Friday 12 January 2018 Afternoon

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1 Oxford ambridge and RS Friday 1 January 018 fternoon FSMQ INTERMEITE LEVEL 6989/01 Foundations of dvanced Mathematics (MEI) * * andidates answer on the nswer Sheet. OR supplied materials: nswer Sheet (MS4) Other materials required: Eraser Scientific calculator Soft pencil Ruler uration: hours * * INSTRUTIONS TO NITES Write your name clearly in capital letters, your centre number and candidate number on the nswer Sheet in the spaces provided unless this has already been done for you. Read each question carefully. Make sure you know what you have to do before starting your answer. o not write in the bar codes. There are forty questions in this paper. ttempt as many questions as possible. For each question there are four possible answers,,, and. hoose the one you consider correct and record your choice in soft pencil on the separate nswer Sheet. Read very carefully the instructions on the nswer Sheet. INFORMTION FOR NITES Each correct answer will score one mark. mark will not be deducted for a wrong answer. This document consists of 8 pages. ny blank pages are indicated. [100/604/6] (LK/SW) 13384/ OR is an exempt harity Turn over

2 Formulae Sheet: 6989 Foundations of dvanced Mathematics a rea of trapezium = 1 (a + b)h h b Volume of prism = (area of cross-section) length crosssection length In any triangle Sine rule a sin = b sin = c sin b a osine rule a = b + c bc cos 1 rea of triangle = ab sin c 4 3 Volume of sphere = πr 3 r Surface area of sphere = 4πr Volume of cone = πr h urved surface area of cone = πrl 1 3 l h r The Quadratic Equation The solutions of ax + bx + c = 0, where a 0, are given by x = b ± (b 4ac) a

3 is a prime number. The cube of 3 is 7. The cube root of 64 is 4. The reciprocal of 3 1 is 0.3. Which one of the following has the largest value? 7% of 00 One third of divided by # 7 = 1+ # (-)# (- 3) + 7 = 1 (-4)-(- 5) = 1 (- 3) =-7 3 Turn over

4 # = = = ' = ' 3 = ' 3 = # 3 3 = = = 135. # # # 10 = 7# ( 5# 10 )#( 4# 10 ) = # ( 6# 10 )' (. 1# 10 ) = 5# 10

5 5 7 sum of money is split in the ratio 9:13. The larger share is Which one of the following is the correct value for the sum of money that is split? to the nearest pound to the nearest pound 8 eth s lawn in her garden is rectangular in shape. The length is 7.5 m, correct to 1 decimal place and the width is 4.7 m, correct to 1 decimal place. The perimeter is no greater than 4.6 m. The area is greater than 34.6 m. The length of a diagonal is definitely greater than 8.8 m. The length is at least.7 m greater than the width. Turn over

6 9 The shape and dimensions of a swimming pool are shown in the diagram. 6 1 m 1 m 1 m 8 m 7 m F E 10 m.5 m 1 m The line E slopes at 1 to the horizontal, correct to the nearest degree. The length of E is 7.16 m, correct to decimal places. When full of water, the swimming pool contains less than 750 m 3. The area of the cross-section EF is m.

7 10 Of the four quadratic equations below, only one has integer roots. Which one is the equation with integer roots? x + 13x+ 4 = 0 x - 00 = 0 4x - 4x+ 1 = 0 x -3x-8 = form tutor records the number of GSEs gained by each member of her tutor group. She summarises the results in the table below to show how many students have gained each number of GSEs. Number of GSEs Frequency Which one of the following is the most appropriate diagram to use to show these frequencies? Pie chart umulative frequency graph Histogram Vertical line graph Turn over

8 1 Fred and George each have a fair 5-sided spinner as shown in the diagram Fred and George spin their spinners. The numbers on the sides ending in contact with the table are noted. Which one of the following is the probability that the two numbers are the same? fruit flies are put into a closed box. The growth of the population of flies in the box can be modelled by the formula P = 5# n where P is the size of the population after n days. fter two days, P = 0. When n = 3, P = 40. fter four days, P = 60. When n = 10, P = 510.

