QUADRATIC EQUATIONS

QUADRATIC EQUATIONS

1. Find the value of k for      kx2 + 2x - 1 = 0, so that it has two equal roots

2. Find the value of k for    k x2   - 2√ 5 x + 4 = 0, so that it has two equal roots.

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

4. Find the discriminant of the quadratic equation 3x2– 4 √3 x + 4 = 0, and hence find the nature of its roots.

5. Find the value of k for       2 x2 + k x + 3 = 0, so that it has two equal roots.

6. Find the value of k for     k x (x – 2) + 6 = 0, so that it has two equal roots.

7. Find the value of k for which the equation x2 + 5kx + 16 = 0 has no real roots.

8 Find the discriminant of the quadratic equation 2x2– 6x + 3 = 0, and hence find the nature of its roots.

9. Find the value of k for    k2 x2 –  2 (2 k - 1) x + 4 = 0, so that it has two equal roots.

10. Find the value of k for (k + 1) x2  – 2 ( k - 1) x + 1= 0, so that it has two equal roots.

11. Determine the positive value of k for which the equation x2 + k x + 64 + 0 and x2 – 8x + k = 0 will both have real roots. (3 Marks)

12. Find the discriminant of the quadratic equation 2x2 – 3 x + 5 = 0, and hence find the nature of its roots.

13. Find the value of k for x2 – 2(k + 10x + k2 ) = 0, so that it has two equal roots.

14. If -4 is a root of the quadratic equation x2 + px–4=0 and the quadratic equation x2+ px +k=0 has equal roots, find the value of k.

15. Find the discriminant of the quadratic equation 2x2 – 4x + 3 = 0, and hence find the nature of its roots.

16. The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.

17. In a class test, the sum of Amit’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 Marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.

18. A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

19. A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in  such  a way that the differences of its distances from two diametrically opposite fixed gates A and   B on the boundary is 7 metres. Is it possible to do so? If yes, at what distances from the two gates should the pole be erected?

20. Two water taps together can fill a tank in 9+ 3/8  hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Guess Paper

  Q1. The sum of two numbers is 15. If the sum of their  reciprocals is 3/10. Find the numbers.

Q2. Divide 19 into two parts such that sum of their squares is 193.

Q3. Divide 41 into two positive parts such that difference of their squares is 369.

Q4.The product of two consecutive odd numbers is 483. Find the numbers.

Q5. Divide 16 into two parts such that twice the square of the larger part exceeds the square of the smaller  part by 164.

Q6. The numerator of a fraction is one more than its denominator. If its reciprocal is subtracted from it, the difference is 11/30. Find the fraction.

Q7. The denominator of a fraction exceeds its numerator by 3. If one is added to both numerator and denominator , the difference between the new and the original fraction is 1/24. Find the original fraction.

Q8. A two digit number is such that the product of the digits is 14. When 45 is added to the number, then the digits interchange their places. Find the number.

Q9. A two digit number is such that the product of the digits is 18. When 63 is subtracted to the number, then the digits interchange their places. Find the number.

Q10. A two digit number is four times the sum of its digits and twice the product of its digits. Find the number.

Q11. The sum of ages of a son and his father is 35 years and the product of their ages is 150. Find their present ages.

Q12. The age of a father is equal to the square of the age of his son. The sum of the age of the father and five times the age of the son is 66 years. Find their present ages.

Q13. The length of hypotenuse of a right triangle is one unit more than twice the length of the shortest side and the other side is one unit less than twice the length of the shortest side. Find the lengths of the other two sides.

Q14. The hypotenuse of a right triangle is 3√5 cm. If the smaller side is tripled and the larger side is doubled, the new hypotenuse will be 15 cm. Find the length of each side.

Q15. The hypotenuse of a right angled triangle is 6m more than twice the shortest side. If the third side is 2m less than the hypotenuse, find the sides of the triangle.

Q16. The area of a right angled triangle is 600 sq. cm. If the base of the triangle exceeds the altitude by  10 cm, find the dimensions of the triangle.

Q17. The length of a rectangle exceeds its width by 8 cm and the area of the rectangle is 240 sq. cm. Find the dimensions of the rectangle.

Q18. The side of a square exceeds the side of another square by 4cm. And the sum of the areas of the two squares is 400 sq. cm. Find the dimensions of the square.

Q19. A rectangular field is 16m long and 10m wide. There is a path of uniform width all around it, having an area of 120 sq.cm. Find the width of the path.

