Math problems and answers will help you to find solutions based on math problems of all grades. We engage  you to practice the topics in your curriculum. We also provide with the answers of this questions.  These solutions are step by step and detailed. So if you are stuck at any point, you can refer to the answers and get it cleared.

How to Find Answers to Math Problems

Few of the topics we cover are given below
  1. Linear equations
  2. Simultaneous equations
  3. Quadratic equations
  4. Binomial Theorem
  5. Function
  6. Exponential and Logarithmic equations
  7. Graphing functions
  8. Quadratic functions
  9. Third degree polynomials
  10. Radical equations
  11. Trigonometry
  12. Geometry
  13. Progressions
Following are some of the problems in the worksheets with answers

Solved Problems: -
Example 1: -
If A + B = 450, Prove that (1+ tan A)(1+ tan B) = 2.

Solution: -
Given A + B = 45
Then tan (A + B) = tan 45 = 1
We know that
That is = 1
Cross multiplying, we get
tan A + tan B = 1 - tan A tan B
Therefore tan A + tan B + tan A tan B = 1
Adding 1 on both sides, we get
1 + tan A + tan B + tan A tan B = 2
Grouping the first two and last two terms, we get
(1+ tan A) + tan B ( 1 + tan A) =2
Taking 1 + tan A common, we get
(1+ tan A) ( 1+ tan B) =2
Hence Proved.

Example 2: -

Find the equation of the circle passing through (0, 5) and (2, 1) and has its center on the line x + y = 1

Solution: -

Let the required equation of the circle be x2+ y2 + 2gx + 2fy + c = 0...(1)
Since (1) passes through (0,5) and (2,1), we get
25 + 10f + c = 0 and 4 + 1 + 4g + 2f  + c  =0
That is 10f + c = -25...(2)
4g +2f + c = -5...(3)
Since the centre (-g, -f) lies on x+ y =1, -g - f =1...(4)
Now we solve the three equations.  For this,
subtract (2) from (3)
4g - 8f = 20...(5)
Dividing equation (5) by 4 we get
g - 2f = 5...(6)
Adding (4) and (6), we get
-3f = 6
f = -2
substituting in (6), we get
g - 2(-2) = 5
g + 4 = 5
g = 1
Substituting  f in (2), we get
10(-2) + c = -25
-20 + c = -25
c = -5
Therefore the required equation is x2+ y2 + 2x -4y - 5 = 0

Example 3: -
The sum of 3 terms in Geometric Progression is 21 and their product is  216.  Find the terms.

Solution: -

Let the three terms of the Geometric Progression be a/r, a , ar
Given sum of 3 terms in Geometric Progression is 21
That is a/r + a + ar = 21...(1)
Also their product is  216
So a/r x a x ar = 216
a3 = 216
That is a = 6
Substituting in (1) we get
6/r + 6 + 6r = 21
That is 6/r + 6r = 15
(6+ 6r2)/r = 15
Cross multiplying
6r2 + 6 = 15 r
Subtracting 15r on both sides, we get
6r2 -15r + 6 = 0
Dividing the whole equation by 3, we get
2r2 - 5r + 2 = 0
We split the mid term
we get2r2 - 4r - r + 2 = 0
2r (r - 2) -(r - 2) = 0
(2r - 1)(r - 2) = 0
r = 1/2 or 2
when r = 1/2 and a = 6, the terms in Geometric Progression are 3, 6 and 12
when r = 2 and a = 6, the terms in Geometric Progression are 12, 6 and 3