# Form 2 Mathematics Quadratic Expressions and Equations Questions and Answers

Form 2 Mathematics Quadratic Expressions and Equations Questions and Answers

Lessons (**43**) * SHARE*

- 1.
The square of a number is 4 more than three times the number. Find the number.

1m 44s - 2.
Given that the lengths of the three sides a right-angled triangle are x, x+ 1 and x + 2 units. Find the value of x.

3m 24s - 3.
A triangle ABC has a base of (x + 3) cm and a height of x cm. If its area is 5 #cm^2#. Calculate the length of its base.

2m 7s - 4.
After reducing by an equal amount the length and width of a rectangle which were originally 8 cm and 5 cm respectively, the area of the new rectangle is 18#cm^2#. Find the dimensions of the new rectangle.

3m 14s - 5.
A number of people bought a 300-hectare farm which they shared equally. If the number of hectares per person was 5 less than their number, find the number of people.

2m 13s - 6.
The figure below shows two concentric circles. If the ratio of their radii is 1:2 and the area of the shaded region is 75 #cm^2#, calculate the area of the larger circle.

2m 48s - 7.
A picture measuring 5 cm by 8 cm is mounted on a frame so as to leave a uniform margin of width x cm all round. If the area of the margin is 30#cm^2#, find x.

3m 26s - 8.
The figure below shows a rectangular lawn of dimensions 6x metres by x metres. In the centre is a rectangular flower garden of length (x + 4) m and width (x - 1) m. If the area of the shaded region is 40 #m^2#, calculate the area of the flower garden.

4m 11s - 9.
There are 240 exercise books to be given to a class. Thirty-four students in the class did not receive the books for various reasons. If the books were then shared equally among the remaining members of the class, the number of books given to each student is equal to the number of students in the class. Find the number of students in class.

2m 32s - 10.
Members of a group decided to raise K£ 100 towards a charity by contributing equal amount. Five of them were unable to contribute. The rest had, therefore, to pay K£ 1 more each to realise the same amount. How many members were in the group originally?

3m 32s - 11.
ABC is an isosceles triangle in which AB = AC. The size of angles ABC and ACB are (3x^2- 2x + 4)° and (9x - 6)° respectively. Calculate the two possible sets of the three angles of triangle ABC.

3m 31s - 12.
Expand and simplify each of the following expressions:
(a) (6x + 2) (4x + 3)
(b) (3x - 2) (x + 5)
(c) (x -1)(x + 2)
(d) (2x - 3)(x + 2)
(e) (6x - 2)(2x + 8)
(f) (2 - x) (x + 4)

4m 27s - 13.
Expand and simplify each of the following expressions.
(a) (x +7) (x + 8)
(b) (3x - 2) (2x + 3)
(c) (5x + 3)(3x + 5)
(d) (7x - 4)(4x - 7)
(e) (m - n)(n - m)
(f) (2x -3)(x + 3)

4m 30s - 14.
Expand and simplify each of the following expressions :
(a) (ax + b)(2ax - 3b)
(b) (4 - 2x)(#1/2# - x)
(c) (6x - 5)(5x + 6)
(d) (y - 2)(y + 2)
(e) (x + 2a) (x + 2a)
(f) (3x - 4)(5x - 6)

5m 12s - 15.
Expand and simplify each of the following expressions
(a) (x + 2a)(x - 2a)
(b) (x - 7)(x + 7)
(c) #(x + 2)#^2
(d) #(4x + 2)#^2

3m 0s - 16.
Expand and simplify each of the following expressions
(a) #(1/2 + x)^2#
(b) #(ax + d)^2#
(c) #(1/4 + 1/x)^2#
(d) #(x- 3)^2#
(e) #(4x - 3/4)^2#
(f) #(1- 1/x)^2 #

5m 1s - 17.
Use the quadratic identities to write down the expansions of each of the following expressions:
(a) #(x + 5)^2#
(b) #(x- 5)^2#
(c) #(4x + 3)^2#
(d) #(2x + 3)^2#

2m 25s - 18.
Use the quadratic identities to write down the expansions of each of the following expressions.
(a) #(3- x)^2#
(b) #(1/2 +x)^2#
(c) #(1/x-1)^2 #
(d) #(1/4+ 3/4 b)^2#

2m 23s - 19.
Use the quadratic identities to write down the expansions of each of the following expressions :
(a) #(1/2 a-1/3 b) ^2#
(b) #(1-1/a) (1+1/a)#
(c) #(1/x+1/y) (1/x-1/y)#
(d) #(-2x - 3y)(-2x + 3y)#

