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\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

Practice Time 1C

1. Write the first 10 triangular numbers. What happens when you multiply the triangular
numbers by 6 and add 1? What sequence do you get? Explain it.
2. Which is the smallest number greater than 1 that is both square and cubic?
3. When a diagonal of a square number is removed, which type of number do you see in the
the remaining dots?
4. If a number is subtracted from its square, what type of number remains?
5. Make some square array (dot pattern), and check whether the number of dots on the outer
layer of the array is a multiple of 4.
6. Look at the adjoining diagram. Here, two copies of the fourth triangular number
have been fitted together to make a rectangle. Explain how to calculate from
this diagram that the fourth triangular number is 10. Hence, calculate the 100th
th
triangular number. Generalize the formula to find the value of 1000 triangular
number.
7. The relation between a square and a cube number is shown alongside.
A number 3 is chosen randomly, and its square (3 × 3 = 9) and cube
(3 × 3 × 3 = 27) are shown diagrammatically here. Try to draw the
two-dimensional and three-dimensional images for the numbers 4
and 5.
8. What is the smallest number that can be written as the sum of two squares of different
numbers in two distinct ways?
9. Make a multiplication table grid by writing a 12 × 12 table as shown below. Colour the multiples of
3 and observe the pattern. Can you make 10 different mathematical and geometrical patterns from
the given table by using different colour shades?

1 2 3 4 5 6 7 8 9 10 11 12

2 4 6 8 10 12 14 16 18 20 22 24
3 6 9 12 15 18 21 24 27 30 33 36

4 8 12 16 20 24 28 32 36 40 44 48
5 10 15 20 25 30 35 40 45 50 55 60
6 12 18 24 30 36 42 48 54 60 66 72

7 14 21 28 35 42 49 56 63 70 77 84
8 16 24 32 40 48 56 64 72 80 88 96

9 18 27 36 45 54 63 72 81 90 99 108
10 20 30 40 50 60 70 80 90 100 110 120
11 22 33 44 55 66 77 88 99 110 121 132

12 24 36 48 60 72 84 96 108 120 132 144

Teacher’s Guide the students to visualise square and cube of a number on a square dotted sheet.
Tip

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