Algebra(6th Grade > Mathematics ) Questions and answers for exam Preparation

6th Grade > Mathematics

ALGEBRA MCQs

Total Questions : 96 | Page 10 of 10 pages

Find the value of 'x'. [3 MARKS]
(i) $4 x + 5 = 25$
(ii) $x - 2 \frac{1}{3} = 5 \frac{1}{2}$
(iii) $(7 x + 8) \div 7 = 8$

Discuss Question

Answer: Option A. ->
:

Each Option: 1 Mark
(i) $4 x + 5 = 25$
$\Rightarrow 4 x = 25 - 5$
$\Rightarrow 4 x = 20$
Divide by 4 on both sides,
$4 x \div 4 = 20 \div 4$
$x = 5$
(ii) $x - 2 \frac{1}{3} = 5 \frac{1}{2}$
   $\Rightarrow x - \frac{7}{3} = \frac{11}{2}$ (Taking LCM of 1 and 3 )
   $\Rightarrow \frac{3 x - 7}{3} = \frac{11}{2}$
   $\Rightarrow 3 x = \frac{11}{2} \times 3 + 7$
   $\Rightarrow 3 x = \frac{33 + 14}{2} = \frac{47}{2}$
   $\Rightarrow x = \frac{47}{6} = 7 \frac{5}{6} = 7.833$
(iii) $(7 x + 8) \div 7 = 8$
$\Rightarrow \frac{7 x + 8}{7} = 8$
$\Rightarrow 7 x = 8 \times 7 - 8 = 56 - 8 = 48$
$\Rightarrow x = \frac{48}{7} = 6 \frac{6}{7} = 6.86$

Question 92.

If $x = 2, y = 5 a n d z = 4$ Find the value of: [4 MARKS]
(i) $\frac{x}{2 x^{2}}$
(ii) $\frac{x z}{y z}$
(iii) $z^{x}$
(iv) $y^{x}$

Discuss Question

Answer: Option A. ->
:
Each option: 1 Mark
(i)

\frac{x}{2 x^{2}} = \frac{1}{2 x} = \frac{1}{2 (2)} = \frac{1}{4}

(ii)

\frac{x z}{y z} = \frac{x}{y} = \frac{2}{5}

(iii)

z^{x} = 4^{2} = 16

(iv)

y^{x} = 5^{2} = 25

Question 93.

The $n^{t h}$ term in a pattern is $2 n^{2} + 5$ . What is the difference between $6^{t h}$ and $4^{t h}$ terms in the pattern? [3 MARKS]

Discuss Question

Answer: Option A. ->
:

6^{t h}

: 1 Mark

4^{t h}

: 1 Mark
Answer: 1 Mark
Given that,

n^{t h}

term is

2 n^{2} + 5

Therefore,

6^{t h} t e r m = 2 \times 6^{2} + 5

2 \times 36 + 5 = 77

4^{t h} t e r m = 2 \times 4^{2} + 5

2 \times 16 + 5 = 32 + 5 = 37

Difference

= 77 - 37 = 40.

Question 94.

Translate each of the following statements into an equation, using x as the variable: [4 MARKS]
a) 13 subtracted from twice a number gives 3.
b) One fifth of a number is 5 less than that number.
c) Two-third of number is 12.
d) 9 added to twice a number gives 13.

Discuss Question

Answer: Option A. ->
:
Each option: 1 Mark
(a) Let the number be x
Twice of number =2x
According to question,

2 x - 13 = 3

(b) Let the number be x
One-fifth of number

= \frac{x}{5}

According to question,

\frac{x}{5} = x - 5

= \frac{2 x}{3}

According to question,

\frac{2 x}{3} = 12

(d) Let the number be x
Twice a number =2x
According to question,

2 x + 9 = 13

Question 95.

The income of a man A is twice the income of B. The income of B is thrice of that of C. Given that the sum of income of A, B and C is ₹72000, find the income of A, B and C? [4 MARKS]

Discuss Question

Answer: Option A. ->
:
A's Income: 1 Mark
B's Income: 1 Mark
C's Income: 1 Mark
Steps: 1 Mark
Let the income of C = ₹ x
Income of B = ₹ 3x
Income of A = twice of income of B = 2(₹ 3x) = ₹ 6x
Sum of their income

\Rightarrow 10 x = 72000 \Rightarrow x = ₹ 7200

Income of C
= ₹ x = ₹ 7200
Income of A

= ₹ 6 x = ₹ 6 \times 7200 = ₹ 43200

Income of B

= ₹ 3 x = ₹ 3 \times 7200 = ₹ 21600

Question 96.

(i) Given that a printer prints 5 pages less in the second minute to what it prints in the first minute. Given that it prints 77 pages in two minutes, how many pages does it print in the first minute?
(ii) The length of a rectangle is 4 metres less than three times the breadth of the rectangle. Express the breadth in terms of length. [4 MARKS]

Discuss Question

Answer: Option A. ->
:

Each option: 2 Marks
(i) Let the number of pages printed in first minute $= x$
Number of pages printed in the second minute $= x - 5$
Total number of pages printed in the first two minutes $= x + x - 5$
$\Rightarrow 2 x - 5 = 77$
$\Rightarrow 2 x = 77 + 5$
$\Rightarrow 2 x = 82$
$\Rightarrow x = 41$
(ii) Let L and B be length and breadth of the rectangle respectively
Given L = 3B - 4
Adding 4 to both sides
L+4 =3B -4 + 4
L + 4 = 3B
Dividing both sides by 3, we get,
$B = \frac{L + 4}{3}$