9 9 14 company owns a chain of 30 shops. The following table shows the numbers of employees of these shops. Number of employees Frequency The range could be as great as 19. n estimate of the mean number of employees is 0. The median could be as great as 0. If a shop is chosen at random the probability that it employs 0 or fewer people is 0.43, correct to decimal places It is required to rearrange the formula + = to make f the subject. u v f Students come up with four different answers, but only one of them is correct. Which one of the following is a correct rearrangement? u v f = + f = u+ v uv f = u + v u v f = + uv Turn over

10 16 Tom is attempting to solve the following simultaneous equations. 10 3x + 4y = 5 4x 5y = 7 (i) (ii) His attempt is shown in the four steps below but the answer is incorrect. In which of the following steps,,,, does the first error appear? Multiply (i) by 4 giving 1x + 16y = 0 (iii) Multiply (ii) by 3 giving 1x 15y = 1 (iv) Subtract (iv) from (iii) giving y = 1 Substitute into (i) giving x = 3 17 Of the four equations given below, three equations have a solution that is not an integer and one has a solution that is an integer. Which one of the following has a solution that is an integer? 4x+ 5 = 3- x ( x+ ) = 3-5( x+ 3) 3( x+ 1) + ( x+ 1) = ( 3 - x) = 1 + ( x ) 3 -

11 11 18 Which one of the following is the correct simplification of - x 1- x -? x 1+ 7x x x The solution of the inequality 3x x is x The solution of the inequality 3 ( x + 5) is x 1. 6 The solution of the inequality 3( x+ 4) - ( x+ 1) 0 is x 10. The solution of the inequality x 1 x - 5 is x Turn over

12 1 0 One of the following quadratic expressions cannot be factorised in the form (x 1)(x + a) where a is a whole number (positive or negative). Which one cannot be factorised in this way? x -x- x - 3x+ x + 3x-4 x - 6x+ 5 1 cookery book gives the following instructions for cooking a turkey. ook for 16 minutes per 500 grams plus 0 minutes T is the cooking time in minutes. M is the mass of the turkey in kilograms. Which one of the following is the correct formula for T? T = 16M+ 0 T = 8M+ 0 T = 3M+ 0 T = 16 ( M+ 0)

13 13 The following formula is to be used to evaluate y for different values of x. ( x ) y = + 3 When x = 7, y = 7. When x = 5, y = 3. y is always a whole number. To find y you add to x, square the result and then divide by 3. 3 Three vectors are given by a = i + 3j, b = 3i + j, c = 4i + 5j. a + b + c = 5i j a = 4i + 6j c b = a b + c a = 11i Turn over

14 4 bigail and Mia visited a coffee shop recently with friends. bigail bought 3 coffees and cakes, which cost Mia bought 4 coffees and 4 cakes, which cost Let x pence be the cost of a coffee and y pence be the cost of a cake. Which one of the following is the correct pair of simultaneous equations for x and y? 14 x y + = 100, 3 x y + = x+ y = 100, 4x+ y = x+ y = 100, x+ y = x+ y = 100, x+ y = 400

15 15 5 harlie and aryl are steering due north in a small motor boat in an estuary. The boat travels at 5 km h 1 through the water, but there is a current flowing from the northeast at 3 km h -. In which one of the following diagrams does the line with the double arrow represent the direction and speed in which the boat is travelling? -1 Turn over

16 16 6 sin37 = cos 53 tan56 = tan 36 This is part of the curve y = 1+ 3cos x. y x In this triangle, i = 50., correct to 1 decimal place. 6 Not to scale 5 i

17 7 The diagram shows the plan of a rectangular house with a rectangular extension. 17 Plan Three of the following elevations are correct and one is incorrect. Which one of the elevations,,, is incorrect? This is the elevation from. This is the elevation from. This is the elevation from. This is the elevation from. Turn over

18 8 The graph below represents the conversion between euros and pounds on one day is roughly equivalent to is roughly equivalent to is worth less than On a later occasion I exchanged 50 for 55. The conversion graph for this exchange rate would be less steep than that drawn above. 9 Which one of the following might reasonably have a mass of 400 g? box of half a dozen eggs pencil 5 litres of milk in a plastic container large cat

