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, find the (a) range of values of x. (b) greatest possible value of (x + y)2. (c) least possible value of ))(( yxyx  .

4 Question 18 The school needs to buy new sets of tables and chairs to replace the damaged ones in the hall. The school found that at least 20 sets of tables and chairs need to be replaced. Each chair costs $90 and each table costs $60. The budget allocated for the replacement of furniture is $4000 for this year. (a) Form two inequalities in x, the number of sets of tables and chairs to be purchased. (b) Solve the inequalities. (c) Hence, find the maximum sets of tables and chairs that the school can buy. Question 19 Simplify 03 63 )3()2( 38 aab aba   giving your answer in positive indices only. Question 20 Simplify 9 4 9 )(4 2 2 22 ca ca ca  . Question 21 Simplify 22 2 3 3 3 4 )5( 6 20 3 40 24 n nm n m n m  , giving your answer in the lowest terms. Question 22 Simplify 2 2 3 2 )(56 14 7 2 xy ab xy ba  . Question 23 Solve xx   113 3216 . Question 24 Simplify 233 6 4 2 8 125.0 )2(  cab cb b c . Question 25 Simplify 0 23 2 1 4 8)16( b baa   , expressing your answer in positive indices only. Question 26 Simplify 5 7 35 3 4 12 6    y x x yx , leaving your answers in positive index form. Question 27 Simplify ba ba ba a 3 2 1 34 2 2 1 3 8 )(15 2 3            , leave your answer in positive indices.

5 Question 28 If kaaa  , find the value of k. Question 29 Matthew has $20 000 to invest in Company A or Company B. Company A offers 3.8% per annum simple interest while Company B offers 3.5% per annum compound interest, compounded half-yearly. Matthew wishes to invest the money for a period of 5 years. Which company should he invest in? Explain your answer. Question 30 A printing company produces magazines, books and banners. (a) The cost of printing a magazine in 2012 was 95 cents. The company produces 50000 magazines in 2012. Find the total cost of producing 50000 magazines in dollars. (b) The company sold each magazine at a profit of 120%. Calculate the profit earned for selling 50000 magazines. (c) The company borrowed $200000 from Bank A which charges simple interest at 8% per annum, find the interest the company has to pay to Bank A after 30 months. (d) The company borrowed the same amount from Bank B which charges interest at 5% per annum, compounded yearly, for 30 months. Find the amount the company could save as compared to Bank A. Question 31 The world’s population is predicted to reach 1110097.0  by 2050. (a) 1110097.0  can be expressed as n million. Find n. (b) The world’s population was 9102.7  in 2013. Find the predicted increase in the world’s population from 2013 to 2050, giving your answer in standard form. Question 32 China India USA Population 9103.1  9102.1  8101.3  Land area (km2) 6106.9  6103.3  6106.9  Use as much information from the table above as necessary to answer the following. (a) Find the ratio of the population of USA to the population of China. (b) How many more people live in India than in USA? Give your answer in standard form. (c) Which country has the highest population density? Explain your answer. Question 33 PQR is a right-angled triangle in which  xPRQ , QR = 24 cm and PR = 25 cm. The point S lies on QR produced. Write down, as a fraction, the value of (a) PRScos . (b)  )90tan( x . (c)  )180sin( x . R S 25 cm x Q P 24 cm

6 Question 34 In the figure, BD = 20 cm, CD = 30 cm,  20ABD and  152CAE . Find (a) the value of x, (b) the area of BCD , correct to 3 significant figures. Question 35 The diagram shows a park ABCD. It is given that AB = 78 m, BC = 108 m, CD = 113 m, AD = 55 m,  77BAD and  45BCD . Calculate the area of the park. Correct your answer to 3 significant figures. Question 36 In the diagram, ABC and XCY are straight lines. It is given that AC = 10.2 cm, BY = 4.7 cm,  42BYC and  90BCY . Calculate (a) the length of AB, (b) the area of ABY . Give your answers correct to 3 significant figures. 77 45 D C B A 113 m 108 m 78 m 55 m E 152 20 x C B A D 30 cm 20 cm 42 C Y X A B 10.2 cm 4.7 cm

7 Question 37 In the diagram, PR = 15 cm, PQ = 12 cm, QR = 9 cm, QRS is an isosceles triangle and PRS is a straight line. (a) Explain why  90PQR . (b) Hence, calculate the shortest distance from Q to PR. (c) Find the (i) value of QRSsin . (ii) area of QRS . Question 38 In the figure, ABCD is a quadrilateral such that  90ABC , AC = 25 cm,  72ADC , AB = 9 cm and  38ACD . Calculate (a) the length of AD, correct to 3 significant figures, (b) the length of BC, correct to 3 significant figures, (c) BCD , correct to 1 decimal place. Question 39 Triangle ABC lies on a horizontal ground. D is on AB produced such that D is