Q20. Two pipes running together can fill a cistern in 6 minutes. If one pipe takes 5 minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.

Q21. The speed of a boat in still water is 11 km/h. It can go 12 Km upstream and return dowmstream to the original point in 2 hours 45 minutes. Find the speed of the stream.

Q22. Two trains leave a railway station at the same time. The first train travels due west and the second due north. The first train travels 35 Km/h faster than the second train. If after two hours, they are 130 Km apart, find the average speed of each train.

Q23. An express train makes a run of 240 Km at a certain speed. Another train whose speed is 12 Km/h less takes an hour longer to cover the same distance. Find the speed of express train in Km/h.

Q24.The angry Arjun carried some arrows for fighting with Bheeshm. With half the arrows, he cut down the arrows thrown by Bheeshm on him and with six other arrows, he killed the rath driver of Bheeshm. With one arrow each, he knocked down respectively the rath, flag and the bow of Bheeshm. Finally, with one more than four times the square root of arrows he laid Bheeshm unconscious of an arrow bed. Find the total number of arrows Arjun had.

Q25. A shopkeeper buys a number of books for Rs 80. If he had bought 4 more books for the same amount, each book would have cost him Re 1 less. How many books did he bought?

Q26. A person on tour has Rs 360 for his daily expenses. If he exceeds his tour by 4 days, he must cut down his daily expenses by Rs 3 per day. Find the number of days of his tour.

Q27. In a flight of 600 Km, an aircraft was slowed down due to bad weather. Its average speed for trip was reduced by 200 Km/h and the time increased by 30 minutes. Find the duration of flight.

Q28. A piece of cloth costs Rs 200. If the piece were 5 m longer and each metre of cloth costs Rs 2 less, the cost of piece would have remained unchanged. How long is piece and what is its original rate per meter?

Q29. Rs 6,500 were 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.

Q30.The sum S of first n natural numbers is given by S = n[ (n + 1)/2] . Find n, if the sum is 351.

 Answers (Word Problems)Ans1. 5, 10 Ans2. 7, 12 Ans3. 25, 16 Ans4.21, 23 Ans5. 10, 6 Ans6. 6/5 Ans7. 5/8 Ans8. 27 Ans9. 92  Ans10. 36 Ans11. 30 years, 5 years Ans12. 36 years, 6 years Ans13. 8 units, 15 units Ans14. 3cm, 6cm Ans15. 10m, 24m, 26m Ans16. 30cm, 40cm, 50cm Ans17. 12cm, 20cm Ans18. 12cm, 16cm Ans19. 2m Ans20. 10 min, 15 min Ans21. 5 Km/h Ans22. 25 Km/h, 60 Km/h Ans23. 60 Km/h Ans24. 100 Ans25. 16 Ans26. 20 Ans27. 1 hour Ans28. length 20m, rate Rs 10 Ans29. 50  Ans30. 26

CIRCLES (revision)

CIRCLES (revision)

1. If a hexagon ABCDEF  circumscribe  a circle ,prove that AB+CD+EF=BC+DE+FA.

2. Let “s” denote the semi-perimeter of a ∆ABC in which BC=a ,CA=b , AB=c. If a circle touches the sides BC, CA, AB at D, E, F, respectively  ,  prove that BD=s-b.

3. From an external point P, two tangents ,PA and  PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If  PA=10 cm , find the perimeter of triangle PCD.

4. ABC is an isosceles triangle , in which AB=AC , circumscribed about a circle. Show that BC is bisected at the point of contact .

5. Two tangents PA and PB from a P to a circle with centre O are inclined to each other at an angle of 80⁰ ,then find ∟POA.

6. In two concentric circles  , a chord of length 24m of larger circles becomes a tangent to the smaller circle whose radius is 5 cm . Find the radius of the larger circle.

7. PQR is a right triangle right angled at Q  . PQ=5cm, QR=12cm .A circle with centre O is inscribed in ∆PQR, touching  its all sides . Find the radius of the circle  .  

8. AB is a chord of length 24cm of a circle of radius 13cm. The tangent at A and B intersects at a point C. Find the length of AC.  

