Grade VIII- Math Concept Maps

 

Credit

Maths Concept Map 8 CBSE by Nilesh Gupta

Grade IX Math Concept Maps

 

Credit

Maths Concept Map 9 CBSE by Nilesh Gupta

Grade X - Concept Maps

Very helpful for quick revision

Credit and thanks: Nilesh Gupta, Scribd

Maths Concept Map_X CBSE by Nilesh Gupta

Polynomials

Quick Revision Polynomials

1. Polynomials of degrees 1, 2 and 3 are called linear, quadratic and cubic polynomials respectively.

2. A quadratic polynomial in $x$ with real coefficients is of the form $a x^{2}+b x+c,$ where $a, b$, $c$ are real numbers with $a \neq 0$

3. The zeroes of a polynomial $p(x)$ are precisely the $x$ -coordinates of the points, where the graph of $y=p(x)$ intersects the $x$ -axis.

4. A quadratic polynomial can have at most 2 zeroes and a cubic polynomial can have at most 3 zeroes.

5. If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $a x^{2}+b x+c,$ then

$\alpha+\beta=-\frac{b}{a}, \quad \alpha \beta=\frac{c}{a}$

6. If $\alpha, \beta, \gamma$ are the zeroes of the cubic polynomial $a x^{3}+b x^{2}+c x+d=0,$ then

$\alpha+\beta+\gamma=\frac{-b}{a} \alpha \beta+\beta \gamma+\gamma \alpha=\frac{c}{a}$

and $\alpha \beta \gamma=\frac{-d}{a}$

7. The division algorithm states that given any polynomial $p(x)$ and any non-zero polynomial $g(x)$, there are polynomials $q(x)$ and $r(x)$ such that

p(x)=g(x) q(x)+r(x)

where $\quad r(x)=0$ or degree $r(x)<$ degree $g(x)$

Real Number Theorems

Quick revision for theorems

Theorem 1.1 (Euclid’s Division Lemma) : Given positive integers a and b,

there exist unique integers q and r satisfying a = bq + r, 0 ≤ r < b.

Theorem 1.2 (Fundamental Theorem of Arithmetic) : Every composite number

can be expressed ( factorised) as a product of primes, and this factorisation is

unique, apart from the order in which the prime factors occur.

Theorem 1.3: Let $p$ be a prime number. If $p$ divides $a^{2},$ then $p$ divides a, where $a$ is a positive integer.

Theorem 1.4: $\sqrt{2}$ is irrational.

Theorem 1.5: Let $x$ be a rational number whose decimal expansion terminates.

Then $x$ can be expressed in the form $\frac{p}{q},$ where $p$ and $q$ are coprime, and the

prime factorisation of $q$ is of the form $2^{\circ} 5^{m},$ where $n, m$ are non-negative integers.

Theorem 1.6: Let $x=\frac{p}{q}$ be a rational mamber, such that the prime factorisation of $q$ is of the form $2^{n} 5^{\text {" }},$ where $n, m$ are non-negative integers. Then $x$ has a

decimal expansion which terminates.

Theorem 1.7: Let $x=\frac{p}{q}$ be a rational number, such that the prime factorisation of $q$ is not of the form $2^{n} 5$ ", where $n, m$ are non-negative integers. Then, $x$ has a decimal expansion which is non-terminating repeating (recurring).

So we can conclude that the decimal expansion of every rational number is either terminating or non-terminating repeating.

Grade 10 Revision Questions Set I

Fast track revision

 Q1 Find the largest four-digit number which when divided by 4,7 and 13 leaves a remainder 3 in each case.

Q2 Show that $\frac{2+3 \sqrt{2}}{7}$ is not a rational number, given that $\sqrt{2}$ is an irrational number.

Q3 Write the number of real roots of the equation $x^{2}+3|x|+2=0$

Q4 Solve for $\mathrm{x}$ $\frac{x+1}{x-1}+\frac{x-2}{x+2}=4-\frac{2 x+3}{x-2} ; x \neq 1,-2,2$

Q5 The longer side of a rectangular hall is $24 \mathrm{m}$ and the length of its diagonal is $26 \mathrm{m}$. Find the area of the hall.

