BOARD EXAM REVISION TEST NO. 01

BOARD EXAM REVISION TEST NO. 01

CLASS: X : REAL NUMBERS

M.M. 20 Marks

T.T. 1 hr

Note: Q. No. 1 to 2 of 1 mark, Q. No. 3 to 4 of 2 marks, Q. No. 5 to 6 of 3

marks, Q. No. 7 to 8 of 4 marks

1. State "Euclid's Division Lemma"

2. Write the condition to be satisfied by q so that a rational number p/q has a terminating expression.

3. Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some integer.

4. Find the HCF of 96 and 404 by the prime factorisation method. Hence, find their LCM.

5. Show that any positive even integer is of the form 6q or 6q + 2, or 6q + 4, where q is some integer.

6. Prove 5 is an irrational number.

7. Use Euclid's division lemma to show that the square of any positive integer is of the form 3m or 3m + 1 for some integer m.

8. Use Euclid's division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8 for some integer m.

BOARD EXAM REVISION TEST NO. 01

CLASS: X : REAL NUMBERS

M.M. 20 Marks

T.T. 1 hr

Note: Q. No. 1 to 2 of 1 mark, Q. No. 3 to 4 of 2 marks, Q. No. 5 to 6 of 3

marks, Q. No. 7 to 8 of 4 marks

1. State "Euclid's Division Lemma"

2. Write the condition to be satisfied by q so that a rational number p/q has a terminating expression.

3. Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some integer.

4. Find the HCF of 96 and 404 by the prime factorisation method. Hence, find their LCM.

5. Show that any positive even integer is of the form 6q or 6q + 2, or 6q + 4, where q is some integer.

6. Prove 5 is an irrational number.

7. Use Euclid's division lemma to show that the square of any positive integer is of the form 3m or 3m + 1 for some integer m.

8. Use Euclid's division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8 for some integer m.

BOARD EXAM REVISION TEST NO. 02 CLASS: X : MATHEMATICS

M.M. 30 Marks SECTION ? A(2 marks each)

T.T. 1 hr

1. If HCF(6, a) = 2 and LCM(6, a) = 60 then find the value of a.

2. Write the condition to be satisfied by q so that a rational number p has non-terminating expression.

q

3. Show that 12n cannot end with the digit 0 or 5 for any natural number n.

SECTION ? B(3 marks each)

4. Using Euclid's division algorithm, find the HCF of 2160 and 3520.

5. Find the HCF and LCM of 144, 180 and 192 by using prime factorization method.

6. Prove that 2 3 5 is an irrational number. 7. In a morning walk, three persons step off together. Their

steps measure 80 cm, 85 cm and 90 cm respectively. What is the minimum distance each should walk so that all can cover the same distance in complete steps?

SECTION ? C(4 marks each)

8. Show that any positive even integer is of the form 6q or 6q + 2 or 6q + 4 where q Z .

9. Prove that 3 is an irrational number. 10. Use Euclid's division lemma to show that the cube of any

positive integer is of the form 9m, 9m + 1 or 9m + 8.

BOARD EXAM REVISION TEST NO. 02 CLASS: X : MATHEMATICS

M.M. 30 Marks SECTION ? A(2 marks each)

T.T. 1 hr

1. If HCF(6, a) = 2 and LCM(6, a) = 60 then find the value of a.

2. Write the condition to be satisfied by q so that a rational number p has non-terminating expression.

q

3. Show that 12n cannot end with the digit 0 or 5 for any natural number n.

SECTION ? B(3 marks each)

4. Using Euclid's division algorithm, find the HCF of 2160 and 3520.

5. Find the HCF and LCM of 144, 180 and 192 by using prime factorization method.

6. Prove that 2 3 5 is an irrational number. 7. In a morning walk, three persons step off together. Their

steps measure 80 cm, 85 cm and 90 cm respectively. What is the minimum distance each should walk so that all can cover the same distance in complete steps?

SECTION ? C(4 marks each)

8. Show that any positive even integer is of the form 6q or 6q + 2 or 6q + 4 where q Z .

9. Prove that 3 is an irrational number. 10. Use Euclid's division lemma to show that the cube of any

positive integer is of the form 9m, 9m + 1 or 9m + 8.

BOARD EXAM REVISION TEST NO. 03

POLYNOMIALS

CLASS: X : MATHEMATICS

M.M. 20 Marks

T.T. 1 hr

SECTION ? A(2 marks each)

1. Find a quadratic polynomial, the sum and product of

whose zeroes are ? 3 and 2, respectively. 2. Check whether g(x) = x2 + 3x + 1 is a factor of the

polynomial p(x)=3x4 + 5x3 ? 7x2 + 2x + 2 by dividing p(x)

by g(x).

3. Find the number of zeroes of the given curves:

(i) y = f(x)

(ii) x = f(y)

BOARD EXAM REVISION TEST NO. 03

POLYNOMIALS

CLASS: X : MATHEMATICS

M.M. 20 Marks

T.T. 1 hr

SECTION ? A(2 marks each)

1. Find a quadratic polynomial, the sum and product of

whose zeroes are ? 3 and 2, respectively. 2. Check whether g(x) = x2 + 3x + 1 is a factor of the

polynomial p(x)=3x4 + 5x3 ? 7x2 + 2x + 2 by dividing p(x)

by g(x).

