| Add the following: |
| (a) \[7{{a}^{2}}bc,-3ab{{c}^{2}},3{{a}^{2}}bc,2ab{{c}^{2}}\] |
| (b) \[5{{x}^{2}}-3xy+4{{y}^{2}}-9,7{{y}^{2}}+5xy-2{{x}^{2}}+13\] |
| Can you find the square of the following numbers? |
| \[{{7}^{2}}\]= 4 9 |
| \[{{67}^{2}}\]= 4 4 8 9 |
| \[{{667}^{2}}\]= 4 4 4 8 8 9 |
| \[{{6667}^{2}}\]= 4 4 4 4 8 8 8 9 |
| \[{{66667}^{2}}\]= 4 4 4 4 4 8 8 8 8 9 |
| \[{{666667}^{2}}\]= 4 4 4 4 4 4 8 8 8 8 8 9 |
| (a)\[{{6666667}^{2}}\] |
| (b) \[{{66666667}^{2}}\] |
| Factorise the following: |
| (a) \[4{{x}^{2}}-20x+25\] |
| (b) \[{{x}^{4}}-256\] |
| Convert the following ratio to percentages. |
| (a) 3 : 4 |
| (b) 2 : 3 |
| Find using distributivity. |
| (a) \[\left\{ \frac{7}{5}\times \left( \frac{-3}{12} \right) \right\}+\left\{ \frac{7}{5}\times \frac{5}{12} \right\}\] |
| (b) \[\left\{ \frac{9}{16}\times \frac{4}{12} \right\}+\left\{ \frac{9}{16}\times \frac{-3}{9} \right\}\] |
| The cells of a bacteria doubles in every 20 min. A scientist begins with a single cell. |
| (a) How many cells will be there after |
| (i) 10 h? |
| (ii) 25 h? |
| (b) What type of value is depicted by the cells of bacteria? |
| Side (in cm) | 1 | 2 | 3 | 4 |
| Area (in cm2) | 1 | 4 | 9 | 16 |
| A shop gives 20% discount. What would the sale price of each of these be? |
| (a) A dress marked at Rs. 120 |
| (b) A pair of shoes marked at Rs. 750 |
| (c) A bag marked at Rs. 250 |
| Find the volume of the following cylinder. |
(a)  |
(b)  |
| Using appropriate properties find |
| (a) \[-\frac{2}{3}\times \frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times \frac{1}{6}\] |
| (b) \[\frac{2}{5}\times \left( -\frac{3}{7} \right)-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}\] |
| A photograph of a bacteria enlarged 50/000 times attains a length of 5 cm as shown in the diagram, what is the actual length of the bacteria? If the photograph is enlarged 20/000 times only, what would be its enlarged length? |
 |
Find its area, if AD = 8 cm, AH = 6 cm, AG = 4 cm, AF = 3 cm and perpendiculars BF = 2 cm, CH = 3 cm, EG = 2.5 cm. | Using\[\left( x+a \right)\left( x+b \right)={{x}^{2}}+\left( a+b \right)x+ab\], find |
| (a) \[103\times 104\] |
| (b) \[5.1\text{ }\times \text{ }5.2~\] |
| (c) \[103\text{ }\times \text{ }98\] |
| (d) \[9.7\text{ }\times \text{ }9.8~\] |
| Arif took a loan for Rs. 80,000 from a bank. If the rate of interest is 10% per annum. Find the difference in amounts he would be paying after \[1\frac{1}{2}\] years if the interest is |
| (a) Compounded annually. |
| (b) Compounded half yearly. |
| Divide the given polynomial by the given monomial. |
| (a)\[\left( 5{{x}^{2}}-6x \right)\div 3x~~\] |
| (b) \[\left( 3{{y}^{8}}-4{{y}^{6}}+5{{y}^{4}} \right)\div \text{ }{{y}^{4}}\] |
| (c) \[8({{x}^{3}}{{y}^{2}}{{z}^{2}}+{{x}^{2}}{{y}^{3}}{{z}^{2}}+{{x}^{2}}{{y}^{2}}{{z}^{3}})\div 4{{x}^{2}}{{y}^{2}}{{z}^{2}}\] |
| (d) \[({{x}^{3}}+2{{x}^{2}}+\text{ }3x)\div 2x\] |
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