9. P  is the mid point of an arc  QPR of a circle .Show that the tangent at P is parallel to the chord QR.

10. Prove that parallelogram circumscribing a circle is a rhombus.

FORMULAE OF COORDINATE GEOMETRY

STATISTICS (CLASS 9)

MEASURES OF CENTRAL TENDENCY

1. Find the median of the following data :61,68,56,72,23,84,76,48,99,58. If 58 is replaced by 85 find the new median ?

2. The median of the observation arranged in ascending order is 24. Find the value of x :

 11,  12, 14, 18, x+2, x+4, 30, 32, 35, 41.

3. Determine the median of 24, 23, a, a-1, 12, 16, where a is the mean of 10,20,30,40, and 50.

4. If the mean of 5, 8, 9, x  and 14 is 10 ,Find the value of x ?

5. The mean of 16 numbers is 8. If 2 is added to every number, what will be the new mean?

6. The mean of 20 numbers is 41. If 6 is subtracted to every number, what will be the new mean?

7. The mean of 100 numbers is 24. If 6 is added to every number and then multiplied by 2.5. what will be the new mean?

8. The mean of certain group of observations is 150. what will be the new mean, if the value of each observation is :

(a) decreased by 26%

(b) multiplied by 2.5

(c) divided by 3.

9. The sum of the deviations of a set of n values x1 ,x2 ,x3,..............xn measured from 50 is -10b and the sum of deviations of the values from 46 is 70. Find the value of n and the mean .

10. A ship sails out to an island at the rate of 16km/h and sails back to the starting point at 20km/h. Find the average speed of the boat during the whole journey.

11. Nine persons went to a hotel for taking the meals . Eight of them spends Rs 12 each on their meals and the ninth person spent Rs 8 more than the average expenditure of all the nine. What was the total monthly spent by them ?

12. The average score of boys in an examination of a school as 71 and that of the girls is 73. The average score of the school in an examination is 71.8. Find the ratio of the number of boys to the number of girls that appeared in an examination .

13. The mean heights of 10 students was 153 cm .But later on it was discovered that 151 cm was wrongly read as 141 cm. Find the correct mean .

14. Find the mean median and mode of the following data :

14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.

      

  

SURFACE AREA AND VOLUME (CLASS 9)

SURFACE AREA AND VOLUME (CLASS 9)

1. Find the volume of the largest right circular cone that has placed in a hollow cube of edge 14cm.

2. how many square metres of a metal sheet is required to make a closed cylindrical tank of height 1.4m and base diameter 2m?

3. A cube of largest volume is cut out from a sphere of radius 4√3cm. Find the volume of the cube.

4. A right triangle PQR with sides 3cm,4cm,and 5cm is revolved about the side of length 4cm. Find the volume of shape so formed.

5. A wall of length 10m was to be built across an open ground .The height of the wall is 4m and its thickness is 24cm. If this wall is to be built up with bricks whose dimensions are 24cmx12cmx8cm, find the number of bricks required ?

6. Find the TSA and CSA of hemisphere of radius √7m.

7. A hemisphere of lead of radius 8cm is cart inyo a right circular cone of base radius 6cm.Determine the height of cone (upto two decimal places )

8. If the radius of a sphere is doubled ,What is the ratio of volume of first sphere to that of the second sphere .

9. If the radius of a sphere is reduced by 5% .how much percent will its surface area decreases ?

 10. What will be the volume of the largest sphere that can be placed in a right circular cylinder of radius 7cm and height 14cm ?

  

QUADRILATERAL AND AREA OF PARELLOGRAM (CLASS IX)

QUADRILATERAL AND AREA OF PARELLOGRAM

Prove that followings:

1. A diagonal of a parallelogram divides it into two congruent triangles.

2. In a parallelogram, opposite sides and angle are equal.

3. If each pair of opposite sides of quadrilateral is equal, then it is a parallelogram.

4. If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram.

5. The diagonals of a parallelogram bisect each other.

6. If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

7. A quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel.

8. The line drawn through the mid-point of one side of a triangle, parallel to another side bisects the third side.

9. The line segment joining the mid- points of the two sides of a triangle is parallel to the third side.

10. Show that each angle of a rectangle is a right angle.

11. Show that the diagonal of a rhombus are perpendicular to each other.

12. ABC is an isosceles triangle in which AB=AC. AD bisects exterior angle PAC and CD||AB. Show tha  (i) angle DAC=angle BCA and(ii) ABCD is a parallelogram (||gm).

