Students of class 10 can take 10th Grade Math help offered by TutorVista to make their learning method easier. This online learning help is organized under the guidance of subject experts. Hence, these are worthy for students. This 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. They can take homework help, as well.

- Algebra
- Liner Algebra
- Calculus
- Trigonometry
- Geometry
- Statistics

Few problems based on 10th grade math are given below:

### Solved Examples

**Question 1: **Aline is 10 years older than Alica. 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:

=> x + 12 + x + 22 = 40

=> 2x + 34 = 40

=> 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

=> n = 2m - 2

Substitute this solution for n in equation (1)

=> 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 * 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 system by elimination method. 5x - y - 1 = 0 and 2x + 3y = 31 (Answer: x = 2 and y = 9.)

Geometry is an imperative part of Maths. It is related to size, shape, volume, area and others. This topic is added in the class 10 Math syllabus in a requisite manner. Moreover, students should learn this topic thoroughly as they can score well in this topic. However, online geometry help is worthy for students and students can opt for this learning help as per their convenience. Additionally, through this learning process, students can understand each geometric concept in a systematic manner.

Few problems based on geometry are given below:

### Solved Examples

**Question 1: **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$^2$.

**Question 2: **Find the missing angles x , y and z in the following figure.

** Solution: **

As the pair 58$^o$, y and x, z are alternate interior angles, they are equal in measure.

So, y = 58$^o$

58$^o$ + x = 180$^o$ (Linear pair)

x = 180$^o$ - 58$^o$

= 122$^o$

Since x and z are alternate interior angles, they are equal in measure

So, z = 122$^o$.

Check tough Geometry problems by opting for 10th grade Geometry practice offered by TutorVista. It is quite useful for students as through this option, students can understand different problems that might come 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:

=> x + 12 + x + 22 = 40

=> 2x + 34 = 40

=> 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

=> n = 2m - 2

Substitute this solution for n in equation (1)

=> 5m + 2(2m - 2) = 14

Solve for m

5m + 4m - 4 = 14

9m = 18

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

Step 2:

2 * 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$^2$.

As the pair 58$^o$, y and x, z are alternate interior angles, they are equal in measure.

So, y = 58$^o$

58$^o$ + x = 180$^o$ (Linear pair)

x = 180$^o$ - 58$^o$

= 122$^o$

Since x and z are alternate interior angles, they are equal in measure

So, z = 122$^o$.

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