Topical Revision Worksheet 1 Algebra, Surds, Indices Solution (LX)

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. Solution: [2] Question 2 [2008 EOY, Q2] marks Evaluate without a calculator, leaving your answer as a fraction in its simplest form. Solution: [2] Question 3 [2009 EOY, Q2] marks Express in the form where a, b and c are rational numbers. Solution: [3] Question 4 [2010 EOY, Q1] marks (a) Simplify . Solution: [M1] 3 327 8 5   [A1] [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. Solution: Height units units units units units [3] Question 5 [2010 EOY, Q2] marks Solve for x when . Solution: However, is rejected as will be undefined. So no solution. [3]

Question 6 [2010 EOY, Q3] marks (a) Make h the subject of the formula . Solution: [2] (b) Simplify . Solution: or [3] Question 7 [2011 EOY, Q1] marks Without using a calculator, simplify . Solution: OR [3]

Question 8 [2011 EOY, Q3] marks (i) Show that . Solution: [1] (ii) Hence simplify . Solution: [4] Question 9 [2012 EOY, Q2] marks Without using a calculator, simplify . Solution: [4]

Question 10 [2012 EOY, Q10 a, b] marks (a) Factorise completely Solution: [2] (b) Given that , express x in terms of p and q. Solution: [2] Question 11 [2013 EOY, Q1 a, b] marks (a) Find the product of and and simplify the answer. Solution: = (x – y)(x +y) = [2] (b) If , simplify . Solution: [3]

Question 12 [2013 EOY, Q6] marks (a) Simplify . Solution: = 0 [3] (b) Simplify . Solution: [3] Question 13 [2014 EOY, Q1] marks (a) Factorise completely . Solution: [3] (b) Simplify . Solution: or      2 2 1 2 1 121 4 2 1 2 2 2 1 22 xx x x x x x x x x x x x x x x             [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. Solution: Length of the side BC [4] Question 15 [2015 EOY, Q3] marks (a) Make p the subject of the formula if . Solution: [3]

(b) Simplify into a single fraction . Solution: [4] Question 16 [2015 EOY, Q4] marks (a) Given that and that , find the value of . Solution: Since , Hence [3] (b) Using a suitable substitution, or otherwise, solve for x if . Solution: Let , equation becomes Solving, ( is rejected since cannot be negative) Hence [4]