Test – 4 (Q.E)

1. If x =1 is a common root of ax2 + ax +3 = 0 and x2 +x + b = 0 , then ab = ?

2. If x2 + 2 (k+2)x + 9k = 0 has a repeated root, then K = ?

3. For what values of k, the roots of the equation x2 – kx + 1 = 0 are imaginary?

4. Solve: 2x2 – 6x + 3 = 0

5. Show that the equation x2 – x +2 = 0 has no real roots.

1. Solve: 3x2 + 2 x – 5 = 0

2. Find two consecutive positive integers, the sum of whose square is 25.

3. Use quadratic formula, Solve abx2 + (b2 - ac)x – bc = 0

4. Solve the Q.E 9x2 – 15 x + 6 = 0 by the method of completing the square.

1. The area of a right- angled triangle is 165m2. Determine its base and altitude if the latter exceeds

the former by 7 meters.

2. Solve 2 (

) - 3(

) = 5, x -3, ½

3. If the roots of the equation (a-b)x2 + (b-c)x + (c-a) = 0 are equal. Prove that b + c = 2a.

4. Solve the given equation

+

+

=

Test 1. For what values of k, the roots of the equation x2 – kx + 1 = 0 are imaginary?

2. Solve: 2x2 – 6x + 3 = 0

3. Show that the equation x2 – x +2 = 0 has no real roots.

4. Solve: 3x2 + 2 x – 5 = 0

5. If x =1 is a common root of ax2 + ax +3 = 0 and x2 +x + b = 0 , then ab = ?

6. If x2 + 2 (k+2)x + 9k = 0 has a repeated root, then K = ?

7. Find two consecutive positive integers, the sum of whose square is 25.

8. Use quadratic formula, Solve abx2 + (b2 - ac)x – bc = 0

9. Solve the Q.E 9x2 – 15 x + 6 = 0 by the method of completing the square.

10. The area of a right- angled triangle is 165m2. Determine its base and altitude

if the latter exceeds the former by 7 meters.

11. Solve 2 (

) - 3(

) = 5, x -3, ½

12. If the roots of the equation (a-b)x2 + (b-c)x + (c-a) = 0 are equal. Prove that b +

c = 2a.

13. Solve the given equation + + =

Worksheet – 1 (Concept Hunt)

I. Hunt the concept.

GRADE: X Worksheet – 3 (M.L) Q.E SUBJECT: MATHEMATICS

Cool, Cool… Solve, Solve…. (By using any method)

1. 6x2 - x -2 = 0 4.

x2 – x -

= 0

2. x2 -5x - = 0 5. -3x2 + 5x + 12=0

3.

+

= 1, x

,5 6. 5x2 -2x -10 = 0

Read my question, Feed ur answer:

1. Check whether the equation 6x2 – 7x + 2 = 0 has real roots, and if it has , find

them by completing square method.

2. Find the natural number whose square diminished by 84 is equal to thrice of 8

more than the given number.

3. A natural number, when increased by 12, equals 160 times its reciprocal. Find

the number.

4. Had Durga scored 10 more marks in her maths test out of 30 marks, 9 times

these marks would have been the square of her actual marks did she get in the

test?

5. In the center of rectangular lawn of dimensions 50m x 40m, a rectangular pond

has to be constructed so that the area of the grass surrounding the pond

would be 1184m2. Find the length and breadth of the pond.

6. At t minutes past 2 pm, the time needed by the minute hand of a clock to

show 3pm was found to be 3 minutes less than

minutes. Find t.

7. A motor boat whose speed is 18km/h in still water takes 1 hour more to go

24km upstream tan to return to the same spot. Find the speed of the steam.

Why swimming is needed for going in motor boat ?(VBQ)

8. If Vasuki were younger by 5 years than what she really is, then the square of

her age would have been 11 more than five times her actual age. What is her

age now ?

9. 300 apples are distributed equally among a certain number of students. Had

there been 10 more students, each would have received one apple less. Find

the number of students. “One apple a day keeps the doctor away”. Comment.

10. Is it possible to design a rectangular park of perimeter 80m and area 400m2? If

so, find its dimensions. How parks are valuable for us ?

Worksheet – (Q.E)

I. Involve, and then Solve:

1. Examine the nature of the roots of Q.E: x2 + 4x + 4 = 0, without actually finding the roots.

For what value of k, does the Q.E: (4-k)x2 + (2k+4)x +8k +1 = 0 have equal roots?

2. If -5 is a root of the Q.E: 2x2 + px -15 = 0, whereas the Q.E: p( x2 + x) = - k has equal roots, find the

values of p and k.

3. Find the nature of the roots of the Q.E: 2x2 – 6x + 3 = 0. If the real roots exist, find them.

4. Find the positive value of k for which x2 + kx + 64 = 0 and x2 – 8x + k = 0 will have real roots.

5. A train covers a distance of 90km at a uniform speed. In case of starting late, due to some reason,

the speed can be increased by 15km/h, and it would take half an hour less for the journey. (a) Find

the original speed. (b) Which value is depicted by this problem?

6. A person on tour has Rs.4200 for his expenses. If he extends his tour for 3 days, he has to cut

down his daily expenses by Rs.70. Find the original duration of the tour.

7. Sum of the areas of two squares is 260m2. If the difference of their perimeter is 24m, then find the

sides of the two squares.

8. 7 years ago Varun’s age was five times the square of Swati’s age. 3 years hence, Swati’s age will be

two-fifth of varun’s age. Find their present age.

9. The sum of the squares of two consecutive odd numbers is 394. Find the numbers.

10. If the roots of the equation (a-b)x2 + (b-c)x + (c-a) = 0 are equal. Prove that b + c = 2a.

Prepare for a maths juice everyday by using ur confident spoon.

Department of Mathematics (SSV, Karur) Page 1

Worksheet

I . Take care of our V.I.P:

1. One day, I asked the son of my closed friend about his age. The child replied in a different way. He said,

“One year ago, my dad was 8 times as old as me and now his age (in years) is equal to the square of my

age “.Represent the above situation in the form of a Q.E.

2. An electric cable cost Rs.200. If the cable was 5 meters longer and each meter of cable cost Rs.2 less, the

cost of cable would have remained unchanged. Represent the above situation in the form of a quadratic

equation.

3. Find the roots of the Q.E : 4x2 – 4px + (p2 – q2) = 0

4. Find the roots of the Q.E: a2b2x2 + b2x – a2x 1 = 0

5. Using quadratic formula, solve the Q.E for x : abx2 + (b2 – ac) x – bc = 0

6. Using quadratic formula, solve the Q.E for x : p2x2 + (p2 – q2) x – q2 = 0

7. Solve the Q.E 9x2 – 15 x + 6 = 0 by the method of completing the square.

8. Solve the given equation: 3x2 + x -14 = 0

9. A train takes 3 hours less than a bus for a journey of 600km. If the speed of the bus is 10km/hour less

than that of the train, find the speeds of the bus and the train.

10. 250 apples were divided equally among a certain number of students. If there were 25 more students,

each would have received half apple less. Find the number of students.

11. Rs.6500 is divided equally among a certain number of persons. Had there been 15 more persons, each

would have got Rs.30 less. Find the original number of persons.

12. A motor boat whose speed is 18km/hour in still water takes 1 hour more to go 24km upstream than to

return downstream to the same spot. Find the speed of the stream.

Dream With Maths…..