2m 48s - 20.
Use the quadratic identities to write down the expansions of each of the following expressions:
(a) #(1/(3y)+1/(4x))^2#
(b) #(-1/3 x-1)^2#
(c) #(1/5 a+4/5 b)^2#
(d) #(3/7 x+1/2 y)^2#

3m 1s - 21.
Factorise each of the following expressions:
(a) #x^2 + 6x + 8#
(b) #x^2 - 5x + 6 #
(c) #x^2 + 4x -21#
(d) #x^2 + x - 2 #
(e) #x^2 + 2x – 35#
(f) #x^2 - 10x + 24#

4m 16s - 22.
Factorise each of the following expressions.
(a) #x^2 - 4x - 32#
(b) #x^2 + 3x - 54#
(c) #x^2 + 2x + 1#
(d) #x^2+ 4x + 4#
(e) #x^2- 2x + 1#
(f) #x^2 - 14x + 49#

4m 53s - 23.
Factorise each of the following expressions :
(a) #x^2- 16x + 64#
(b) #x^2- 4#
(c) #1 - x^2#
(d) #(x^2 - 16)#
(e) #x^2 - 5x + 6#
(f) #x^2 - 5x - 6#

6m 20s - 24.
Factorise each of the following expressions
(a) #x^2 + 2x + ax + 2a #
(b)# t^2 + 8t + 12 #

1m 28s - 25.
Factorise each of the following expressions:
(a) #2x^2 + 3x – 2#
(b) #3x^2 – 2x – 8#
(c) #4x^2 + 7x + 3#
(d) #5x^2 – 21x +4#

3m 43s - 26.
Factorise each of the following expressions:
(a) #14x^2 – 16x + 2#
(b) #3x^2 + 11x + 6#
(c) #8 – 2x – 3x^2 #
(d) #16x + 24 + 2x^2 #

4m 37s - 27.
Factorise each of the following expressions:
(a) #35x^2 + 43x + 12#
(b) #–21x^2 + 58x – 21#
(c) #150x^2 – 25x – 21#
(d) #17x^2 +82x –15#

5m 17s - 28.
Factorise each of the following expressions:
(a) #8x^2 + 6x + 1#
(b) #x^2 – 4x – 117#
(c) #9x^2 + 48x + 64#
(d) #75x^2 + 10x – 21#

4m 9s - 29.
Factorise each of the following expressions:
(a) #1 + 7x – 30x^2 #
(b) #19x^2 –22x + 3#
(c) #63x^2 + 130x + 63#
#(d) x^2 – 2/15x – 1/15#

6m 31s - 30.
Factorise each of the following expressions:
(a) #4x^2 – 12x + 9#
(b) #9x^2 + 6x + 1#
(c) #2x^2 – 32y^2#
#(d) 1 – 2/y +1/y^2 #

5m 3s - 31.
Factorise each of the following expressions:
(a) #t^8 – t^4#
(b) #35x^2 – x – 12#
(c) #4x^2 + 2x + 1/4#
(d) #2x^2 + 4x – 6#

4m 20s - 32.
Factorise each of the following expressions:
(a) #21x^2 + 17x – 4#
(b) #25x^2 – 5/2x + 1/16#
(c) #26x – 29x^2 + 3#
(d) #1/16 x^2 – 7/2x + 49#

5m 30s - 33.
Factorise each of the following expressions:
(a) #24x^2 – 43x – 56#
(b) #33x^2 – 16x – 4#
(c) #1/x^2 – 4/x + 4#
(d) #w^4 – t^4 + t^2 + w^2#

6m 47s - 34.
Solve each of the following equations:
(a) #x^2 + 6x + 8 = 0 #
(b) #2x^2 + 3x - 2 = 0#
(c) #14x^2 - 16x + 2 = 0 #
(d) #4x^2 + 7x - 5 = x^2 - 9 #

5m 19s - 35.
Solve each of the following equations:
(a) #x^2 - 25 = 0 #
(b) #3x^2 - 2x = 5#
(c) #3x^3 + x^2 – 4x = 0 #
(d)# 1-6x^2 = x#

6m 4s - 36.
Solve each of the following equations:
(a) #4x^2 - x - 1/2 = 0 #
(b) #x + 20/x = 9#
(c) #16x+24+2x^2 = 0 #
(d) #1/4 -1/9 x^2 = 0#

5m 59s - 37.
Solve each of the following equations:
(a) #3/x^2 - 8/x = 16#
(b) #(2x-1)^2 - 1 = 3#
(c) #x^2 + 5/6x = 1/6#
#(d) (1-1/x)^2 - 1 = 35 #

