Topical Revision Worksheet 2 Equations and Inequalities Student Version

Adapted from HCI Resources 1 Hwa Chong Institution Integrated Programme Secondary Three Mathematics Name: _______________________________ ( ) Class: _________ Date: _____________ Topical Revision Worksheet 2 _________________________________________________________________________________ Topic: Equations and inequalities Question 1 [2008 EOY, Q3] marks It is given that , where , is an answer to the pair of simultaneous equations and . (i) Show that . [2] (ii) Find the other answer to the above pair of simultaneous equations. Answer: , [4] Question 2 [2009 EOY, Q7] marks (a) Given , where p is real. Find the value(s) of p for which the graph of y = f(x) is tangent to the x-axis. Answer: [4] (b) Find the range of values of x for which Answer: [3] Question 3 [2010 EOY, Q17 EITHER i, ii] marks (a) A power generator works in such a way that it takes 10 minutes to warm up before it is able to generate electricity. It is expected to generate 500 units of electricity every 20 minutes after it warms up. (i) Write down an equation in E and t, where E units represent the amount of electricity generated and t minutes (where represents the time after which the generator is turned on. Answer: [1] (ii) Show that it is expected to take at least 5.5 hours to generate at least 8000 units of electricity.

Adapted from HCI Resources 2 **Question 4 [2011 EOY, Q10b] marks The roots of the equation are and . Without finding the value of and of , construct a quadratic equation whose roots are and . Answer: Quadratic equation : [5] Question 5 [2012 EOY, Q9] marks (a) Given that is always positive for all real values of x. Find the range of values of k. Answer: k > 1 [4] **(b) The roots of the quadratic equation are and , such that . Find the possible values of k. Answer: [5] Question 6 [2013 EOY, Q4] marks (a) Find the range of values of h , , for which the line y = x – h meets the curve . Answer: [3] (b) Find the range of values of k for which is always positive for all real values of x. Answer: [3] Question 7 [2013 EOY, Q11] marks Solve the equation Answer: x = 3 or [4] Question 8 [2014 EOY, Q5] marks Find the range of values of m for which is always positive for all real values of x. Answer: [4]

Adapted from HCI Resources 3 Question 9 [2014 EOY, Q6] marks It is given that the equation has two real roots . (i) Find the range of values of k. Answer: [3] **(ii) If , determine the value(s) of k. Answer: k = 3 [4] **Question 10 [2015 EOY, Q1] marks The roots of the quadratic equation are and . (i) Write down the values of and . Answer: and [2] (ii) Find an equation whose roots are given by and . Answer: The Equation is [3] Question 11 [2015 EOY, Q2] marks (a) Explain why cannot be greater than 3 for all real values of x. [3] (b) Find the range of values of p such that is always positive for all real values of x. Answer: [5]