Q6 Prove the trigonometric identity:

$\frac{\sin \theta}{1+\cos \theta}+\frac{1+\cos \theta}{\sin \theta}=2 \operatorname{cosec} \theta$

Q7 If $A=B=60^{\circ},$ verify that $\cos (A-B)=\cos A \cos B+\sin A \sin B$

Q8 From a point $\mathrm{P}$ on the ground the angle of elevation of the top of a $10 \mathrm{m}$ tall building is $30^{\circ} . \mathrm{A}$ flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from $\mathrm{P}$ is $45^{\circ} .$ Find the length of the flagstaff and distance of building from point $\mathrm{P}$. $\sqrt{3}=1.732]$

Q9 A pole casts a shadow of length $2 \sqrt{3} \mathrm{m}$ on the ground, when the Sun's elevation is $60^{\circ} .$ Find the height of the pole.

Q10 Find the values of $\mathrm{k}$ for which the given equation has real and equal roots:

$x^{2}-2 x(1+3 k)+7(3+2 k)=0$

Q11 If $\tan \theta=\frac{12}{13},$ evaluate $\frac{2 \sin \theta \cos \theta}{\cos ^{2} \theta-\sin ^{2} \theta}$

Q12 A solid metal cone with radius of base $12 \mathrm{cm}$ and height $24 \mathrm{cm}$ is melted to form solid spherical balls of diameter $6 \mathrm{cm}$ each. Find the number of balls formed.

Polynomials Questions

Q1 Number of zeroes in $X^3-1$. are ...... Give reason to support your answer.

Sol  Number of zeroes in $X^3 -1$ are 3. As the equation is cubic or has degree three.

Q2 The sum and product of the zeroes of the quadratic polynomial are 2 and 15 then what will be the polynomial is
Sol 
Given $\alpha + \beta=2$
 $\alpha\beta=15$

Quadratic polynomial is given by
$x^2-(\alpha+\beta)x + \alpha\beta$
Hence the equation is 
$x^2-2x+15$

Let us paint

Concept Painting

 Flying Balloons

Color Spray

POEM

Trust

Trust is like a glass

Once broken would never last

No matter how much you try to repair,

So it's better to be beware

Never-ever try to break 
it because it's must 

And once broken every relation will then turn into dust

Trust is like the glass

Once broken would never last

Once you are trustworthy,
 you are loved, valued, respected.

And once the trust is broken you are left dissociated 

Trust is important,

It must be supported,

But never try to break it,

Just create it and keep it

because..

Trust is like a glass

Once broken would never last....

Written by Rhea

unedited intentionally :)

Lines and Angles Map

Lines and Angles

Map

Polynomial Map

Polynomial Map

Number System map

Grade 9

Number system 

Memory Map

Number System

Infate Academy

Number System

Natural Numbers (N)

Counting numbers are known as natural numbers N= {1,2,3,4,5…………………}

Whole Numbers (W)

Whole Numbers together with 0 form whole numbers W = {0,1,2,3,4,5……….}

Integers (I or Z)

All natural numbers, 0 and the negatives of natural numbers form the collection of integers

Z= {-$\infty$  ……….-5,-4,-3,-2,-1,0,1,2,3,4,5,…………….$\infty$}

Rational Numbers (Q)

The number of the form  $\frac{P}{Q}$ where P and Q are integers and Q$\ne$0   is in the lowest form i.e P and Q  have no common factor, is called a rational numbers.

All integers and fractions are a rational number. The set of rational numbers is denoted by Q. A rational numbers is said to be positive if its numerator and denominator are either both positive or both negative

Irrational Numbers

$\frac{5}{2}$ = 2.5 is rational number

π =3.14159… this number cannot be expressed in the form of ratio. So any number that cannot be represented in the form of ratio is called irrational number

Real numbers include whole numbers, rational numbers and irrational numbers. Real numbers can also be positive, negative and zero.

$\sqrt {-2}$    ie of any negative number is called imaginary numbers and such numbers are not real numbers

Also infinity is not a real number

Real Numbers

The collection of rational and irrational numbers are called real numbers and is denoted by R

Grade 7 Science worksheet

Science worksheet

Science formulae of acid, bases and salts

Note:This is a mere support extended towards students. It does not mean to replace classroom solutions.

