profit and loss

        A man finds that it costs $ (300+4N) per day to make N articles. If the selling price of each article is $7, what are the minimum articles to be produced per day if he has to make a profit?

average

        If the average of m numbers is a, and on adding x to the m numbers, the average of the (1+m) numbers is b. Then find the value of x.?

percentage

       A person split his property amongst his three sons. The youngest one got 50% of the entire property, the second got $10,000. The eldest got 20% less than the youngest. How much did the eldest son get?

profit and loss

        I bought some oranges at the rate of 5 for a $. I sold all of them to you at the rate of 4 for a $, bought all of them again from you at the rate of 3 for a $ and sold them all to you in the end at the rate of 2 for a $. What is my percentage profit in this whole transaction?

profit and loss

The cost price of an item increases by 10% first, then by 10% next and by 10% yet again finally. If the last10% increase is equivalent to an increase of $ 121, what was the first 10% equivalent to?

Average

1.     The average age of a group of people is increased by 10 when a person aged 19 years is replaced by a new person aged 59 years. How many people are there in the group?

trignometry

    

Simultaneous equation

If  S = x² + y²

And T = xy

Express x and y in terms of S and T

Arithmetic Progression

1.        Find the average of all 5 digit numbers that leave a remainder of 2 when divided by 7.

Circle -- coordinate geometry

A circle passes through the points (2,0) and (8,0) and has the y axis as a tangent. Find the two possible equations. 

motion

quadratic equation

 

Rationalization

Quadratic equation

Solve the equation

2^2x – 2^x – 6 = 0

physics

In an elastic head on collision, a ball of mass 1kg moving a 4m/s collides with a stationary ball of mass 2kg. Calculate the velocities of the balls after the collision, indicating the direction in which they are travelling.

numbers

Where X = 100²⁰⁰⁶ + 9x100²⁰⁰² – 2

Find the sum of digits of X

range of expression

if (3 - x)(6 - x) <=0

find the range of values of x for which this expression is true.

number problem

What is the sum of the digits of the number x;

Where X = 10²⁰⁰⁶ + 9.10²⁰⁰² – 2?

Quadratic Equation

Solve for X:

  

harder problems in square root

 

factorization

Factorize:

•      2x² – xy – y²

•      4p² – 4pq + q² – 4x²

Algebra

 

Algebra

 

Algebra

If x = (b – c)(a – d), y = (c – a)(b – d), z = (a – b)(c – d)

Find the value of x³ + y³ + z³ – 3xyz

harder Simultaneous equation

Solve the simultaneous equation:

x + y + z = 1

ax + by + cz = 0

a²x + b²y + c²z = 0

Algebra

 

Algebra

If (a + b + c)x = (-a + b + c)y = (a – b + c)z = (a – b – c)w

Then show that: 1/y + 1/z + 1/w = 1/x

trignometry

  

trignometry

Simultaneous Equation

Solve for x and y

x² + xy = 8   ---------------------  (1)

x - y = 6    ------------------------ (2)

Algebra

4x² + y² = 10   ---------------------  (1)

2x + y = 4    ------------------------ (2)

indices

indicies

indicies

Indicies

indicies/ factors

Express as factors: x^-2c + x^-c – 20

Express as factors: x^3m + 27  

indicies / factors

Express as factors: a + 7√a + 12

Express as factors: x – 4x^-½ - 12

Express as factors: x^a – 49  

Express as factors: 3a^½  + 5a^¼  + 2

STD VI

Use of Brackets

Factorize

Find the factors of

(m² – n²)t – mn(t² – 1)

Factorize

Factorize: x⁴ – 7x²y² + y⁴

Remainder theorem

Show that x² + qx + 1 and x³ + px² + qx + 1 have a common factor of the form (x + a) when

(p – 1)²- q(p – 1) + 1 = 0

Algebra

If x + 1/x = y, then show that 

Show that x⁵ + 1/x⁵ = y⁵ – 5y³ + 5y

find the value

Given that abc = -9

And ab + bc + ca = 6

And a + b + c = 6

Find the value of (a² + b² + c²) (1/a² + 1/b² + 1/c²)

Quadratic equation

Solve for x:

x²/3 + 3/ x² = 5(x/3 – 1/x)

inequality

Show that: a² + b² + c² ≥ bc + ca + ab

Show that:  a³ + b³ ≥ a²b + ab²

inequality

Show that a⁴ + b⁴ > a³b + ab³ for a ≠b

inequality,

For a given sum of two numbers, when will the product be maximum?

inequality

Show that the sum of a real positive quantity and reciprocal is never less than 2.

inequality

Prove that:

m² + 1/m² > m + 1/m

inequality,

Prove that:

a/b² + b/a² >  1/a + 1/b

Inequality

Prove that:

(a+ b). (b + c). (c + a) ≥ 8abc

Prove that:

(ab + cd).(ac + cd) ≥ 4abcd

indeterminate equation

A man spent Rs 8100 in buying fowls at Rs 250, ducks @ Rs 350 and pheasants @ Rs 400. The number of birds bought was 25. How many were there of each?

indeterminate equation

A man spends Rs 130000 in buying sheep @ Rs 3000 each, and cows @ Rs 17000 each; hoe many of each can he buy?

