Worksheet - Poly-Le - Tri

WORKSHEET – POLYNOMIALS ( 2018-19) – ROYALE SECONDARY SCHOOL - BY :- SARVESH KOTKAR.
Q1) Determine the sum of the Zeroes of the Polynomial 6x2 - 3x -3.
Q2) Determine the product of the Zeroes of the Polynomial 7x2 +4x -1
Q3) If the sum and the product of the Zeroes of the Polynomials are 5 and -3
Respectively. Determine the Polynomial.
Q4) Verify that 3, -1 , are the zeroes of the Polynomial. p(x) = 3x3 – 5x2 – 11x – 3 and
Verify the relationship between the zeroes and the co-efficient.
Q5) On dividing x3 – 2x2 + x + 3 by a polynomial g (x) , the quotient and remainder are
( x – 2 ) and ( 4x -3 ) respectively .Find g (x)
Q6) Find the sum and product of zeroes of following polynomials.
1) s2 +4s -5 2) -1/3 x2 +6x +4 3) 2/5 x2 +4x -3 4) 2x2 +8x +8 5) r2 +4r -6 6. x2 -7/2 x -4I
Q7) Find the other zeroes of polynomial x +x -9x -3x+18, if it is given that two of its zeroes are √3 and - √3
4 3 2
Ans..( x2 + x – 6, -
3 & 2).
Q8) On dividing 2x4 + x3 – 14 x2 – 21 x – 8 by g(x), the quotient obtained is ( x2 + 3x +2) and the remainder is ( -2x-2).
Find g(x).
Q9) Obtained all the zeroes of 9z3 –27z2 – 100 z + 300 ; if -10 /3 is one of its zeroes.
Q 10) Determine whether -2 is a zero of the polynomial x3 +3 x2 + 5x + 6
Q11) Find the product of the zeros of the quadratic polynomial 3x2 + 5x -2 .
WORKSHEET – TRIANGLE ( 2018-19) – ROYALE SECONDARY SCHOOL - BY :- SARVESH KOTKAR.

1) ∆ ABC ∆ XYZ. If ar(ABC)=25sq.m. and ar (XYZ)=64sq.m. then BC/YZ=_____.
arDPQ 18 YZ
2) ∆ DPQ, ∆ XYZ , = , then =_______
arXYZ 98 PQ
3) In ∆ ABC, M and N are points on the sides of AB and AC respectively. MN//BC , If AM=3.5cms, MB=4.5cm, AN=10.5 then
NC=______.
4) The areas of two similar triangles are in the ratio 81:64, therefore the ratio of their corresponding sides is______.
5) In ∆ DEF ∆ PQR, if EF/QR=9/4, then arDEF/arPQR=_______.
6) In trapezium ABCD, AB//PQ//DC, where P and Q are the pint on AD and BC respectively. AP=15cm, PD=12cm, QC=14cm, then
BQ=____
7) The area of a rhombus whose diagonals are of length 10cm and 20cm is ______ sq.cm [200, 300, 100, 15]
8) The area of a square is 36cm2 . Therefore the length of its diagonal is ______ cm [6√2 , 6√3, 9√2, 9√3]
9) In ∆ABC, MN // BC such that line MN intersect AB and AC in the points M & N respectively. If AM = 8 cm, AB = 15 cm and
AN = 16 cm, then AC = ------- cm
[ 30, 15, 14, 2 ]
10)In ∆ ABC, DE II BC, A-D-B, A-E-C and AD:DB = 2:3 if AC=4.5cm then
AE= ________ cm. [4.5, 3.0, 1.8, 0.9 ]
11)A tower of height 20 m casts shadow of 12 m on the ground at the same time; a pole casts shadow of length 3 m on the ground.
Answer the following.
I) Draw an appropriate figure.
II) Find the height of the pole in cms.
12)A ladder of length 5 m rests against a vertically erected pole at the top.The base end of ladder is 3 m away from the foot of the
pole. Answer the following.
I) Draw an appropriate figure
Find the height of the pole
D A
13) With reference to the given figure & the given
Conditions , write only the proof with reasons
Given :- In Δ ABC , EF // BC where E & F lie on E
AB & AC respectively. CE is produced at D such F
That DA // BC B
Prove that CF = CE C
AF DE
WORKSHEET – LIN. EQUATION ( 2018-19) – ROYALE SECONDARY SCHOOL - BY :- SARVESH KOTKAR.
1) If x = 3 and y = 2 is a solution of the equation ax + by = 4 and bx + ay = - 14 then

