CBSE CLASS 10 QUADRATIC EQUATION, A.P. AND C.G

 CLASS 10 CBSE

QUADRATIC EQUATIONS

ARITHMETIC PROGRESSION

COORDINATE GEOMETRY


1. Check whether the following are quadratic equations:

(i) (x + 1)2 = 2(x – 3)

(ii) x2 – 2x = (–2) (3 – x)


2. Represent the following situations in the form of quadratic equations:

(i) The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

(ii) The product of two consecutive positive integers is 306. We need to find the integers.


3. Factorise

(i) 2x2 – x +1/8 = 0


(ii) 100x2 – 20x + 1 = 0


4. Find two consecutive positive integers, sum of whose squares is 365.


5. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.


6. Find the roots of the quadratic equations by applying the quadratic formula.


(i) 2x2 – 7x + 3 = 0


 (ii) 4x2 + 4√3x + 3 = 0


7. For the following A.P.s, write the first term and the common difference.


(i) 3, 1, – 1, – 3 …


(ii) -5, – 1, 3, 7 …


8. Which of the following are APs? If they form an A.P. find the common difference d and write three more terms


(i) 0, – 4, – 8, – 12 …

(ii) 1, 3, 9, 27 …


(iii) a, a2, a3, a4 …


(iv) √2, √8, √18, √32 …


9. If the 3rd and the 9th terms of an A.P. are 4 and − 8 respectively. Which term of this A.P. is zero.
Solution:



10. Show that a1, a2 … , an , … form an AP where an is defined as below

(i) an = 3+4n


11. Which term of the A.P. 3, 15, 27, 39,.. will be 132 more than its 54th term?


12. Find the sum of first 40 positive integers divisible by 6.


13. A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.


14. How many multiples of 4 lie between 10 and 250?


15. Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.

2

16. Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (- 3, 4).


17. Find the point on the x-axis which is equidistant from (2, – 5) and (- 2, 9).


18. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.


19. Find the coordinates of the points of trisection of the line segment joining (4, -1) and (-2, -3).


20. If A and B are (-2, -2) and (2, -4), respectively, find the coordinates of P such that AP = 3/7 AB and P lies on the line segment AB.


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