Free Algebra 02 Practice Test - 6th grade

Question 1

The equation 5t - 4 = 1 is satisfied when the value of t = 1.

True

False

SOLUTION

Solution : A

In order to check whether the above equation 5t-4 =1 is satisfied for t =1, we simply put 1 in place of t, So substituting t = 1 in the equation , we get
LHS = 5 $\times$ (1) - 4 =1 and RHS = 1.
Since, LHS=RHS, t =1 satisfies the equation 5t-4 =1.

Question 2

The cost of two red balls and five blue balls is ₹160. Then the correct equation for this situation among the given options is _______.

$(r : price of one red ball)$
$(b : price of one blue ball)$

2 r + 5 b = ₹ 160

3 r + 5 b = ₹ 160

r + 5 b = ₹ 80

2 r - 5 b = ₹ 160

SOLUTION

Solution : A

Let the cost of one Red ball be $r$ .

Let the cost of one Blue ball be $b$ .

So, the algebraic equation will be $2 r + 5 b = ₹ 160$

Question 3

$(2 x^{2} + 3 x y + 4 x y^{2} + 5 z) is an algebraic expression.$

A. True

B. False

SOLUTION

Solution : A

2x², 3xy, 4xy²and 5z are terms and they are combined using the operator "+”.
Therefore, it is an algebraic expression.

Question 4

Tulika is 3 times as old as her cousin. The sum of their ages is 36 years. How old is Tulika?

A. 8 years

B. 9 years

C. 27 years

D. 32 years

SOLUTION

Solution : C

Let Tulika’s cousin's age be $x .$
Then Tulika’s age will be $3 x .$
Given that the sum of their ages is 36.
$∴ x + 3 x = 36$
$\Rightarrow 4 x = 36$
$\Rightarrow x = \frac{36}{4} = 9$

$\Rightarrow Tulika's age = 3 x = 3 \times 9 = 27 years.$

Question 5

Which of the following is/are algebraic expression/s?

A. 2

\times

8 + 9

B. 2

x

+ 3

\frac{21}{5}

+ 8

\frac{5}{x}

\times

SOLUTION

Solution : B and D

An algebraic expression should have numbers or constants, variables or unknowns (usually represented by alphabets) and mathematical operation like multiplication, addition etc.
Hence from the given option $2 x + 3$ and $\frac{5}{x} \times 12$ are algebraic expressions.

Question 6

Which of the given expressions represent/s the pattern 1, 4, 7, 10, 13..... ?

A. 3n+1

B. 3n+2

C. 3n-2

D. 3n

SOLUTION

Solution : A and C

On careful observation, you can see that each term in the pattern is one more than multiples of three.
Since the multiples of 3 can be represented by 3n, the pattern can be represented by 3n+1 (where n is 0, 1, 2...)
But each term can also be thought of two less than multiples of 3.
So, the pattern can also be represented by 3n-2 (where n is 1, 2, 3....)
Hence 3n + 1 and 3n -2 are the correct options.

Question 7

Raju's age is 5 more than twice of Ram's age. If Ram's age is represented by $x$ , then the expression which represents Raju's age is ________.

2 x

2 x

+ 5

5 x + 2

2 x - 5

SOLUTION

Solution : B

Given Ram's age is $x$ .
Twice of Ram's age is $2 x$ .
$∴$ 5 more than twice Ram's age is $2 x + 5$ which gives Raju's age.

Question 8

Which of the pairs given in options will add up to give (9x+5y)?

3 x + 2 y

2 x + 7 y

4 x + 4 y

5 x + y

3 x + 7 y

6 x - 2 y

3 x + 3 y

4 x + 7 y

SOLUTION

Solution : B and C

$3 x + 2 y$ + $2 x + 7 y$ = $5 x + 9 y$ $\neq 9 x + 5 y$
$4 x + 4 y$ + $5 x + y$ = $9 x + 5 y$ $= 9 x + 5 y$
$3 x + 7 y$ + $6 x - 2 y$ = $9 x + 5 y$ $= 9 x + 5 y$
$3 x + 3 y$ + $4 x + 7 y$ = $7 x + 10 y$ $\neq 9 x + 5 y$

Question 9

If $3 x - 2 = 13$ , then $x$ is

A. 2

B. 3

C. 4

D. 5

SOLUTION

Solution : D

$Given, 3 x - 2 = 13$
$\Rightarrow 3 x = 13 + 2$ [Transposing 2 to the other side]
$\Rightarrow 3 x = 15$
$\Rightarrow x = \frac{15}{3}$ [Transposing 3 to the other side]
$\Rightarrow x = 5$

Question 10

Solve the equation $\frac{5 x - 3}{12} = 1$ .

A. 2

B. 3

C. 4

D. -3

SOLUTION

Solution : B

$\frac{5 x - 3}{12} = 1 \Rightarrow 5 x - 3 = 1 \times 12 \Rightarrow 5 x - 3 = 12 \Rightarrow 5 x = 12 + 3 \Rightarrow 5 x = 15 \Rightarrow x = \frac{15}{5} \Rightarrow x = 3$

Free Algebra 02 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

Related ExamsBasic Geometrical Ideas 03Knowing Our Numbers 03Data Handling 03

Related Exams
Basic Geometrical Ideas 03
Knowing Our Numbers 03
Data Handling 03