emath revision questions

1 Name: ____________________ ( ) Date: ___________ Class: __________ June Holiday Revision Question 1 Find the solutions of )117(13)117)(35(  nnn . Question 2 Solve x2 = 7x. Question 3 (a) By completing the square, express 1582  xx in the form of bax  2)( . (b) Hence, solve 01582  xx . Question 4 Solve the equation 7)2)(1(2  xx , giving your answers correct to 2 decimal places. Question 5 A quadratic function is given by 0)32)(2()53(2  xxx . Solve the equation leaving your answer correct to 3 significant figures. Question 6 Solve 73)4()12( 22  xxx , leaving your answer to 3 significant figures. Question 7 Solve 2)3( 8 3 54   p p pp . Question 8 (a) Solve the equation 412 3 144 1 2  xxx . (b) Hence, without solving, deduce the solutions for the equation 41 3 )1( 1 2  aa . Question 9 A lorry was driven 45 km from Town P to Town Q at an average speed of y km/h. It returned from Town Q to Town P by the same route. The average speed for the return journey was 5 km/h less than the outward journey. (a) Write down an expression, in terms of y, for the number of hours taken to travel from Town P to Town Q. (b) Write down an expression, in terms of y, for the number of hours taken to travel from Town Q to Town P. (c) If the return journey was 1 hour 30 minutes more than the outward journey, (i) write down an equation in y, and show that it reduces to 015052  yy , (ii) solve the equation 015052  yy , (iii) find the total time the lorry was being driven.

2 Question 10 (a) Express 462  xxy in the form baxy  2)( . (b) Hence, sketch the graph 462  xxy , indicating clearly the points of intersection with the axes and the turning point. (c) Sketch the graph of )5( xxy  . (d) Write down the equation of the line of symmetry of the curve. Question 11 The diagram shows the graph 432  xxy . It cuts the x-axis at A and B. (a) Find the coordinates of A and B. (b) Find the equation of the line of symmetry for the graph. A B y x y x O y x O

3 Question 12 (a) Sketch the quadratic graph of 2)2(5  xy . (b) Write down the coordinates of the maximum point of the curve 2)2(5  xy . Question 13 Solve the inequality 74 1 3 2  mm . Question 14 Given that the inequality )1(2)2(6)7(5  xxx , find the greatest possible value of x if x is (a) an integer, (b) a prime number. Question 15 (a) Solve the inequalities 45 22 3 1  xx . (b) Hence, find the perfect square values of x which satisfy the inequalities 45 22 3 1  xx Question 16 Given that 3 7 5 23 2 11  xxx , find (a) the range of values of x that satisfy the inequality and represent your solutions on a number line. (b) the least integer value of x. (c) the greatest prime value of x. Question 17 Given that 50 and 1134 2  yxx , where x and y are integers, fin