Free Algebra Subjective Test 02 Practice Test - 6th grade

Question 1

Write the given statement in algebraic form "28 more than twice of $x$ is equal to 45." [1 MARK]

SOLUTION

Solution : Solution: 1 Mark

The algebraic form of the given statement is $2 x + 28 = 45$

Question 2

Subtract: [2 MARKS]

(i) $3 a - 4 b + 5 c$ from $4 a - b + 6 c$

(ii) $5 a - 3 b + 2 c$ from $a - 4 b - 2 c$

SOLUTION

Solution : Solution: 1 Mark each

(i) $(4 a - b + 6 c) - (3 a - 4 b + 5 c)$
= $4 a - b + 6 c - 3 a + 4 b - 5 c$
= $4 a - 3 a - b + 4 b + 6 c - 5 c$
= $a + 3 b + c$

(ii) $(a - 4 b - 2 c) - (5 a - 3 b + 2 c)$
= $a - 4 b - 2 c - 5 a + 3 b - 2 c$
= $a - 5 a - 4 b + 3 b - 2 c - 2 c$
= $- 4 a - b - 4 c$

Question 3

Kimmy went to play with her friends. If Kimmy rolls a die, say 13 times, her score will be the addition of all the numbers appearing on the die each time. Kimmy got 'a' 2 times, 'b' 5 times and 'd' 6 times. What is the total score of Kimmy? [2 MARKS]

SOLUTION

Solution :
Concept: 1 Mark
Solution: 1 Mark

Total score of Kimmy $= 2 a + 5 b + 6 d$

Question 4

A number is decreased by 15 and the new number so obtained is multiplied by 3; the result is 81. Find the number. [3 MARKS]

SOLUTION

Solution : Equation: 1 Mark
Steps: 1 Mark
Answer: 1 Mark

Let the number be $x$ .

The number decreased by 15 $\Rightarrow (x - 15)$

The number so obtained is multip[lied by 3 $\Rightarrow 3 \times (x - 15)$

Given: $3 (x - 15) = 81 \Rightarrow 3 x - 45 = 81$

$\Rightarrow 3 x = 81 + 45$

$\Rightarrow x = \frac{126}{3} = 42$

$∴$ The required number = $42$

Question 5

Find the value of 'x'. [3 MARKS]

(i) $4 x + 5 = 25$

(ii) $x - 2 \frac{1}{3} = 5 \frac{1}{2}$

(iii) $(7 x + 8) \div 7 = 8$

SOLUTION

Solution :
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 6

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]

SOLUTION

Solution : $6^{t h}$ : 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 7

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) $y^{x}$

SOLUTION

Solution : 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 8

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.

SOLUTION

Solution : 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, $\frac{x}{5} = x - 5$

(c) Let the number be x

Two-third of number $= \frac{2 x}{3}$

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 9

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]

SOLUTION

Solution : 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 10

(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]

SOLUTION

Solution :
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,
$B = \frac{L + 4}{3}$

Free Algebra Subjective Test 02 Practice Test - 6th grade

Question 1

SOLUTION

Question 2

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Question 3

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Question 4

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Question 5

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Question 6

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Question 7

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Question 8

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Question 9

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Question 10

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