8m 31s - 38.
Solve each of the following equations:
(a) #1/3 x^2 = 2x - 3#
(b)# -12/x = -x+4#
#(c) x^2 y^2 - x^2- y^4 + y^2 = 0 #

4m 58s - 39.
Solve each of the following equations:
(a) #7x^2 - 15x+8 = 0#
(b) #8x^2 +6x+1 = 0#
(c) #x^2 - 2/15x - 1/15= 0#
(d) #(2x^2-15)/x= 7#

4m 35s - 40.
Solve each of the following equations:
(a) #x^2/2+ 1 = 9x/4 #
(b)# 1-x= 1/x + 3#
(c) #x^2 - 1/18 = x/6#
(d)# 4(1/y^2 )-4(1/y) + 1= 0#

5m 18s - 41.
Solve each of the following equations:
(a) #6/(x-4) = (x+4)/x #
(b) #(6x+8)/2 + 1/x = 0#

3m 25s - 42.
For each of the following pairs of roots, obtain a corresponding equation in the form #ax^2# + bx +c = 0, where a, b and c are constants.
(a) (-2, 2)
(b) #(1/2, 1/3,)#
(c)# (1/4, -3)#
(d) (-3, -5)
(e) (0.5, 0.75)

5m 25s - 43.
For each of the following pairs of roots, obtain a corresponding equation in the form #ax^2# + bx +c = 0, where a, b and c are constants.
(a) (0, -3)
(b) (-3, -3)
(c)# (-2 1/2, 31/2) #
(d) (p, q)
(e) #(1/p, 1/q) #

7m 40s

### Related Content

- Form 2 Mathematics Questions and Answers on Surface Area of Solids
Form 2 Mathematics Questions and Answers on Surface Area of Solids

10 Video Lessons

- Form 2 Mathematics Questions and Answers on Area of Part of a Circle
Form 2 Mathematics Questions and Answers on Area of Part of a Circle. All answers are in video format.

16 Video Lessons

- Form 2 Mathematics Questions and Answers on Area of Quadrilaterals
Form 2 Mathematics Questions and Answers on Area of Quadrilaterals

10 Video Lessons

- Form 2 Mathematics Questions and Answers on Area of a Triangle
Form 2 Mathematics Questions and Answers on Area of a Triangle

8 Video Lessons

- Form 2 Mathematics Mixed Revision Questions With Answers Set 2
Form 2 Mathematics Mixed Revision Questions With Answers Set 2

59 Video Lessons

- Form 2 Physics Topical Questions and Answers on Fluid Flow
Form 2 Physics Topical Questions and Answers on Fluid Flow

20 Video Lessons

- Form 2 Mathematics Mixed Revision Questions With Answers Set 1
Form 2 Mathematics Mixed Revision Questions With Answers Set 1

100 Video Lessons

- Form 2 Physics Sound Questions and Answers
Form 2 Physics Sound Questions and Answers. The answers are well explained in video format.

15 Video Lessons

- Form 2 Physics Magnetic Effect of Electric Current Questions and Answers
Form 2 Physics Magnetic Effect of Electric Current Questions and Answers

20 Video Lessons

- Form 2 Geography Exam Questions With Answers
Form 2 Geography Exam Questions With Answers

25 Video Lessons

- Form 2 Computer Studies: Email and Internet Questions and Answers
Form 2 Computer Studies: Email and Internet Questions and Answers

46 Video Lessons

- Form 2 Computer Studies: Desktop Publishing Questions and Answers
Form 2 Computer Studies: Desktop Publishing Questions and Answers

42 Video Lessons

- Form 2 Mathematics Trigonometry 1 exam questions and answers
Form 2 Mathematics Trigonometry 1 exam questions and answers. Answers are in video format.

72 Video Lessons

- Form 2 Computer Studies Questions and Answers on Databases
Form 2 Computer Studies Questions and Answers on Databases

39 Video Lessons

- Form 2 Computer Studies Questions and Answers on Spreadsheets
Form 2 Computer Studies Questions and Answers on Spreadsheets

38 Video Lessons

- Form 2 Computer Studies Questions and Answers: Word Processing
Form 2 Computer Studies Questions and Answers: Word Processing

23 Video Lessons

- Form 2 Mathematics Revision Questions and Answers Set 3
Form 2 Mathematics Revision Questions and Answers Set 3. The answers are in video format and very comprehensive.

50 Video Lessons

- Form 2 Chemistry Sample Revision Questions With Answers
Form 2 Chemistry Sample Revision Questions With Answers. In this session, we are going to cover Form 2 Chemistry with help of some solved questions. Answers are in video format.

