Advertisements
Advertisements
प्रश्न
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.
उत्तर
(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
संबंधित प्रश्न
Plot the following points on a graph sheet. Verify if they lie on a line
A(4, 0), B(4, 2), C(4, 6), D(4, 2.5)
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.
The ordinate of a point is its distance from the y-axis.
The coordinates of the origin are (0, 0).
Match the coordinates given in Column A with the items mentioned in Column B.
| Column A | Column B |
| (1) (0, 5) | (a) y coordinate is 2 × x - coordinate + 1. |
| (2) (2, 3) | (b) Coordinates of origin. |
| (3) (4, 8) | (c) Only y–coordinate is zero. |
| (4) (3, 7) | (d) The distance from x-axis is 5. |
| (5) (0, 0) | (e) y coordinate is double of x-coordinate. |
| (6) (5, 0) | (f) The distance from y-axis is 2. |
Explain the situations represented by the following distance-time graph.
The following table gives the growth chart of a child.
| Height (in cm) | 75 | 90 | 110 | 120 | 130 |
| Age (in years) | 2 | 4 | 6 | 8 | 10 |
Draw a line graph for the table and answer the questions that follow.
- What is the height at the age of 5 years?
- How much taller was the child at the age of 10 than at the age of 6?
- Between which two consecutive periods did the child grow more faster?
This graph shows the per cent of students who dropped out of school after completing High School. The point labelled A shows that, in 1996, about 4.7% of students dropped out.
- In which year was the dropout the rate highest? In which year was it the lowest?
- When did the per cent of students who dropped out of high school first fall below 5%?
- About what per cent of students dropped out of high school in 2007? About what per cent of students stayed in high school in 2008?
Consider this input/output table.
| Input | 1 | 2 | 4 | 5 | 7 |
| Output | 2 | 5 | 11 | 14 | 20 |
- Graph the values from the table by taking Input along horizontal axis from 0 to 8 and Output along vertical axis from 0 to 24.
- Use your graph to predict the outputs for inputs of 3 and 8.
The graph given below compares the price (in Rs) and weight of 6 bags (in kg) of sugar of different brands A, B, C, D, E, F.
- Which brand(s) costs/cost more than Brand D?
- Bag of which brand of sugar is the heaviest?
- Which brands weigh the same?
- Which brands are heavier than brand B?
- Which bag is the lightest?
- Which bags are of the same price?
