10th Grade students can take Math help offered by TutorVista to make their learning method easier. This online learning help is prepared under the guidance of subject experts thus helping students. The online learning help covers all essential topics, which are added in the class 10 Math syllabus. Geometry, algebra, calculus, precalculus, statistics and trigonometry are some important Math topics of Class 10 and students should understand these thoroughly to score well in exams. However, students can choose online Math help to brush up their subject knowledge before exams. Students can also take homework help and solve tough Math problems immediately with our expert virtual tutors and enhance the understanding.

- Algebra
- Liner Algebra
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Few problems based on 10th Grade math are given below:

### Solved Examples

**Question 1: **Aline is 10 years older than Alice. In 12 years, the sum of their ages will be 40. How old are Aline and Alice now ?

** Solution: **

Let Alica's age be represented with x and Aline's age represented with x + 10.

In 12 years:

Add 12 to both ages

Alica's age = x + 12 and Aline's age = (x + 10) + 12 = x + 22

The sum of their ages in 12 years will be 40, so the equation is as follows:

$\Rightarrow$ x + 12 + x + 22 = 40

$\Rightarrow$ 2x + 34 = 40

$\Rightarrow$ 2x = 40 - 34 = 6

or x = $\frac{6}{2}$ = 3

So Alica is 3, and Aline is 13 (i.e. 3 + 10).

**Question 2: **Solve the system of linear equation 5m + 2n = 14 and 2m - n = 2.

** Solution: **

Given: 5m + 2n = 14 ..........(1)

2m - n = 2 ..............(2)

Use the**substitution method** to solve the given system

Step 1: Solve the second equation for n

$\Rightarrow$ n = 2m - 2

Substitute this solution for n in equation (1)

$\Rightarrow$ 5m + 2(2m - 2) = 14

Solve for m

5m + 4m - 4 = 14

9m = 18

or m = $\frac{18}{9}$ = 2

Step 2: Again substitute this solution for m in equation (2)

2 $\times$ 2 - n = 2

4 - n = 2

n = 2

The solution for the given system is (2, 2).

Online 10th grade Math practice is quite useful for students as by using this learning option, students can clear their doubts and understand each Math concept in a right manner.

Some practice problems of 10th grade Math are given below:

### Practice Problems

**Question 1: **Jastin's age is four years more than thrice Salina's age. Two years ago,
the sum of their ages was 24. How old is Salina right now? (Answer: 6 years)

**Question 2: **Solve the problem by elimination method. 5x - y - 1 = 0 and 2x + 3y = 31 (Answer: x = 2 and y = 9.)

Geometry is a part of Mathematics, a subject about shapes and symbols. Geometry is related to size,shape, volume, area and lots more. The topic is added in Class 10 Math syllabus in order to apply the concepts of geometry and learn the topic thoroughly so as to score well in the topic. Online geometry help is useful for students as they can opt for the learning help as per their convenience. Through this learning process, students can understand each geometric concept efficiently.

Few problems based on geometry are given below:

### Solved Example

**Question: **Find the area of segment of a circle whose angle is 130$^o$ and its radius is 10 cm.

** Solution: **

Given that the angle is 130$^o$ and its radius is 10 cm.

The formula to find the area of segment of a circle is $\frac{r^2}{2}$ $((\frac{\pi}{180^o})$ $\theta$ - sin $\theta)$

Substitute the given values in the formula

= $\frac{r^2}{2}$ $((\frac{\pi}{180^o})$ $\theta$ - sin $\theta)$

= $\frac{10^2}{2}$ $((\frac{\pi}{180^o})$ $\times$ 130$^o$ - sin 130$^o$)

= 75.1 cm$^2$.

Students can check difficult Geometry problems by opting for 10th Grade Geometry practice offered by TutorVista. It is useful for students, through this option students can understand different problems that might appear in exams. ### Practice Problems

**Question 1: **Find the volume of a cuboid whose length = 4 m and height = 6 m and width = 3m?

**Question 2: **Prove that Cose $\theta$ = $\frac{Cot \theta}{Cos \theta}$

Let Alica's age be represented with x and Aline's age represented with x + 10.

In 12 years:

Add 12 to both ages

Alica's age = x + 12 and Aline's age = (x + 10) + 12 = x + 22

The sum of their ages in 12 years will be 40, so the equation is as follows:

$\Rightarrow$ x + 12 + x + 22 = 40

$\Rightarrow$ 2x + 34 = 40

$\Rightarrow$ 2x = 40 - 34 = 6

or x = $\frac{6}{2}$ = 3

So Alica is 3, and Aline is 13 (i.e. 3 + 10).

Given: 5m + 2n = 14 ..........(1)

2m - n = 2 ..............(2)

Use the

Step 1

$\Rightarrow$ n = 2m - 2

Substitute this solution for n in equation (1)

$\Rightarrow$ 5m + 2(2m - 2) = 14

Solve for m

5m + 4m - 4 = 14

9m = 18

or m = $\frac{18}{9}$ = 2

Step 2:

2 $\times$ 2 - n = 2

4 - n = 2

n = 2

The solution for the given system is (2, 2).

Some practice problems of 10th grade Math are given below:

Few problems based on geometry are given below:

Given that the angle is 130$^o$ and its radius is 10 cm.

The formula to find the area of segment of a circle is $\frac{r^2}{2}$ $((\frac{\pi}{180^o})$ $\theta$ - sin $\theta)$

Substitute the given values in the formula

= $\frac{r^2}{2}$ $((\frac{\pi}{180^o})$ $\theta$ - sin $\theta)$

= $\frac{10^2}{2}$ $((\frac{\pi}{180^o})$ $\times$ 130$^o$ - sin 130$^o$)

= 75.1 cm$^2$.

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