10 Question MCQ (including Assertion)

Question 1 of 10

Which is the complete factorisation of \(x^{4}-y^{4}\)?

A \((x-y)(x+y)(x^{2}+y^{2})\) B \((x-y)^{2}(x+y)^{2}\) C \((x^{2}-y^{2})^{2}\) D \((x-y)(x^{3}+y^{3})\)

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Question 2 of 10

If \(x+\frac{1}{x}=3\), what is \(x^{2}+\frac{1}{x^{2}}\)?

A \(5\) B \(7\) C \(9\) D \(11\)

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Question 3 of 10

Which is the correct expansion of \((2x-y+3z)^{2}\)?

A \(4x^{2}+y^{2}+9z^{2}-4xy+12xz-6yz\) B \(4x^{2}+y^{2}+9z^{2}-2xy+6xz-3yz\) C \(4x^{2}-y^{2}+9z^{2}-4xy+12xz+6yz\) D \(4x^{2}+y^{2}+9z^{2}+4xy+12xz+6yz\)

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Question 4 of 10

What is the expansion of \((7x+4y)^{2}\)?

A \(49x^{2}+16y^{2}\) B \(49x^{2}+56xy+16y^{2}\) C \(49x^{2}+28xy+16y^{2}\) D \(14x^{2}+8y^{2}\)

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Question 5 of 10

What is \((-98)^{3}\)?

A \(-941,192\) B \(-960,392\) C \(941,192\) D \(-970,299\)

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Question 6 of 10

In 750 CE, Śhrīdharāchārya proposed a method. Using his identity \(a^{2}=(a+b)(a-b)+b^{2}\), evaluate \(55^{2}\).

A 3025 B 2525 C 3125 D 2925

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Question 7 of 10

A student tries to factor \(x^{2}+9x+20\) by splitting \(9x\) as \(2x+7x\). Why does this split fail?

A Because \(2+7\ne 9\) B Because \(2\times 7\ne 20\) C Because both numbers must be negative D Because the coefficient of \(x^{2}\) is \(1\)

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Question 8 of 10

What is the side of the cube whose volume is \(p^{3}+6p^{2}q+12pq^{2}+8q^{3}\)?

A \(p+4q\) B \(p+q\) C \(p+2q\) D \(2p+q\)

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Question 9 of 10

Why is \(n^{3}-n\) divisible by \(6\) for every natural number \(n\)?

A Because \(n^{3}-n=n(n-1)(n+1)\), a product of three consecutive integers. B Because every cube is divisible by \(6\). C Because \(n^{3}-n=(n-1)^{3}\). D Because \(n^{3}\) and \(n\) are always even.

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Question 10 of 10

Factorise \(27x^{3}+64y^{3}\).

A \((3x+4y)(9x^{2}-12xy+16y^{2})\) B \((3x-4y)(9x^{2}+12xy+16y^{2})\) C \((3x+4y)(9x^{2}+12xy+16y^{2})\) D \((27x+64y)(x^{2}-xy+y^{2})\)

Select one option. Answers are shown after the test.

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10 Question MCQ (including Assertion)