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1 * * NGINRING MISSIONS SSSSMNT 564/ Wednesday November 06 STION INSTRUTIONS TO NITS 80 minutes Please read these instructions carefully, but do not open this question paper until you are told that you may do so. This paper is Section of. separate answer sheet is provided for this paper. Please check you have one. You also require a soft pencil and an eraser. Please complete the answer sheet with your candidate number, centre number, date of birth, and name. t the end of 80 minutes, your supervisor will collect this question paper and answer sheet before giving out Section. This paper contains two parts, and, and you should attempt both parts. Part Part Mathematics and Physics (8 questions) dvanced Mathematics and dvanced Physics (6 questions) This paper contains 54 multiple choice questions. There are no penalties for incorrect responses, only marks for correct answers, so you should attempt all 54 questions. ach question is worth one mark. Questions ask you to show your choice between options. hoose the one option you consider correct and record your choice on the separate answer sheet. If you make a mistake, erase thoroughly and try again. You can use the question paper for rough working, but no etra paper is allowed. Only your responses on the answer sheet will be marked. ictionaries and calculators may NOT be used. Please wait to be told you may begin before turning this page. PV5 This question paper consists of 44 printed pages and 4 blank pages. ULS 06

2 LNK PG ULS 06

3 PRT Mathematics and Physics ULS 06 [Turn over

4 4 Find the complete set of solutions to 8 < 6 < 4 > 4 < 0 > 0 < F > G < 8 H > 8 4 nuclide 8 Pb changes by radioactive decay into the nuclide 0 8 Pb. Which combination of emissions produces this change? alpha alpha and beta alpha and beta alpha and beta beta ULS 06

5 Which one of the following is a simplification of ( )? 5 5 F G 5 + H 5 5 ULS 06 [Turn over

6 4 The graph shown of quantity y against quantity represents the motion of a body. y (The scales on both aes are in the appropriate S.I. units, and the gravitational field strength g is 0 N kg.) Which two of the following could the graph represent? kinetic energy against velocity for an object of mass 0 kg undergoing free-fall potential energy against height for an object of mass 0 kg being lifted by a constant eternal force velocity against time for an object of mass 0 kg being accelerated by a resultant force of 00 N 4 work done by an eternal force of 5 N against distance moved for an object of mass kg being moved at constant speed by (and in the direction of) the eternal force and and and 4 and and 4 F and 4 ULS 06

7 7 5 The ratio of Q:R is 5: and the ratio of R:S is :0 Which one of the following gives the ratio Q:S in its simplest form? : : :4 :5 4: F 5: ULS 06 [Turn over

8 6 uranium-5 nucleus can undergo fission to produce two smaller nuclei. Which of the diagrams, if any, could represent this process? 8 diagram a diagram 7 54 Xe p 5 9U 0 n 0 n 0 n 5 9U 0 n 0 n 89 6Kr 0 n 96 8Sr diagram 0 n 5 9U 0 n 87 5 r 0 n 0 n La F G none of them only only only and only and only and only H, and ULS 06

9 9 7 The mean age of the twenty members of a running club is eactly 8. The mean age increases by eactly years when two new members join. What is the mean age of the two new members? F 0 years years 0 years 40 years 50 years 5 years 8 circuit consists of a 5.0 Ω resistor and a variable resistor connected in series with a 4 V battery. The variable resistor has a minimum resistance of.0 Ω and a maimum resistance of 5 Ω. The battery and the connecting wires have negligible resistance. What is the maimum power dissipated in the 5.0 Ω resistor? F 7. W 8 W 7 W 45 W 7 W 75 W ULS 06 [Turn over

10 0 9 medical scanner is bought for The value of the scanner depreciates by 0% every year. y how much has the scanner reduced in value after years? F 9600 G The total power P radiated by a star is given by: P = kr T 4 where R is the radius of the star, T is its surface temperature and k is a constant. The power currently radiated by the Sun is W. Towards the end of the Sun s life its radius will increase by a factor of a hundred and its surface temperature will decrease by a factor of two. What will be the power radiated by the Sun when these changes have occurred? F G H W W W W W W.5 0 W W ULS 06

