Download Subject: Mathematics Topic : Numbers Grade :9 Worksheet No : 2

Subject: Mathematics
Topic : Numbers
Grade :9
Date :10/10/’10
Worksheet No : 2
Name:………………………….
Section : …………
1. Write in order of size, smallest first,
Answer ..............`..............`...................
2.In 1950, the population of Switzerland was 4 714 900.
In 2000, the population was 7 087 000.
(a) Work out the percentage increase in the population from 1950 to 2000.
Answer (a)......................................... %
(b) (i) Write the 1950 population correct to 3 significant figures.
Answer (b)(i) .........................................
(ii) Write the 2000 population in standard form.
Answer (b)(ii) ........................................
3. A rectangular field is 18 meters long and 12 meters wide.
Both measurements are correct to the nearest meter.
Work out exactly the smallest possible area of the field.
Answer..............................................m2
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4. For each of the following sequences, write down the next term.
(a) 2, 3, 5, 8, 13, …
Answer(a)…………………
(b) x6, 6x5, 30x4, 120x3, …
Answer(b) ………………..
(c) 2, 6, 18, 54, 162, ...
Answer(c) ………………
5. Use the formula
to calculate the value of P when V = 6 × 106 and R = 7.2 × 108.
Answer P = ………………….
6. A rectangle has sides of length 6.1 cm and 8.1 cm correct to 1 decimal place.
Calculate the upper bound for the area of the rectangle as accurately as possible.
Answer ………………….cm2
7. (a) Express 99 as the product of its prime factors.
(b) Find the smallest possible integer value of n for which 99n is a multiple of 24.
Answer (a) ..............................
(b)...............................
8.
The first four terms in a sequence are 1, 3, 6 and 10.
They are shown by the number of dots in the four diagrams above.
(a) Write down the next four terms in the sequence.
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(b) (i) The sum of the two consecutive terms 3 and 6 is 9.
The sum of the two consecutive terms 6 and 10 is 16.
Complete the following statements using different pairs of terms.
The sum of the two consecutive terms…………. and………… is……….. .
The sum of the two consecutive terms………….. and………… is ………..
(ii) What special name is given to these sums?
(c) (i) The formula for the nth term in the sequence 1, 3, 6, 10… is
where k is an integer.
Find the value of k.
(ii) Test your formula when n = 4, showing your working.
(iii) Find the value of the 180th term in the sequence.
(d) (i) Show clearly that the sum of the nth and the (n + 1)th terms is (n + 1)2.
(ii) Find the values of the two consecutive terms which have a sum of 3481.
9.
The natural numbers 1, 2, 3, … are written, in a clockwise direction, on a circular grid as shown
in the diagram.
There are four numbers in each ring.
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The numbers 1, 2, 3, and 4 are in the first ring.
The numbers 5, 6, 7 and 8 are in the second ring.
The following numbers fill up the other rings in the same way.
(a) Write down the numbers in the fourth ring.
(b) Write down the largest number in the tenth ring.
(c) The sum, Sn of the four numbers in the nth ring, where n = 1, 2 and 3, is given in the table
below.
(i) Write down the value of S4
(ii) Find, in its simplest form, an expression, in terms of r, for Sr
(iii) In which ring is the sum of the four numbers equal to 1018?
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