bounced 8 cm.  A 30 cm drop bounced 24 cm.  A 100 cm drop bounced 80 cm.  A 70 cm drop bounced 56 cm.  Which of the following graphs best describes these results?

 

 

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