Advertisements
Advertisements
Question
Observe the toothpick pattern given below:
(a) Imagine that this pattern continues. Complete the table to show the number of toothpicks in the first six terms.
| Pattern | 1 | 2 | 3 | 4 | 5 | 6 |
| Toothpicks | 4 | 13 |
(b) Make a graph by taking the pattern numbers on the horizontal axis and the number of toothpicks on the vertical axis. Make the horizontal axis from 0 to 10 and the vertical axis from 0 to 30.
(c) Use your graph to predict the number of toothpicks in patterns 7 and 8. Check your answers by actually drawing them.
(d) Would it make sense to join the points on this graph? Explain.
Advertisements
Solution
(a) On the basis of given patterns, we can arrange the following table which show the number of toothpicks in the first six terms.
| Pattern | 1 | 2 | 3 | 4 | 5 | 6 |
| Toothpicks | 4 | 7 | 10 | 13 | 16 | 19 |
Pattern and toothpicks shows the following relation as
1 → 4, 2 → 4 + 3 = 7
3 → 7 + 3 = 10, 4 → 10 + 3 = 13
5 → 13 + 3 = 16, 6 → 16 + 3 = 19
(b) On the basis of given condition, we can draw the following graph
(c) The graph follows the y = 3x + 1 pattern. If x = 7, then y = 3 × 7 + 1 = 21 + 1 = 22 and if x = 8, then y = 3 × 8 + 1 = 24 + 1 = 25.
| x | 7 | 8 |
| y | 22 | 25 |
(d) Yes, it shows the relation between x and y follows the given pattern y = 3x + 1.
APPEARS IN
RELATED QUESTIONS
State whether True or False. Correct those are false.
A point whose y coordinate is zero and x-coordinate is 5 will lie on y-axis.
Decide which of the following statement is true and which is false. Give reasons for your answer.
A point whose x-coordinate is zero, will lie on the y-axis.
The following table gives the information regarding length of a side of a square and its area:
| Length of a side (in cm): | 1 | 2 | 3 | 4 | 5 |
| Area of square (in cm2): | 1 | 4 | 9 | 16 | 25 |
Draw a graph to illustrate this information.
All points with y-coordinate as zero lie on the ______.
The points (3, 5) and (5, 3) represent the same point.
Match the ordinates of the points given in Column A with the items mentioned in Column B.
| Column A | Column B |
| (a) (7, 0) | (i) The ordinate is double the abscissa. |
| (b) (11, 11) | (ii) The ordinate is zero. |
| (c) (4, 8) | (iii) The ordinate is equal to the abscissa. |
| (d) (6, 2) | (iv) The abscissa is double the ordinate. |
| (e) (0, 9) | (v) The abscissa is triple the ordinate. |
| (f) (6, 3) | (vi) The abscissa is zero. |
Write the y-coordinate (ordinate) of the given point.
(3, 5)
Write the y-coordinate (ordinate) of the given point.
(2, 7)
Study the graph given below of a person who started from his home and returned at the end of the day. Answer the questions that follow.
- At what time did the person start from his home?
- How much distance did he travel in the first four hours of his journey?
- What was he doing from 3 pm to 5 pm?
- What was the total distance travelled by him throughout the day?
- Calculate the distance covered by him in the first 8 hours of his journey.
- At what time did he cover 16 km of his journey?
- Calculate the average speed of the man from (a) A to B (b) B to C.
- At what time did he return home?