S#	Chemical  Name	Formula	Uses	Special Point
1	Acetic Acid	CH3COOH	Used in vinegar	Ethanoic acid
2	Hydrochloric acid	HCL	Clean washrooms	Muriatic acid
3	Nitric acid	HNO3	Used in making fertilizers and plastic Purification of gold	Spirit of niter or aqua fortis Highly corrosive
4	Sulphuric acid	H2SO4	Used in chemical industries	Oil of vitriol
5	Carbonic acid	H2CO3	Used in cold drinks	Carbonated water, acid of air, carbon di oxide solution
6	Phosphoric acid	H3PO4	Toothpaste, food industry	Weak acid also called orthophosphoric acid
7	Calcium hydroxide	Ca(OH)2	White wash walls	Slaked lime
8	Magnesium hydroxide	Mg(OH)2	Antacid, also used as food additive	Milk of magnesia
9	Sodium hydroxide	NaOH	Chemical pulping, tissue digestion, used in soaps	Caustic soda
10	Potassium hydroxide	KOH	Used as an electrolyte Used in making soft soaps. Used as ph control agent and food stabilizer Used in manicure as chemical cuticle removing agent	Caustic potash
11	Ammonium hydroxide	NH4OH	Used in window cleaners Used in making of Nylon	Aqua ammonia or ammonia water
12	Sodium bicarbonate	NaHCO3	Used in baking cakes, biscuits etc	Baking soda
13	Sodium Chloride	Nacl	Food preservation, taste agent in food, fire extinguisher, cleaning agent	Common salt
14	Ammonium chloride	NH4Cl	Used in metal work, medicine, food etc	Nushadir salt, Sal ammoniac
15	Magnesium sulphate	MgSO4	Food preparation, medicine, agriculture etc	Epsom salt
16	Copper sulphate	CuSO4	Used in pesticides,soil sterilization, disinfecting agent. It is toxic.	Cuprous sulfate or Dicopper sulfate
17	Calcium Carbonate	CaCO3	Used to make cement, health and dietary applications	Limestone, marble, chalk
18	Potassium  nitrate	KNO3	Use in production of nitric acid, meat processing, pharmacological use, fertilizer etc	Salt peter, nitrate of potash
19	Potassium chloride	KCl	Used in fertilizers, medical uses and culinary	Sylvite, muriate of potash
20	Iron oxide	Fe2O3.10H2O	Used in iron ores, pigments, catalysts and in thermite. Used as pigment in color concrete, paints and durables	Rust
21	Sodium carbonate	Na2CO3	Used in glass manufacturing, washing powders. It is also used as water softner	Soda ash, washing soda

Data Structures

Grade BCA

Data structures

Question Bank

• Write advantages of Hashing.
• Explain the difference between B- Tree and B+ Tree.
• Explain traversal of graph.
• What is m-way Search tree?
• What is Data structure?
• List out the areas in which data structures are applied extensively?
• Explain variable length record.
• What is topological sorting?
• What is the basic difference between direct and access and index sequential files?
• Describe two applications of general trees?
• What is B+ tree?
• What are the data structures used to perform recursion?
• What is the difference between graph and tree?
• Discuss advantages of graphs.
• Discuss major features of B-trees.
• Explain AVL Tree.
• Describe the complexity of heap sort.
• Discuss the complexity of Binary search.
• Draw all binary search trees with 5 nodes A,B,C,D and E that        

 satisfy the balance requirement of AVL trees.

• Explain Sorting.
• What is spanning tree?
• Explain File.
• Write the use and advantages of files.
• What is file organization?
• Discuss few important applications of search trees.
• What is binary search tree? Explain in detail the insertion and        deletion in a binary search tree.
• What are threaded binary trees? What are the applications?

                                         OR

     What is meant by threading? Discuss its relevance.

                                                OR

     What are threads?  What are its advantages and

     disadvantages? How threads are implemented in trees?

      Explain through an example.

• Explain the role of threads in binary search tree with suitable Example.
• What do you mean by AVL tree? How to insert node into AVL  tree? Explain.
• Discuss uses and advantages of AVL search tree with suitable   
• What uses and advantages of AVL search tree with suitable

examples.

• What is B-Tree? write an algorithm to insert a key into a B-

Tree and delete a key from B-Tree?

• Write short note on B-Tree?
• Explain B+ trees and its advantages with suitable

examples.

                                              OR

Write a short note on B+ Tree?

• Give a brief Idea about general trees?

                                                         OR

          What are general Trees? discuss the steps for conversion of

          general Trees to binary Trees?

• What are huffman‘s algorithm ?how it is useful and used?

  Discuss with Examples?

                                                   OR

Describe Huffman ‘s algorithm?

• Describe m-way search Tree?
• Describe the various operation on graph?

                                             OR

Explain the different operations performed on graph ?

• Describe Warshall algorithm for shortest path with

Example?

                                                 OR

What do you mean by shortest path? explain Warshall

algorithm for shortest path?