41 Video Lessons

- Form 2 Mathematics Revision Questions and Answers Set 2
Form 2 Mathematics Revision Questions and Answers Set 2

50 Video Lessons

- Form 2 Mathematics Revision Questions and Answers Set 1
Form 2 Mathematics Revision Questions and Answers Set 1

48 Video Lessons

- Form 2 Geography Revision Questions and Answers Set 1
In this session, we are going to discuss on Form 2 Geography Revision Questions and Answers Set 1

34 Video Lessons

- Form 2 business studies revision questions and answers set 3
Form 2 business studies revision questions and answers set 3

25 Video Lessons

- Form 2 business studies revision questions and answers set 2
Form 2 business studies revision questions and answers set 2

25 Video Lessons

- Form 2 business studies revision questions and answers set 1
Form 2 business studies revision questions and answers set 1

23 Video Lessons

- Form 2 History and Government: Democracy and Human Rights Online Lessons
Form 2 History and Government: Democracy and Human Rights Online Lessons

20 Video Lessons

- Form 2 History and Government Lessons: Constitution and Constitution Making
Form 2 History online lessons on constitution and constitution making

22 Video Lessons

- Form 2 Business Studies: Warehousing online lessons
Form 2 Business Studies: Warehousing online lessons. The lessons are in video format.

13 Video Lessons

- Form 2 business studies: Communication online lessons
Form 2 business studies: Communication online lessons. The lessons are in video format.

31 Video Lessons

- Chemistry: Effect of an Electric Current on Substances questions and answers
Form 2 Chemistry: Effect of an Electric Current on Substances questions and answers

10 Video Lessons

- Form 2 Chemistry lessons on chemical families
Form 2 Chemistry lessons on chemical families. All lessons are in video format.

58 Video Lessons

- Form 2 Biology questions and answers on excretion and homeostasis
Form 2 Biology questions and answers on excretion and homeostasis. Covers excretion and homeostasis in plants and animals.

48 Video Lessons

- Social, Economic and Political Organization of African societies upto 19th C
Social, Economic and Political Organization of African societies upto 19th Century online lessons

13 Video Lessons

- Form 2 History and Government online lessons on urbanization
Form 2 History and Government online lessons on urbanization

27 Video Lessons

- Form 2 History and Government Development of Industries Online Video Lessons
Form 2 History and Government Development of Industries Online Video Lessons

44 Video Lessons

- Form 2 History and Government online lessons on communication
Form 2 History and Government online lessons on communication

23 Video Lessons

- Form 2 Business Studies Online Lessons on Transport
Form 2 Business Studies Lessons on Transport. The lessons are in video format.

26 Video Lessons

- Form 2 History and Government online lessons on transport
Form 2 History and Government online lessons on transport

30 Video Lessons

- Form 2 Mathematics online video lessons on trigonometric ratios
Form 2 Mathematics online video lessons on trigonometric ratios

14 Video Lessons

- Form 2 Business Studies online lessons on government and business
Form 2 Business Studies online lessons on government and business

17 Video Lessons

- Form 2 Mathematics: Pythagoras theorem online video lessons
Form 2 Mathematics: Pythagoras theorem online video lessons

16 Video Lessons

- Form 2 Business Studies: Forms of business units lessons
Form 2 Business Studies: Forms of business units online online lessons

54 Video Lessons

- Form 2 CRE: The passion, death and resurrection of Jesus lessons
Form 2 CRE online lessons: The passion, death and resurrection of Jesus

26 Video Lessons

- Form 2 Mathematics similarity and enlargement online lessons
Form 2 Mathematics similarity and enlargement online lessons

18 Video Lessons

- Form 2 CRE lessons: Jesus teaches in Jerusalem
Form 2 CRE lessons: Jesus teaches in Jerusalem

24 Video Lessons

- Form 2 CRE: Wealth, poverty, faith and prayer online lessons
Form 2 CRE: Wealth, poverty, faith and prayer online lessons

18 Video Lessons

- Form 2 Mathematics online lessons on rotation
Form 2 Mathematics comprehensive online lessons on rotation

6 Video Lessons

- Form 2 Chemistry Online Lessons: Atomic structure and the periodic table
Form 2 Chemistry Online Lessons: Atomic structure and the periodic table. The lessons are in video format.

27 Video Lessons

- Form 2 CRE online lessons on The Kingdom of God
In this session, we are going to Form 2 CRE lessons on The Kingdom of God

20 Video Lessons

- Form 2 CRE Lessons: Some major teachings of Jesus
Form 2 CRE online lessons on some major teachings of Jesus

25 Video Lessons

- Form 2 CRE lessons about Jesus and the twelve disciples
Form 2 CRE lessons about Jesus and the twelve disciples

10 Video Lessons