Mathematics carries the highest weight in AISSEE — 150 of 300 marks in Class 6 and 200 of 400 marks in Class 9 — and it is also a key section of the RMS CET. Practise these 10 MCQs on Algebraic Identities and Factorisation, then check your answers and step-by-step solutions in the answer key at the end.
Quick facts: AISSEE 2027 will be held on Sunday, 31 January 2027. There is no negative marking, so attempt every question. Online applications are open until 2 December 2026 on exams.nta.nic.in/sainik-school-society.
Practice Questions
Q1. Using (a + b)² = a² + 2ab + b², expand (x + 8)².
(A) x² + 64
(B) x² + 16x + 64
(C) x² + 8x + 64
(D) x² + 16x + 16
Q2. Using an algebraic identity, find 102².
(A) 10504
(B) 10403
(C) 10506
(D) 10404
Q3. Find the value of 105² − 95² using an identity.
(A) 2000
(B) 100
(C) 2100
(D) 4000
Q4. Factorise: x² + 7x + 10
(A) (x + 5)(x + 2)
(B) (x + 7)(x + 1)
(C) (x − 5)(x − 2)
(D) (x + 10)(x + 1)
Q5. Using an identity, find 49².
(A) 2411
(B) 2352
(C) 2402
(D) 2401
Q6. Factorise: x² + 8x + 7
(A) (x + 8)(x + 1)
(B) (x − 1)(x − 7)
(C) (x + 1)(x + 7)
(D) (x + 4)(x + 4)
Q7. Using (a + b)² = a² + 2ab + b², expand (x + 7)².
(A) x² + 49
(B) x² + 14x + 49
(C) x² + 7x + 49
(D) x² + 14x + 14
Q8. Factorise: x² + 12x + 35
(A) (x + 12)(x + 1)
(B) (x − 5)(x − 7)
(C) (x + 5)(x + 7)
(D) (x + 35)(x + 1)
Q9. Using (a + b)² = a² + 2ab + b², expand (x + 5)².
(A) x² + 10x + 25
(B) x² + 25
(C) x² + 5x + 25
(D) x² + 10x + 10
Q10. Using an algebraic identity, find 103².
(A) 10709
(B) 10608
(C) 10609
(D) 10712
Answer Key with Explanations
(B) x² + 16x + 64 — (x + 8)² = x² + 2·x·8 + 8² = x² + 16x + 64.
(D) 10404 — (100 + 2)² = 10000 + 400 + 4 = 10404.
(A) 2000 — a² − b² = (a + b)(a − b) = 200 × 10 = 2000.
(A) (x + 5)(x + 2) — Find two numbers whose sum is 7 and product is 10: 5 and 2.
(D) 2401 — (50 − 1)² = 2500 − 100 + 1 = 2401.
(C) (x + 1)(x + 7) — Find two numbers whose sum is 8 and product is 7: 1 and 7.
(B) x² + 14x + 49 — (x + 7)² = x² + 2·x·7 + 7² = x² + 14x + 49.
(C) (x + 5)(x + 7) — Find two numbers whose sum is 12 and product is 35: 5 and 7.
(A) x² + 10x + 25 — (x + 5)² = x² + 2·x·5 + 5² = x² + 10x + 25.
(C) 10609 — (100 + 3)² = 10000 + 600 + 9 = 10609.
How did you score?
9–10 correct: excellent — move on to a full-length mock test. 6–8: good — revise the explanations of the questions you missed. Below 6: study this topic again from your NCERT book and retry these questions after two days.
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