13. Show that the bisectors of the angles of a parallelogram form a rectangle.

14. ABCD is a parallelogram (||gm) in which P and Q are mid-points of opposite side AB and CD. If AQ intersects DP at S and BQ intersects CO at R, show that (i) APCQ is ||gm

(ii)DPBQ is ||gm(iii) PSQR is ||gm]

15 If the diagonal of a parallelogram are equal, then show that it is a rectangle.

16. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus

17. Show that the diagonals of a square are equal and bisect each other at right angles.

18. Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.

19. In a parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ. Show that

(I) ∆ APB cong ∆ CQB

(ii) AP=CQ

(iv) ∆ AQB cong ∆ CPD

(iv) AQ=CP

(v) APCQ is a parallelogram.

20. ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA. AC is a diagonal. Show that:

(i) SR||AC and SR =1/2 AC

(ii) PQ=SR (iii) PQRS is a parallelogram.

21. ABCD is a rhombus and P, Q, R and S are the mid- point of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

22 ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

23. Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

24 ABC is a triangle right angle at C. A line through the mid-points M of hypotenuse AM and parallel to BC intersects AC at D. Show that (i) D is the mid –point of AC (ii) MD ┴ AC(iii) CM=MA=1/2 AB.

25. Parallelograms on the same base and between the same parallels are equal in area.

IMPORTANT N.C.E.R.T QUESTIONS

IMPORTANT N.C.E.R.T QUESTIONS

 (MATHEMATICS-X)-IITERM

·       QUADRATIC EQUATION :-   EX4.1-Q1,Q2  EX4.2- Q1,Q5 EX 4.3- Q1,Q2 Q3(II)  EX 4.4- Q1,Q2  EXAMPLES-3,4,5,8,9,10,11,13,14,15,16

·       ARITHEMATIC PROGRESSION  :- EX 5.1-Q2(a) Q3(a) Q4(V)                  EX 5.2-Q4,Q7,Q11,Q16,Q17,Q18  EX 5.3-Q1(I,II)Q3(I,III) Q7,Q10,Q12,Q11,Q6  EX 5.4-Q1

          EXAMPLE-1,2,3,7,8,11,13,15

·       COORDINATE GEOMETRY :- EX7.1:-Q1,Q2,Q3,Q4,Q7,Q8, EX7.2:-Q1,Q2,Q4,Q5,Q6, Q8,Q9  EX7.3:-Q4,Q12  EX7.4:-Q2 EXAMPLES-6,7,9,10

·       APPLICATIONS OF TRIGNOMETRY:-  EX9.1:- Q2,Q5,Q10,Q12,Q13,Q14,Q15,Q16  EXAMPLES-2,3,4.

·       CIRCLES:-  EX10.1-Q3 EX10.2-  Q1,Q6,Q7,Q8,Q9,Q10,Q12,A13 .EXAMPLES-4 THEOREM 10.1,10.2.

·       CONSTRUCTIONS :- EX11.1-Q1,Q2,Q4,Q5,Q7  EX7.1:--Q1,Q4 EXAMPLE-11.1

·       AREARELATED TO CIRCLES :- EX12.1-Q1,Q2,Q4  EX12.2-Q1,Q2,Q5,Q4,Q7,Q9,Q3 EX12.3-Q1,Q4,Q6,Q7,Q9,Q12,Q15. EXAMPLES -1,5,2,4,5.

·       SURFACE AREA AND VOLUME:-EX13.1-Q1,Q3,Q6,Q7,Q8  EX13.2-Q1,Q2,Q5,Q6 EX13.3-Q1,Q2,Q4,Q6,Q5  EX13.4-Q1,Q3,Q4,Q5  EX13.5-Q5 EXAMPLES -1,2,3,6,8,10,12,14

·       PROBABILITY :- EX15.1- Q4,Q8,Q9 EX15.2-Q1,Q13,Q15,18,24  EXAMPLES-1,2,4 6, 13

Creating a Study Plan

                                       
                                                  Creating a Study Plan

As the exam nears, you will need to create a plan to help you study effectively and minimize stress. The first step is to figure out how much time and effort you must dedicate to studying for the exam by asking the following questions:
How much material do you need to cover?
How difficult is the material?
How much time is available?
Do you have any other priorities during the study period?
What is the format of the exam?
How important is the exam?
What is your performance target for the exam?

To prepare the study plan, map out all of the material that has to be covered and make a schedule showing what, when and how much you will study each day. If you have kept up with the course work, studying will involve revision of the material that you have already covered. If you are behind in the course, you will have to finish the readings and other uncompleted work before starting the revision (if there isn't enough time to go over everything, you must decide what is most important for the exam).

