| (a) Express 49 as the sum of 7 odd numbers. |
| (b) Express 121 as the sum of 11 odd number. |
| Factorise the following : |
| (a) \[18+11x+{{x}^{2}}\] |
| (b) \[{{y}^{2}}-2y-15\] |
| Construct the following quadrilaterals |
| Quadrilateral ABCD |
| AB = 4.5 cm |
| BC = 5.5 cm |
| CD = 4 cm |
| AD = 6 cm |
| AC = 7 cm |
| Top surface of a raised platform is in the shape of a regular octagon as shown in the figure. Find the area of the octagonal surface. |
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| Two persons could fit new windows in a house in 3 days. |
| (a) One of the persons fell ill before the work started. How long would the job take now? |
| (b) How many persons would be needed to fit the windows in one day? |
| Let a, b, c, be the three rational numbers where a \[a=\frac{2}{3},b=\frac{4}{5}\] and \[c=-\frac{5}{6}.\] |
| Verify: |
| (a) \[a+\left( b+c \right)=\left( a+b \right)+\text{ }c\](Associative property of addition). |
| (b) \[a\times \left( b\times c \right)=\left( a\times b \right)\text{ }\times c\](Associative property of multiplication). |
| (a) After 12 years I shall be 3 times as old as I was 4 years ago. Find my present age. |
| (b) Verify that \[x\text{ }=\text{ }4\]is a root of the equation \[2x-3=5.\] |
| The students of Anju's class sold posters to raise money. Anju wanted to create a ratio for finding the amount of money her class would make for different numbers of posters sold. She knew they could raise Rs. 250 for every 60 posters sold. |
| (a) How much money would Anju's class make for selling 102 posters? |
| (b) Could Anju's class raise exactly Rs. 2,000? If so, how many posters would they need to sell? If not, why? |
NA, OC, QD and RB are perpendiculars to diagonal MP. | Factorise and divide the following: |
| (a) \[\left( 2{{x}^{3}}-12{{x}^{2}}+16x \right)\div \left( x-2 \right)\left( x-4 \right)\] |
| (b) \[\left( 3{{x}^{4}}-1875 \right)\div \left( 3{{x}^{2}}-75 \right)\] |
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