Free Algebra 03 Practice Test - 6th grade

Question 1

Value of $2 x y$ when $x = 4$ and $y = 0$ is _________.

SOLUTION

Solution : A

$2 x y = 2 \times x \times y$

On substituting the values of $x$ and $y$ , we get

$2 x y = 2 \times 4 \times 0 = 8 \times 0 = 0$

Question 2

A number when multiplied by 2 and decreased by 41 gives 3. Find the number.

SOLUTION

Solution : C

Let the number be $x$ .
$∴ 2 x - 41 = 3 \Rightarrow 2 x = 44 \Rightarrow x = \frac{44}{2} = 22$

Question 3

The coefficient of term $x y^{2}$ in expression $4 x y^{2} + x^{3} - x^{5} + 2 x y^{2}$ is ______.

A. 4

B. 2

C. 3

D. 6

SOLUTION

Solution : D

Since $4 x y^{2}$ and $2 x y^{2}$ are like terms, the given expression can be written as follows.

$4 x y^{2} + x^{3} - x^{5} + 2 x y^{2} = 6 x y^{2} + x^{3} - x^{5}$
Therefore, the coefficient of $x y^{2}$ is 6.

Question 4

Which of the following is a variable?

A. Number of days in a week

B. 5

C. Temperature of a place in a day at different times

D. Number of months in a year

SOLUTION

Solution : C

The temperature of a place in a day at different times will be different. So it is a variable.

The number of days in a week and the number of months in a year always remain the same. So these are constants.

5 has a fixed value. So it is a constant.

Question 5

When $5$ is added to a number, we get $15$ . How do we represent this in the form of an equation in variable $x$ ?

$x = 15 + 5$

$x - 5 = 15$

$x + 15 = 5$

$x + 5 = 15$

SOLUTION

Solution : D

Let us take the number to be $x$ .
When $5$ is added to the number, we get $x + 5.$
Now, we know that when $5$ is added to that number, we get $15$ .
Hence, $x + 5 = 15$ .

Question 6

The variable in the expression $(9 x + 32) \div 9$ is ___.

SOLUTION

Solution : Variable is the unknown quantity which can have different values at different instances and they are usually represented by alphabets. In above expression, $x$ is the variable.

Question 7

Identify the binomial(s) among the given expressions.

A. 7x+8xy

B. 1+2x+3y

C. 3x+7xy+yx

D. 3x+2y

SOLUTION

Solution : A, C, and D

7x +8 xy has two unlike terms. So, it is a binomial.
1 + 2x +3y has three unlike terms. So, it is a trinomial.
3x + 7xy + yx = 3x + 8xy which has two unlike terms. So, it is a binomial.
3x + 2y has two unlike terms. So, it is a binomial.

Question 8

If the sum of successor and predecessor of a number is 14, then the number should be _____.

A. 6

B. 8

C. 7

D. 10

SOLUTION

Solution : C

Let the number be $x$ .
Therefore, the successor of number is $x$ + 1 and the predecessor is $x$ - 1.
Given that the sum of successor and predecessor is 14.
$∴ x + 1 + x - 1 = 14 \Rightarrow 2 x = 14 \Rightarrow x = \frac{14}{2} \Rightarrow x = 7$
So, the number should be 7.

Question 9

Solve for $x : \frac{x - 2}{3} = \frac{2 x}{7}$

-14

-7

SOLUTION

Solution : C

$\frac{x - 2}{3} = \frac{2 x}{7} \Rightarrow 7 \times (x - 2) = 3 \times 2 x \Rightarrow 7 x - 14 = 6 x \Rightarrow 7 x - 6 x = 14 \Rightarrow x = 14$

Question 10

If $\frac{2}{x + 10} = \frac{8}{x}$ , then the value of x is

$\frac{- 40}{3}$

-40

$\frac{40}{3}$

SOLUTION

Solution : A

$\frac{2}{x + 10} = \frac{8}{x} \Rightarrow 2 x = 8 \times (x + 10) \Rightarrow x = 4 \times (x + 10) \Rightarrow x = 4 x + 40 \Rightarrow - 40 = 4 x - x \Rightarrow - 40 = 3 x \Rightarrow x = \frac{- 40}{3}$

Free Algebra 03 Practice Test - 6th grade

Question 1

SOLUTION

Question 2

SOLUTION

Question 3

SOLUTION

Question 4

SOLUTION

Question 5

SOLUTION

Question 6

SOLUTION

Question 7

SOLUTION

Question 8

SOLUTION

Question 9

SOLUTION

Question 10

SOLUTION

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