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This mock test of Olympiad Test: Algebraic Expressions - 1 for Class 7 helps you for every Class 7 entrance exam.
This contains 20 Multiple Choice Questions for Class 7 Olympiad Test: Algebraic Expressions - 1 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Which expression is obtained when 2x^{2} – 5x + 7 subtracted from 5x^{2} – 2x + 6?

Solution:

5x^{2} – 2x + 6 – (2x^{2} – 5x + 7)

= 5x^{2} – 2x + 6 – 2x^{2} + 5x – 7

= 3x^{2 }+ 3x – 1

QUESTION: 2

What is the sum of 5x – 2x^{2} + 3, 3x^{2} – 2x + 7 and 4x^{2} – 5x – 6 ?

Solution:

(5x – 2x^{2} + 3) + (3x^{2} – 2x + 7) + (4x^{2} – 5x – 6)

= (5x – 2x –5x) + (–2x^{2} + 3x^{2} + 4x^{2}) + (3 + 7 – 6)

= –2x + 5x^{2} + 4 = 5x^{2} – 2x + 4

QUESTION: 3

What is the result when x^{2} – xy + y2 subtracted from 2xy – 3y^{2} + 2x^{2} ?

Solution:

(2xy – 3y^{2} + 2x^{2}) – (x^{2} – xy + y^{2})

= 2xy – 3y^{2} + 2x^{2} – x^{2} + xy – y^{2}

= x^{2} + 3xy – 4y^{2}

QUESTION: 4

Find the expression if the sum of 6a – 5a^{2} + 7 and –7a – 8 + 7a^{2} is subtracted from –5.

Solution:

–5 – [(6a + 5a^{2} + 7) + (–7a – 8 + 7a^{2})]

= –5 – [5a^{2} +6a + 7 + 7a^{2}– 7a – 8]

= –5 – [12a^{2} – a – 1] = –5 – 12a^{2} + a + 1

= –12a^{2} + a – 4

QUESTION: 5

What is obtained after simplification of the expression [7 – 2x + 3y –{2x – y}] – (4x + 7y – 5)?

Solution:

[7 – 2x + 3y – {2x – y}] – (4x + 7y – 5)

= 7 – 2x + 3y – 2x + y – 4x – 7y – 5

= –8x – 3y + 12

QUESTION: 6

What is the product of –3m^{2}np, 1/3nm^{3}p^{2} and 2/3m^{2}n^{2}p^{2}?

Solution:

QUESTION: 7

What is the product of – xyz^{2}, –2yx^{2}z and 1/3x^{3}yz?

Solution:

QUESTION: 8

5 – (3x + 2y) – 3(x – y) + 7x + y =?

Solution:

5 –(3x + 2y) –3(x – y) + 7x + y

= 5 – 3x – 2y – 3x + 3y + 7x + y

= 5 + x + 2y

QUESTION: 9

Find the product of the sum of 3x^{2} + 5y^{2} and x^{2} – 4y^{2} and the difference of (x^{2} – y^{2}) and 2x^{2} + 3y^{2}.

Solution:

Sum = (3x^{2 }+ 5y^{2}) + (x^{2}– 4y^{2}) = 4x^{2} + y^{2}

Difference = (2x^{2} + 3y^{2}) –(x^{2} –y^{2})

= 2x^{2} + 3y^{2} –x^{2} + y^{2}

= x^{2} + 4y^{2}

Product = (4x^{2} + y^{2}) (x^{2} + 4y^{2})

= 4x^{4} + 16x^{2}y^{2} + x^{2}y^{2} + 4y^{4}

= 4x^{4 }+ 17x^{2}y^{2} + 4y^{4}

QUESTION: 10

Find the value of (2.3a^{5}b^{2}) × (1.2a^{2}b^{2}) when a = 1 and b = 0.5.

Solution:

(2.3 a^{5}b^{2}) × (1.2a^{2} – b^{2})

= 2.3 × 1.2 a^{7}b^{4}

= 2.76 × (1)^{7} × (0.5)^{4}

= 2.76 × 0.25 × 0.25 = 0.1725

QUESTION: 11

Find the value of (2.6 m^{2}n) × (5mn^{2}) when m = 1/2 and n = 1/3.

Solution:

(2.6 m^{2}n) × (5 mn^{2})

= 2.6 × 5 × m^{2}× m × n × n^{2}

QUESTION: 12

Find the product of ab^{2}c, – a^{2}bc^{2}, –abc^{3} and –a^{2}bc.

Solution:

(ab^{2}c) (–a^{2}bc^{2}) (–abc^{3}) (–a^{2}bc)

= –a × a^{2} × a × a^{2} × b^{2} × b × b × b × c× c^{2} × c^{3} × c

= –a^{6}b^{5}c^{7}

QUESTION: 13

What is obtained when is multiplied by

Solution:

QUESTION: 14

Find the numerical value of the product 3s(s^{2} – st) when s = 2 and t = 5.

Solution:

3s(s^{2}– st)

= 3s^{3} – 3s^{2}t

= 3(2)^{3} – 3(2)^{2}×5

= 3×8 – 3×4×5

= 24 – 60 = –36

QUESTION: 15

What is the simplified value of a(b – c) + b(c – a) + c(a – b)?

Solution:

a(b – c) + b(c – a) + c(a – b)

= ab – ac + bc – ab + ac – bc = 0

QUESTION: 16

Simplify a(b – 2c) + 2b(c – 2a) + c(3a – 2b).

Solution:

a(b – 2c) + 2b(c – 2a) + c(3a – 2b)

= ab – 2ac + 2bc – 4ab + 3ac – 2bc

= ac – 3ab

QUESTION: 17

What is the product of –3x^{2}y^{2}z^{2} and –5xy^{2}z

Solution:

(–3x^{2}y^{2}z^{2}) (–5xy^{2}z)

= (–3)(–5)x^{3}y^{4}z^{3}

= 15x^{3}y^{4}z^{3}

QUESTION: 18

Find the simplest expression of a(b – c) – b(c – 2a) – c(2a – b)

Solution:

a(b – c) –b(c – 2a) – c(2a – b)

= ab – ac – bc + 2ab – 2ac + bc

= 3ab – 3ac = 3(ab – ac)

QUESTION: 19

What is product of

Solution:

QUESTION: 20

What is the product of (x^{3} + y^{3}) and (x^{2} – y^{2})?

Solution:

(x^{3} + y^{3}) (x^{2}– y^{2})

= (x^{3}) (x^{2}) – (x^{3}) (y^{2}) + (y^{3}) (x^{2}) – (y^{3})(y^{2})

= x^{5} – x^{3}y^{2 }+ x^{2}y^{3} – y^{5}

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