Represent the numbers on the number line. -5/6
Answer: A number line is a pictorial representation of numbers on a straight line. It’s a reference for comparing and... View Article
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Saloni took a piece of burning charcoal and collected the gas evolved in a test tube. (a) How will she find the nature of the gas? (b) Write down word equations of all the reactions taking place in this process.
Answer: (a) In the test tube where the gas is collected, Saloni needs to add some water. She must cover... View Article
Should the handle and bristles of a tooth brush be made of the same material? Explain your answer
Answer: No, a toothbrush’s handle and bristles should be made of different materials. A toothbrush’s handle should be hard and... View Article
Show that: (3x + 7)2 – 84x = (3x – 7)2
Answer: (3x + 7)2 – 84x = (3x – 7)2 LHS = (3x + 7)2 – 84x RHS = (3x... View Article
Show that: (4pq + 3q)2 – (4pq – 3q)2 = 48pq2
Answer: (4pq + 3q)2 – (4pq – 3q)2 = 48pq2 LHS = (4pq + 3q)2 – (4pq – 3q)2 RHS... View Article
Show that: (9p – 5q)2 + 180pq = (9p + 5q)2
Answer: (9p – 5q)2+ 180pq = (9p + 5q)2 LHS = (9p – 5q)2+ 180pq RHS = (9p + 5q)2... View Article
Show that: (a – b)(a + b) + (b – c)(b + c) + (c – a) (c + a) = 0
Answer: (a – b)(a + b) + (b – c)(b + c) + (c – a)(c + a) = 0... View Article
Show that: cos 38° cos 52° – sin 38° sin 52° = 0
Answer: cos 38° × cos 52° – sin 38° × sin 52° = 0 Consider LHS LHS = cos 38°... View Article
Show that: tan 48° tan 23° tan 42° tan 67° = 1
Answer: tan 48° × tan 23° × tan 42° × tan 67° = 1 Consider LHS LHS = tan 48°... View Article
Simplify 3x (4x – 5) + 3 and find its values for (i) x = 3 (ii) x = 1/2
Answer: 3x (4x – 5) + 3 3x (4x – 5) + 3 = (3x × 4x) – (3x ×... View Article
Simplify a (a3 + a + 1) + 5 and find its value for (i) a = 0, (ii) a = 1 (iii) a = -1.
Answer: a (a2 + a + 1) + 5 ⇒ (a × a2)+ (a × a) + (a + 1)... View Article
Simplify: (1.5x – 4y)(1.5x + 4y + 3) – 4.5x + 12y
Answer: 2.25x2 – 16y2 (1.5x – 4y)(1.5x + 4y + 3) – 4.5x + 12y Consider (1.5x – 4y)(1.5x +... View Article
Simplify: (2.5p – 1.5q)2 – (1.5p – 2.5q)2
Answer: 4p2 – 4q2 Using the identities (a + b) 2 = a2 + b2 + 2ab (a – b)... View Article
Simplify: (2x + 5)2 – (2x – 5)2
Answer: 40x Using the identities (a + b) 2 = a2 + b2 + 2ab (a – b) 2 =... View Article
Simplify: (4m + 5n)2 + (5m + 4n)2
Answer: 41m2 + 41n2 + 80mn Using the identities (a + b) 2 = a2 + b2 + 2ab (a... View Article
Simplify: (7m – 8n)2 + (7m + 8n)2
Answer: 98m2 + 128n2 Using the identities (a + b) 2 = a2 + b2 + 2ab (a – b)... View Article
Simplify: (a + b + c)(a + b – c)
Answer: a2 + b2 – c2 + 2ab (a + b + c)(a + b – c) (a + b... View Article
Simplify: (a + b) (c – d) + (a – b) (c + d) + 2 (ac + bd)
Answer: 4ac (a + b) (c – d) + (a – b) (c + d) + 2 (ac + bd)... View Article
Simplify: (a2 – b2)2
Answer: a4 + b4 – 2a2b2 Using the identity (a – b) 2 = a2 + b2 – 2ab (a2... View Article
Simplify: (a2 + 5) (b3 + 3) + 5
Answer: a2b3 + 5b3 + 3a2 + 20 (a2 + 5)(b3+ 3) + 5 (a2 + 5)(b3+ 3) (a2 +... View Article