Here are some tips to follow in creating your study plan:

budget your time realistically;
allocate the study time into several manageable study sessions;
divide the course material into small segments and assign them to the study sessions;
set clear and specific goals for the study sessions;
prioritize to ensure that material weighted more heavily in the exam gets sufficient study time;
take into account your familiarity with the material and the difficulty level;
don't make the study sessions too long;
study sessions should have enough variety in terms of topics and activities to prevent boredom and loss of effectiveness;
avoid cramming before the exam; and
don't forget to include regular breaks.

VOLUME AND SURFACE AREA (revision-1)

VOLUME AND SURFACE AREA (revision-1)

Q1. A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice-cream. The ice-cream is to be filled into cones of height 12 cm and diameter 6 cm ,having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream .

Q 2. Two solid right circular cones have the same height. the radii of their bases are r1 and r2. They are melted and recast into a cylinder of same height. Find the radius of the base of the cylinder .

Q3. Water flows at the rate of 10 metres per minute through a cylinder pipe 5mm in diameter . how long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm ? (Ans= 51 minutes 12 seconds)

Q4. From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm,a conical cavity of same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2. ( Ans = 18 cm 2)

 Q5. A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots,each of which is a sphere of radius 0.5 cm are dropped into the vessel,one-fourth of the water flows out. Find the number of lead shots dropped in the vessel. (Ans = 100 )

 Q6. Water in a canal 6 m wide and 1.5 m deep, is flowing with a speed of 10Km/h .How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed ? ( Ans = 56.25 hectares)

 Q7. A copper wire,3 mm in diameter , is wound about a cylinder whose length is 12 cm, and diameter 10 cm,so as to cover the curved surface area of the cylinder.Find the length and mass of the wire, assuming the density of copper to be 8.88 g per cm2. ( Ans = 125.6 m ,111.533 Kg)

Q 8. If the radii of the circular ends of a conical bucket which is 45 cm high, are 28 cm and 7 cm. Find the capacity of the bucket.

Q 9. The perimeters of the ends of a frustum are 48 cm and 36 cm . If the height of the frustum be 11 cm , find its volume.

Q10. A container made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with radii of itslower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fil the container at the rate of Rs. 15 per litre and the cost of metal sheet used , If the cost is Rs 5 per 100 cm2 (Ans: Rs. 156.75, Rs 97.96(approx.))

Q11. The radii of the circular ends of a frustum of a cone of height 6cm are 14 cm and 6 cm respectively. Find the lateral surface area and the total surface area of the frustum. (Ans: 628.57 cm2,1357.71 cm2)

Q12. A friction clutch is in the form of a frustum of a cone, the diameter of the ends being 32 cm and 20 cm and length 8 cm. Find its bearing surface and volume . (Ans: 817.14 cm2,4324.57 cm3)

Q13. The slant height of the frustum of a cone is 4 cm , and the perimeter of its circular bases are 18 cm and 6 cm respectively. Find the surface area of the frustum. (Ans: 48 cm2)

PROBABILITY (revision)

PROBABILITY

Q1. Nidhi and nisha are two friends .What is the probability that will have

A) Same birthday

B) Different birthday (ignore the leap year )

Q2. Tom was born in Feburary 2000. What is the probability that he was born on 13^th Feb ?

Q3. Are the following outcomes equally likely or not ? A baby is born “it is a boy or a girl”

Q4. A letter is selected from the letter of word MATHEMATICS . What is the probability that it is M ?

Q5. Find the probability of getting 53 Sundays in a

A) Leap year

B) Non leap year .

Q6. In a lottery there are 10 prizes and 25 blanks. Find the probability of getting a prize.

Q7. What is the probability of sure and certain event ?

Q8. Write a sample space of

A) Tossing a coin

B) Throwing a die.

Q8. Two coins are tossed once. Find the probability of getting

A) Exactly one head

B) Almost one head

Q9. Someone is asked to take a number from 1 to 100. Find the probability  that it is not a prime number.

Q10. Out of 400 bulbs in a box 15 bulbs are defective . One bulb is taken out at random from the box. Find the probability that the drawn bulb is not defective.

Q11. If a number x is chosen from a number 1,2,3, and a number y is selected from the numbers 1,4,9. Find the probability that xy=10.

Q12. A number is selected at random from the numbers 3,5,5,7,7,7,9,9,9,9. Find the probability that the selected number is their average .