a + b = ______ (-10, -2, 2, 10,).
2) If 3 + 4 = 13 and 4 + 3 =78 then the value of 1 + 1= _________ (54, 21, 15, 13)
x y x y x y
3) Mithun is ‘x’ years old and his son is ‘y’ years old. If twice Mithun’s age is added to thrice his son’ age, then the sum of their
ages will be _________. [ x+y, (x+2) + (y+3), 2x +3y, 5xy)
4) Following is a given pair of linear equation.
2x – 3y = 1 and kx + 5y = 7
Answer the following questions with reference to the given equations.
i) Write down the condition for unique solution.
ii) Find the value of ‘k’.
5) kx + 2y = 5 and 3x + y = 1,
i) Write down the condition for no solution.
6) x – ky = 2 and 3x + 2y = -5
i) Write down the condition for unique solution.
7) 3x – 2y = 7 and 5x + ky =1.
i) Write down the condition for no solution.
8) 3x + 4y = -2 and 9x +12y = k
i) Write down the condition for infinitely many solutions.
9) Following is a given pair of linear equations.
3x + 3y = 1 (2k – 1 )x + (k – 1) y = 2k + 1
Answer the following with reference to the given questions.
i) write down the condition for pair of linear equation have no solution.
ii) Find the value of ‘k’ for which given equation has no solution.
10) Find the solution of the following equation by Graphical Method
1) x + y = 5 and y - x = 1
2) 2x + y = 4 and 2y = 3x + 1
3) y = 3x - 5 and y = 5 - 2x
11) Find the solution of the following equation by Cross Multiplication Method
1. 3X + 2Y = 5 and X + 2Y = -1
2. X + Y = 8 and Y = X + 2
3. 2X + Y = 4 and 3X - 2Y = -1
4. 3a - b = 8 and a + 4b = 7
5. 4X + Y = 34 and X + 4Y = 16
6. 7X + 13Y = 27 and 13 X + 7Y = 33
12) A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes ¼ when 8 is added to its denominator. Find
the fraction.
13) 2x – (a – 4)y = 2b + 1 & 4x – (a – 1) y = 5b – 1
Find the value of ‘a’ and ‘ b’. for which given system of linear equation has infinite solution.
14) A fraction is such that if the numerator is multiplied by 2 and the denominator is increased by 3 we get ½ . But if the numerator is reduced by
one and the denominator is multiplied by 3 we get 1/15. Find the fraction.
15) In a School Children’s were arranged for a mass drill. If each row contained 4 children less. 10 more rows would have been formed. But if 5
more children were added to each row, the number of rows would have been reduced by 8. How many children were present for the mass drill.
16) The area of a rectangle reduces by 3 sq. mts. If its length is reduced by 3 mts, and the breadth is increased by 2 mts. If we increase the length by
4 mts and breadth by 3 mts the area increases by 76 sq.mts. Find the length and breadth of the rectangle.
17) A fraction is such that if the numerator is multiplied by 2 and the denominator is increased by 3 we get ½ . But if the numerator is reduced by
one and the denominator is multiplied by 3 we get 1/15. Find the fraction.
18) The area of rectangle gets reduced by 80sq. unit if its length is reduced by 5 units and the breadth is increased by 2 units. If we increase the
length by 10 units and decrease the breadth by 5 units the area increased by 50 Sq. units. Find the length and breadth of the rectangle.
19) If a certain two digit number is divided by the sum of its digits, the quotient is 4 and the remainder is 6. If the digits are interchanged and the
resulting number is divided by the sum of the digits, the quotient is 6 and the remainder is 7. Find the number.
20) Ten years ago, father was twelve times as old as his son and ten years hence he will be twice as old as his son will be. Find their present ages.
21) In a certain examination the number of candidates passed was 4 times of those who failed. If the number of candidates that appeared had
been 35 less and the number that failed had been 9 more, the number of passing would have been twice the number that failed. Find the total
number of candidates that appeared in the

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WORKSHEET – POLYNOMIALS ( 2018-19) – ROYALE SECONDARY SCHOOL - BY :- SARVESH KOTKAR.

WORKSHEET – TRIANGLE ( 2018-19) – ROYALE SECONDARY SCHOOL - BY :- SARVESH KOTKAR.

WORKSHEET – LIN. EQUATION ( 2018-19) – ROYALE SECONDARY SCHOOL - BY :- SARVESH KOTKAR.

1) If x = 3 and y = 2 is a solution of the equation ax + by = 4 and bx + ay = - 14 then

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