19 19 30 train travels from station to station. It accelerates uniformly from rest at to a speed of 0 m s 1 which it maintains for 160 seconds before decelerating uniformly to rest at station. This motion is shown in the graph below. Speed (m s 1 ) Time (s) The acceleration of the train in the first 100 seconds is 0. m s. The train decelerates at a greater rate than it accelerates. 0 m s 1 = 7 km h 1. The distance between the stations is 5400 metres. Turn over

20 0 31 The line L 1 below is a graph of the equation y = 5- x. The line L has equation y = 3x- 5. y 6 4 L x 4 6 To answer this question you are advised to plot the graph of the line L on the grid above. The graph of L 1 above shows that the solution of the equation 5- x = 0 is x = 5.. The gradient of the line L 1 is. Lines L 1 and L meet at the point with coordinates (, 1). The y intercept of L is ( x- ) + x = 7x -1 x + 4xy = x( x+ y) ( x+ y)( x- y) = x -y ( x+ 1)( x- 1) = x -1

21 33 Three of the following statements involve sensible metric units and one does not. Which one does not? 1 The mass of a banana is measured in milligrams. The density of a metal is measured in grams per cubic centimetre. The speed of a sprint runner is measured in metres per second. The distance from London to York is measured in kilometres. 34 Four sequences are as follows. is a linear sequence with the first three terms 3, 7, 11. is a quadratic sequence with the first three terms 3, 7, 13. is an exponential sequence with the first three terms 3, 6, 1. is a linear sequence with the first three terms 3, 1.5, 0. The next two terms of sequence are 15, 19. The next two terms of sequence are 1, 9. The next two terms of sequence are 4, 48. The next two terms of sequence are 1.5, 3. Turn over

22 35 Flora draws a triangle in which = 6 cm, = 5 cm and the angle is 60. She claims that the angle = 46., correct to 1 decimal place. Josie draws a triangle EF in which E = 6 cm, EF = 8 cm and F = 9 cm. She claims that angle E = 78.6, correct to 1 decimal place. Which one of the following is a true statement? Flora is right and Josie is wrong. oth Flora and Josie are right. Flora is wrong and Josie is right. oth Flora and Josie are wrong. 36 The number is written below in four different ways. orrect to 1 decimal place, it is orrect to 3 significant figures, it is 434. orrect to 1 significant figure, it is #. orrect to the nearest 100, it is 4300.

23 3 37 The map below shows a lake. The rectangle round it is a fence. The map is drawn on a centimetre square grid and 1 centimetre represents 0 metres. The actual length of the fence is 50 m. The surface area of the lake is between 8000 m and m. The nearest the fence is to the lake is approximately m. The scale of the map is 1 : 00. Turn over

24 4 38 Morven investigates the number of items that people buy on a single visit to the local supermarket. She stands outside the exit door at midday one Saturday and asks the first 70 people who come out of the store how many items they have purchased. She draws the following bar chart to show her summarised results. 5 Frequency Number of items The sample is not random. The chart is misleading. The modal group is The number of people in the 11 0 group is twice the number in the 1 10 group.

25 5 39 local authority began to allocate students starting secondary school to their nearest school in order to reduce the cost of transport. The bar chart below displays the percentage of students in the local authority walking and being transported to school for five years after the implementation of this policy. 70 Percentage Year Key transported to school walked to school Equal numbers of students walked to school and were transported to school in 01. The chart indicates that the percentage of students walking to school is increasing over time. The chart indicates that all students in the local authority were included in the data. The chart indicates that the cost in pounds of transporting students to school is decreasing over time. Turn over

26 40 The table below gives some values for the function y = x + x -3x x y 4 To answer this question you are advised to complete the table and draw the graph on the grid below. y x The point ( 3, ) lies on the curve. 3 There are two points on the curve y = x + x -3x- at which the gradient is zero. When x = 0 the gradient is positive. 3 The equation x + x -3x- = 0 has three roots, none of which are integers. EN OF QUESTION PPER

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