• Describe Dijkstra algorithm for shortest path?
• What do you mean by shortest path?
• Describe Dijkstra algorithm for shortest path with example?
• Discuss topological sorting and in the advantage with suitable example?
• Explain topological sorting?
• What is traversal of graph? How is it useful and use Explain with suitable example?
• Explain Traversal of graph?
• What do you mean by graph traversal? Explain depth first and breadth first traversal of graph.
• Explain various types of graph?
• What is the quick sort? how it is use and useful? Explain its complexity with suitable examples?
• Explain quick sort algorithm?
• Explain merge sort and its complexity with examples?
• Explain merge sort algorithm?
• Explain linear search and its advantages, disadvantages and complexity?
• Describe binary search?
• Write an algorithm to search an aliment using binary search?
• Differentiate between linear search and binary search?
• What are the differentiate between internal and external sorting?
• Which sorting algorithm is the best on the basis of complexity and why?
• Compare various sorting algorithm on basis of complexity?
• Describing merging?
• Define File. Describe constituent of a file?
• Write a short note on file operations?
• Describe various kind of operations required to maintain files briefly?
• Explain various types of file? According to function they perform?
• Discuss serial file organisation its advantages and disadvantages?
• Write a short note on sequential file organisation?
• What are the steps to access a record of a file? Also draw flow chart of this.
• What are the steps for updating a sequential file?
• Discuss the advantages and disadvantages of sequential file processing?
• Explain direct access file organisation there use and advantages?
• What do you understand by indexed by sequential file? Discuss the different technique for handling overflows in indexed sequential file?
• What is multi list file organisation? Explain by an example.
• Explain inverted list file organisation by taking examples.
• Differential between inverted list and multi list file organisation?
• Describe fixed and variable length records with examples?
• Describe primary and secondary key with Examples?
• Differentiate between fixed and variable length record?
• Explain hashing function and their relatives and merits and demerits?
• Write a short note on hashing?
• What do you understand by hashing? Explain various hashing function using suitable examples?
• What do you mean by hashing function? Describe various types of hashing function. Give suitable examples.
• What are the collisions? How are these harmful and resolved? Discuss with Examples?

 

Grade 4 Revision

Grade 4 

Mock Test

Q 1 Convert 5 hours 20 minutes to minutes.

Q2 Convert 18 minutes to seconds.

Q3 Convert 540 minutes to hours.

Q4 Convert 875 seconds to minutes.

Q5 Is “Wednesday at 24:00” and “ Thursday at 00:00 mean exactly the same time?

Q6 Convert the following in 24-hour clock time

1. 02:15 am
2. 02:15 pm
3. 10:10 am
4. 10:20 pm

Q7 Can we write 12 midnight as 12am?

 

Q8 Time 12 noon can be written as 12 pm. State the statement as true or false.
Q9 Convert to 12 hour clock time.

1. 23:24 hours
2. 10:00 hours

Q10 Ajita left Delhi at 6:30 am and reached Jaipur in 6 hours 25 minutes. At what time did she reach Jaipur?

 

Q11 Find the difference between 6 hours 20 min and 12 hours 25 min.

 

Q12 Find 3 hours 20 minutes before 10:00 pm.

 

Q13 My father’s office timing are 10:30 am to 6:30 pm. How  many hours does he spend in office?

 

Q14 Convert the following

1. 8 km 200 m into m
2. 9 m 82 mm into mm
3. 50 mm into cm
4. 625 cm into m
5. 12 kg into g
6. 19 g to mg
7. 2385 gm to kg
8. 4200 mg to g
9. 15kl to l
10.  29 l to ml

Q15 Add

1. 15 m 25 cm + 8 m 65 cm
2. 75 kg 250g + 62 kg 100 g

 

Q16 A pack of juice contains 2l 200 ml of juice. Rahul drank 750 ml of juice. How much juice is left in the pack?

 

Q17 Subtract

1. 11 km 375m - 8 km 215 m
2. 96 l 545 ml - 47 l 400ml

Q18 The perimeter of a square is 120 m. Find the length of the side of the square.

 

Q19 The perimeter of an equilateral triangle  is 36 cm. Find the side of the equilateral triangle.

 

Q20 Reduce 85/100 in lowest form.

Annual exam practice

Annual Exam 2020 Practice

Grade 4

Practice Dodging with 12 and 13

https://quizizz.com/admin/quiz/5e1ebc897ef318001f93ff31


Fractions 1

https://quizizz.com/admin/quiz/5e2a8f8a703e48001b5d7cb8