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× (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)
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 2r+5b=₹160
Question 3
(2x2+3xy+4xy2+5z) is an algebraic expression.
SOLUTION
Solution : A
2x2, 3xy, 4xy2 and 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?
SOLUTION
Solution : C
Let Tulika’s cousin's age be x.
Then Tulika’s age will be 3x.
Given that the sum of their ages is 36.
∴x+3x=36
⇒4x=36
⇒x=364=9
⇒Tulika's age=3x=3×9=27 years.
Question 5
Which of the following is/are algebraic expression/s?
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 2x+3 and 5x×12 are algebraic expressions.
Question 6
Which of the given expressions represent/s the pattern 1, 4, 7, 10, 13..... ?
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 ________.
SOLUTION
Solution : B
Given Ram's age is x.
Twice of Ram's age is 2x.
∴ 5 more than twice Ram's age is 2x+5 which gives Raju's age.
Question 8
Which of the pairs given in options will add up to give (9x+5y)?
SOLUTION
Solution : B and C
3x+2y + 2x+7y =5x+9y ≠9x+5y
4x+4y + 5x+y =9x+5y =9x+5y
3x+7y + 6x−2y =9x+5y =9x+5y
3x+3y + 4x+7y =7x+10y ≠9x+5y
Question 9
If 3x−2=13, then x is
SOLUTION
Solution : D
Given, 3x−2=13
⇒3x=13+2 [Transposing 2 to the other side]
⇒3x=15
⇒x=153 [Transposing 3 to the other side]
⇒x=5
Question 10
Solve the equation 5x−312=1.
SOLUTION
Solution : B
5x−312=1⇒5x−3=1×12⇒5x−3=12⇒5x=12+3⇒5x=15⇒x=155⇒x=3