Indeterminate equations

In how many ways may Rs 1200 be paid in Rs 20 and Rs 10 denomination notes, using both the denomination or only one?

polynomial

Solve for x:

(a + x)^2/3  + 4(a – x)^2/3 = 5(a² – x²)^1/3

Polynomial

Solve for x:

(x – 4)³ + (x – 5)³ = 31{(x – 4)² - (x – 5)²}

reciprocal equations

Solve for x:
12(x⁴ + 1)  + 89x² = 56x(x² + 1)

STD VI word problems in simple equation

• Divide Rs 24 between A,B and C so that A may have 5 times, B 6 times as much as C.

• Divide Rs 3.50 between A and B so that B may have 4 paise for every paisa that A has.

        (1 Rs = 100 paisa)

• Divide Rs 2.25 between A, B and C so that A and C may each have 7 times as much as B

• Divide Rs 48 in wages for a man, a women and a boy on the supposition that the man gets 4 times as much as the boy, and the women 3.

•  A man is 4 times as old as his daughter and the difference between their ages is 36 years. Find their ages.

• Divide Rs 42 between a man and a women so that the man may have Rs 4 to every Rs3 that the women has.

•  A man is twice as old as his son and 10 times as old as his grandson. their combined ages add up to 96 years; how old are they.

• A father is 9 times as old as his son and 3 times as old as his daughter and their combined ages amount to 65 years; find them.

STD VII class test

(ICSE) class test SUBJECT: MATHEMATICS STD VII

DUR:40 min MARKS:25

Answer to this paper must be written on the paper provided separately. You will not be allowed to write during first 5 minutes. This time is to be spent in reading the question paper. The time given at the head of this paper is the time allowed for writing the answers. Attempt all questions from Section A and any one question from Section B. All working, including rough work, must be clearly shown and must be done on the same sheet as the rest of the answer. Omission of essential working will result in the loss of marks. The intended marks for questions or parts of questions are given in brackets [  ].

STD. VI -- exercise on word problems in simple equation

There are two numbers, one of which is 7 times as great as the other, if the sum of the numbers is 96, then find the numbers?

Divide 70 into two parts so that one may be four times the other.

One number is 16 times as great as another, and their difference is 75, find them.

Find two numbers differing by 57 so that one of them is 20 times the other.

Find two numbers whose sum is 52, such that one of them is one twelfth of the other.

Find two numbers differing by 88 so that one of them is one ninth of the other.

Find the sum of three numbers whose sum is 56, such that the second number is twice the first number and the third number equals to four times the first.

Divide 84 into three parts, such that two of the parts are equal and the third part is five times as great as either of the equal parts.

Having thought of a number I multiplied it successively by 4, 5 and 8 and added the result. I then subtract the double of the number thought of and find that the result comes to 45. What number did I think of?

Quadratic equation

if one of the roots of the equation is 2 + √3. Form the quadratic equation?

STD. VI - exercise

Distributive property in multiplication.

(a + b + c). x = ax + bx + cx

quadratic equation

Solve for x:



  

quadratic equation

Solve for x:

6x^3/4 =  7x^1/4 - 2 x^-1/4

quadratic equation

Solve for x:

4^x - 9.2^x + 8 = 0

QUADRATIC EQUATION,

 Solve for x:

3x^1/2 - 8 = 3. x^-1/2)

Quadratic Equation

Solve for x:

3^2x+1 + 9 = 28. 3^x

quadratic equation

Solve for x:

3^2x+3 - 55 = 28(3^x- 2)

Quadratic equation

Solve for x:

6(6^x + 6^-x) = 27

 

Polynomial

Solve for x:

(x + 9)(x - 3)(x - 7)(x + 5) = 385

Polynomial

Solve for x:

2x⁴ – 13x³ + 24x² – 13x + 2 = 0

Polynomial

Solve for x:

6x⁴ – 35x³ + 62x² – 35x + 6 = 0

polynomial

Solve for: 
3x⁴ – 16x³ + 26x² – 16x + 3 = 0

Polynomial

Solve the polynomial:

-2x³ +17x - 3 = 0

Polynomial

Find the roots of the

 x³ - 5x² +10x - 8 = 0

x³ - 2x² - 2x - 3 = 0

Factorization

If 3 is one of the root of the equation x³ -49x + a = 0, find the other roots.

factorization

show that (x -1) is a common factor of x³ -3x +2 and x³ + 3x - 4. Find another common factor.

factorization

Factorize:

2x²(x+y) – y(x + y)²

Factorization

Tougher Factorization

x³ +x + 2

x³ +3x - 2

factorization

Tougher Factorization

(1 – 2x – x²)(1 – 2x – 3x²) + 4 x⁴,

-x³ – x² + x + 1

x⁴ – 5x² + 4

 

STD VI

Algebraic multiplications

logarithm

Solve for x:

Logarithm

Solve for x:

Logarithm

Solve for x: