Topical Revision Worksheet 1 Algebra, Surds, Indices Student Version

Adapted from HCI Resources 1 Hwa Chong Institution Integrated Programme Secondary Three Mathematics Name: _______________________________ ( ) Class: _________ Date: _____________ Topical Revision Worksheet 1 _________________________________________________________________________________ Topic: Algebraic manipulation, Surds and Indices (including Exponential Equations) Question 1 [2008 EOY, Q1] marks Express in the form , where a and b are real numbers. Answer: [2] Question 2 [2008 EOY, Q2] marks Evaluate without a calculator, leaving your answer as a fraction in its simplest form. Answer: [2] Question 3 [2009 EOY, Q2] marks Express in the form where a, b and c are rational numbers. Answer: [3] Question 4 [2010 EOY, Q1] marks (a) Simplify . Answer: 5 [2] (b) A triangle has an area of units 2 and the length of its base is unit. Find its height in the form units, where a, b, c and d are integers. Answer: units [3] Question 5 [2010 EOY, Q2] marks Solve for x when . Answer: No solution [3]

Adapted from HCI Resources 2 Question 6 [2010 EOY, Q3] marks (a) Make h the subject of the formula . Answer: [2] (b) Simplify . Answer: or [3] Question 7 [2011 EOY, Q1] marks Without using a calculator, simplify . Answer: –3 [3] Question 8 [2011 EOY, Q3] marks (i) Show that . [1] (ii) Hence simplify . Answer: [4] Question 9 [2012 EOY, Q2] marks Without using a calculator, simplify . Answer: [4] Question 10 [2012 EOY, Q10 a, b] marks (a) Factorise completely Answer: [2] (b) Given that , express x in terms of p and q. Answer: [2]

Adapted from HCI Resources 3 Question 11 [2013 EOY, Q1 a, b] marks (a) Find the product of and and simplify the answer. Answer: [2] (b) If , simplify . Answer: [3] Question 12 [2013 EOY, Q6] marks (a) Simplify . Answer: 0 [3] (b) Simplify . Answer: [3] Question 13 [2014 EOY, Q1] marks (a) Factorise completely . Answer: [3] (b) Simplify . Answer: [3] Question 14 [2014 EOY, Q2] marks The area of a rectangle ABCD is given by m 2, and the length of side AB is m. Find, without using a calculator, the length of side BC in the form of m, where a and b are real numbers. Answer: [4]

Adapted from HCI Resources 4 Question 15 [2015 EOY, Q3] marks (a) Make p the subject of the formula if . Answer: [3] (b) Simplify into a single fraction . Answer: [4] Question 16 [2015 EOY, Q4] marks (a) Given that and that , find the value of . Answer: [3] (b) Using a suitable substitution, or otherwise, solve for x if . Answer: [4]