Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 3

EASY

AS and A Level

IMPORTANT

Earn 100

Solve the inequality: $| 2 x - 3 | < | 2 - x |$ .

Important Questions on Algebra

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 4

Solve the equation:

|x^{2} - 14| = 11

.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 5

The polynomial

a x^{3} - 13 x^{2} - 41 x - 2 a

, where

a

is a constant, is denoted by

p (x)

. It is given that

x - 4

is a factor of

p (x)

. Find the value of

a

.

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 5

The polynomial

a x^{3} - 13 x^{2} - 41 x - 2 a

, where

a

is a constant, is denoted by

p (x)

. It is given that

x - 4

is a factor of

p (x)

. Factorise

p (x)

completely.

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 6

The polynomial

6 x^{3} - 23 x^{2} - 38 x + 15

, is denoted by

f (x)

. Show that

(x - 5)

is a factor of

f (x)

and hence factorise

f (x)

completely.

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 6

The polynomial

6 x^{3} - 23 x^{2} - 38 x + 15

, is denoted by

f (x)

. Show that

(x - 5)

is a factor of

f (x)

. Write down the roots of

f (x) = 0

.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 7

The polynomial

f (x) = x^{3} - 5 x^{2} + a x + b

, where

a

and

b

are constants. It is given that

x + 2

is a factor of

f (x)

, and that when

f (x)

is divided by

x - 1

, the remainder is

- 6

. Find the value of

a

and the value of

b

.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 8

The polynomial

x^{3} - 5 x^{2} + 7 x - 3

, is denoted by

p (x)

. Find the quotient and remainder when

p (x)

is divided by

(x^{2} - 2 x - 1)

.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 1 - Algebra>END-OF-CHAPTER REVIEW EXERCISE 1>Q 8

The polynomial

x^{3} - 5 x^{2} + 7 x - 3

, is denoted by

p (x)

. Use the factor theorem to show that

x - 3

is a factor of

p (x)

.