maths portfolio sachin tyagi X(H).pptx aa

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1. Maths portfolio Class –Xth H Sachin Tyagi

2. Quadratic equation Q1.Check whether the following are quadratic equation? Ans.(i) (x-2) (x+1)=(x-1)(x+3) = x+x-2x-2 = x+3x-x-3 = x-2x-2 = 3x-x-3 =2x-5x =-3+2 = +3x = -1 x=1/3 Quadratic equation because ax^2+bx+c=0

3. Arthmetic progressions.. Q 1 . W r i t e f i r s t fo u r t e r m of t h e A P w e n t f i r s t t e r m a and common difference d Are given as follows. (I) a=10 ,d= 10 Ans. So a, a+d ,a+ 2d ,a+3d . 10,20,30,40

4. Some application of trigonometry.. Q1. the shadow of a tower standing on a level ground is found to be 40m longer when the sun’s altitude is 30 ° then when it is 60 degree find the height of the tower? 1. Ans. Let the CB be x s o, D B =40+ x In ∆ ABC AB/BC =Tan60° H/x = √3 In ∆ ABC, AB/BD = tan 30° h / x +40=1/√ 3 H=x√3 We get , ( x√3)√3= x+40 3x =x+40 X=20 H=20 √3 There fore the height of the tower is 20√3m.

5. Circle … Q1 Two tangents TP and tQ are drawn to a circle with centre o from an external point t prove that ∆PTQ = 2∆OPQ? Ans. Prove that ∆ PTQ = 2∆OPQ Let the ∆PTQ=Q NOW,by theorem 10.2 TP=TQ an isosceles triangle Therefore,. ∆TPQ = ∆TQP=1/2(180-Q)=90-1/2Q Also, by theorem 10.1 ∆DPT=90° So, ∆OPQ =∆QPT-∆TPQ =90°-(90-1/2Q) 1/2Q=1/2∆ 2PTQ THIS GIVES ∆PTQ=2∆OPQ. (HENCE PROVED)

6. Surface area and volume… Q1 . The decorative black shown in figure is made up of two solid cube and hemisphere the base of the black is a cube with age 5 cm and the hemisphere fixed on the top has a diameter of 4 and 2 cm find the total surface area of the block.? Ans. Total surface area = 6×s ^2 • =6×5×5=150 cm So, the surface area of the block= TSA of cube = - base area hemisphere • = 150 –πr^2+2πr=(150+πr^2) cm^2 • =150cm^2+(22/7×4•2/2×4.2/2)cm ^2 • =150+13.86cm^2

7. Statistics.. Q1. a survey was conducted by a group of students as part of the environment awareness programme in which they collected the following data regarding the number of plants in 20 houses in a locality find the mean of number of plants for house. Ans b b .

8. Construction. Take point b as its centre, 5,6 cmAnd then a triangle similarTo It whose side 2/3cm of the corresponding sideOf the first give the justificationOf construction? Ans.

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