  

REVISION FOR SECOND TERM MATHEMATICS (CLASS IX)

REVISION FOR SECOND TERM MATHEMATICS (CLASS IX)

Q 1: Classify the following as linear, quadratic and cubic polynomial :x2 + x

a) cubic b) quadratic c) linear

Q 2: Line segment joining the centre to any point on the circle is a radius of the circle.

a) True b) False

Q 3: Of all the line-segments that can be drawn from a point to a line not containing it, the perpendicular line-segment is the shortest.

a) True b) False

Q 4: Given statement is true or false? Give reason : Every natural number is a whole number.

a) True b) False

Q 5: The triangle formed by joining the mid-point of the sides of an isosceles triangle is ______

a) an isosceles triangle b) obtuse triangle

Q 6: Find : 321/5

Q 7: Find the value of the polynomial 5x – 4x2 + 3 at x = 0

Q 8: Use the factor theorem to determine whether g(x) is a factor of p(x) in the following cases : p(x) = 2x3 + x2 - 2x - 1, g(x) = x + 1

Q 9: AD is the bisector of ∠A of ABC, where D lies on BC. Prove that AB > BD and AC > CD. Q 10: Find the mean and median of first ten prime numbers . <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> Q 11: The class marks of a distribution are 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97, 102 Determine the class size, the class limits and the true class limits. Q 12: Write four solutions for the following equation : x = 4y <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> Q 13: Find the value of the following equation for x = l, y = l as a solution. ax – 2y = 10 Q 14: Factorise : 3x2 - x - 4 Q 15: Is (x + 1) is a factor of given polynomial ? x4 + 3x3 + 3x2 + x + 1 Q 16: Find the remainder when x3 + 3x2 + 3x + 1 is divided by 5 + 2x. Q 17: Evaluate the following product without multiplying directly : 104 × 96 Q 18: Given two points A and B and a positive real number k. Find the locus of a point P such that ar( PAB) = k. Q 19: A closed iron tank 12 m long, 9 m wide and 4 m deep is to be made. Determine the cost of iron sheet used at the rate of Rs. 50 per metre, the sheet being 2 m wide. Q 20: A room is 5 m long, 3.5 m wide and 3 m high. Find the cost of cementing the inner portion of the walls at Rs. 20 per square metre. Q 21: The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the diameter of the base of the cylinder. Q 22:Prove that diagonals of a parallelogram divides it into four congurent triangles. <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> Q 23: A powder tin has a square base with side 8 cm and height 13 cm. Another is cylindrical with the radius of its base 7 cm and its height 15 cm. Find the difference in their capacities. Q 24: A conical pit of top diameter 3.5 cm is 12 m deep. What is its capacity in kilolitres ? Q 25: Two chords PQ and RS of a circle are parallel to each other and AB is the perpendicular bisector of PQ. Without using any construction, prove that AB bisects RS. Q 26: In the following figure, D, E and F are respectively the mid-points of sides BC, CA and AB of an equilateral triangle ABC. Prove that DEF is also an equilateral triangle. Q 27: The diameter of a roller 120 cm long is 84 cm. If it takes 500 complete revolutions to level a playground, determine the cost of leveling at the rate of Rs. 25 per square metre. Q 28: The diameter of the base of a right circular cylinder is 28 cm and its height is 21 cm. Find its (i) curved surface area (ii) total surface area and volume. Q 29: If the radius of a sphere is halved then what is the decrease in its surface area ? Q 30: An exterior angle of a triangle is 115o and one of the opposite angles is 35o. Find the other two angles. Q 31: Find solutions of the form x = a, y = 0 and x = 0, y = b for the following pairs of equations. Do they have any common such solution? 3x + 2y = 6 and 5x + 2y = 10 Q 32: Factorise : x3 + 13x2 + 32x + 20 Q 33: Given below are the seats won by different political parties in the polling outcome of a state assembly elections: <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> Political party A B C D E F Seats won 75 55 37 29 10 37 (i) Draw a bar graph to represent the polling results. (ii) Which political party won the maximum number of seats? <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> <><><><> Q 34: Give the geometric representation of 2x + 9 = 0 as an equation in one variable.  Q 35: If the work done by a body on application of a constant force is directly proportional to the distance traveled by the body, express this in the form of an equation in two variables and draw the graph of the same by taking the constant force as 5 units. Also read from the graph the work done when the distance traveled by the body is 2 units.