3. Find the number of zeroes of the given curves:

(i) y = f(x)

(ii) x = f(y)

SECTION ? B(3 marks each)

4. Find the quotient and remainder when 4x3 + 2x2 + 5x ? 6 is divided by 2x2 + 3x + 1.

5. On dividing x3 ? 3x2 + x + 2 by a polynomial g(x), the

quotient and remainder were x ? 2 and ?2x + 4,

respectively. Find g(x).

SECTION ? C(4 marks each)

6. Find the zeroes of the quadratic polynomial 3x2 + 5x ? 2,

and verify the relationship between the zeroes and the

coefficients.

7. Obtain all the zeroes of 3x4 6x3 2x2 10x 5 , if two

of its zeroes are

5 3

and

5

3.

SECTION ? B(3 marks each)

4. Find the quotient and remainder when 4x3 + 2x2 + 5x ? 6 is divided by 2x2 + 3x + 1.

5. On dividing x3 ? 3x2 + x + 2 by a polynomial g(x), the

quotient and remainder were x ? 2 and ?2x + 4,

respectively. Find g(x).

SECTION ? C(4 marks each)

6. Find the zeroes of the quadratic polynomial 3x2 + 5x ? 2,

and verify the relationship between the zeroes and the

coefficients.

7. Obtain all the zeroes of 3x4 6x3 2x2 10x 5 , if two

of its zeroes are

5 3

and

5

3.

BOARD EXAM REVISION TEST NO. 04

CIRCLES

CLASS: X : MATHEMATICS

M.M. 20 Marks

T.T. 1 hr

SECTION ? A(2 marks each)

1. The length of a tangent from a point A at distance 5 cm from

the centre of the circle is 4 cm. Find the radius of the circle.

2. If tangents PA and PB from a point P to a circle with centre

O are inclined to each other at angle of 80?, then find POA.

3. Two concentric circles are of radii 5 cm and 3 cm. Find the

length of the chord of the larger circle which touches the

smaller circle.

SECTION ? B(3 marks each)

4. In the below figure, XY and XY are two parallel tangents to

a circle with centre O and another tangent AB with point of

contact C intersecting XY at A and XY at B. Prove that

AOB = 90?.

BOARD EXAM REVISION TEST NO. 04

CIRCLES

CLASS: X : MATHEMATICS

M.M. 20 Marks

T.T. 1 hr

SECTION ? A(2 marks each)

1. The length of a tangent from a point A at distance 5 cm from

the centre of the circle is 4 cm. Find the radius of the circle.

2. If tangents PA and PB from a point P to a circle with centre

O are inclined to each other at angle of 80?, then find POA.

3. Two concentric circles are of radii 5 cm and 3 cm. Find the

length of the chord of the larger circle which touches the

smaller circle.

SECTION ? B(3 marks each)

4. In the below figure, XY and XY are two parallel tangents to

a circle with centre O and another tangent AB with point of

contact C intersecting XY at A and XY at B. Prove that

AOB = 90?.

5. Prove that the parallelogram circumscribing a circle is a rhombus. SECTION ? C(4 marks each)

6. A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.

7. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

5. Prove that the parallelogram circumscribing a circle is a rhombus. SECTION ? C(4 marks each)

6. A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.

7. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

BOARD EXAM REVISION TEST NO. 05

CLASS: X : MATHEMATICS

M.M. 20 Marks

T.T. 1 hr

SECTION ? A(2 marks each) 1. The length of a tangent from a point A at distance 13 cm

from the centre of the circle is 12 cm. Find the radius of the circle. 2. If TP and TQ are the two tangents to a circle with centre O so that POQ = 110?, then find the value of PTQ 3. Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.

SECTION ? B(3 marks each) 4. A quadrilateral ABCD is drawn to circumscribe a circle.

Prove that AB + CD = AD + BC 5. In the below figure, XY and XY are two parallel tangents to

a circle with centre O and another tangent AB with point of contact C intersecting XY at A and XY at B. Prove that AOB = 90?.

BOARD EXAM REVISION TEST NO. 05

CLASS: X : MATHEMATICS

M.M. 20 Marks

T.T. 1 hr

SECTION ? A(2 marks each) 1. The length of a tangent from a point A at distance 13 cm

from the centre of the circle is 12 cm. Find the radius of the circle. 2. If TP and TQ are the two tangents to a circle with centre O so that POQ = 110?, then find the value of PTQ 3. Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.

SECTION ? B(3 marks each) 4. A quadrilateral ABCD is drawn to circumscribe a circle.

Prove that AB + CD = AD + BC 5. In the below figure, XY and XY are two parallel tangents to

a circle with centre O and another tangent AB with point of contact C intersecting XY at A and XY at B. Prove that AOB = 90?.

SECTION ? C(4 marks each) 6. Prove that "The ratio of the areas of two similar triangles is

equal to the square of the ratio of their corresponding sides." 7. Prove that "The lengths of the tangents drawn from an

external point to a circle are equal".

SECTION ? C(4 marks each) 6. Prove that "The ratio of the areas of two similar triangles is

equal to the square of the ratio of their corresponding sides." 7. Prove that "The lengths of the tangents drawn from an

external point to a circle are equal".

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