11 The point is 4 km due ast of the point. The bearing of the point from is 0 and the bearing of from is 060 Find the distance. km km 4 km 5 km 4 km transverse wave travelling through a medium has a frequency of 5.0 Hz, a wavelength of 4.0 cm and an amplitude of.0 cm. What is the total distance travelled by a particle of the medium in one minute? F 900 cm 00 cm 800 cm 400 cm 600 cm 4800 cm ULS 06 [Turn over

12 The quantities and y are positive. is inversely proportional to the square root of y. When = 8, y = 9. What is the value of y when = 6? F 6 ULS 06

13 4 motor is used to lift a mass of 5.0 kg using a pulley system as shown in the diagram. The pulley is secured to the roof using a coupling. coupling pulley roof force from motor rope 5.0 kg The motor needs to cause the mass to accelerate upwards at 0.80 m s. What is the minimum tension force that the coupling must be able to withstand without breaking? (The gravitational field strength g is 0 N kg. The pulley system is frictionless and has negligible mass. The rope has negligible mass and is inetensible.) F G H 4.0 N 8.0 N 46 N 50 N 54 N 9 N 04 N 08 N ULS 06 [Turn over

14 4 5 In a trapezium PQRS, the parallel sides are PQ and RS. PQ = ( ) cm, RS = ( + 5) cm and the vertical height QR = cm. P Q [diagram not to scale] S + 5 R The area of the trapezium is 0 cm. What is the length of RS? F 9 cm 0 cm cm cm 5 cm 7 cm ULS 06

15 6 heater is connected in series with a resistor and a 6.0 V battery in the circuit shown. 5 battery resistor heater The total resistance of the circuit is 5 Ω. In.0 minutes, 80 J of electrical energy is transferred into other forms in the heater. How much charge flows through the heater in the.0 minutes and what is the voltage across the heater? charge / voltage / V F 7.5 G H ULS 06 [Turn over

16 6 ULS 06 7 Make b the subject of the formula: + = b b a + + = ± a a b + = ± a a b + = ± a a b = ± a a b + = ± a b F = ± a b

17 7 8 cubic block has a hole through it with a square cross-section. The dimensions are shown on the diagram. The weight of the block is 0 N. 5.0 cm 0 cm What is the density of the material from which the block is made? (The gravitational field strength g is 0 N kg.) 0.0 g cm 0.40 g cm 0.60 g cm. g cm.0 g cm F 4.0 g cm G 6.0 g cm H g cm ULS 06 [Turn over

18 8 9 thin rectangular sheet of metal 0 m by 5 m is made into an open ended cylinder by joining the edges PS and QR. The height of the cylinder is 0 m. What is the volume, in cubic metres, enclosed by this cylinder? P 5 m Q r [diagram not to scale] 0 m 0 m 0 m S 5 m R F 5 π 5 4π 5 π 6.5π 5 π 50 π ULS 06

19 9 0 The diagram shows four solid steel balls P, Q, R and S which are of identical size. alls P and R have shiny surfaces. alls Q and S have dull surfaces. alls P and Q are in a room at 0. alls R and S are in a room at 40. The temperature of each ball at a given moment in time is shown on the diagram. room room at at 0 0 o room room at at o 0 0 o 0 0 o o o P Q R S Which two balls lose thermal energy by convection, and which ball emits thermal radiation at the greatest rate? lose thermal energy by convection greatest rate of emission of thermal radiation P and Q P P and Q Q P and Q R P and Q S R and S P F R and S Q G R and S R H R and S S ULS 06 [Turn over

20 0 Which one of the following is a simplification of + 4? 4 F ULS 06

21 The diagram shows the velocity-time graph for an object travelling in a straight line over a period of 0 s. velocity / m s time / s What total distance did the object travel in the 0 s, how far from its starting position was it at the end of the 0 s, and what was its average speed over the 0 s? total distance travelled / m distance from starting position / m average speed / m s F G H ULS 06 [Turn over

22 uring summer activities week 0 students each chose one activity from swimming, archery, and tennis. 46 of the students were girls. 6 of the students chose tennis, and of these were boys; 5 girls chose swimming, and 7 students chose archery. boy is picked at random. What is the probability that he chose swimming? ULS 06

23 4 ronze is a miture of tin and copper. particular sample of bronze contains 0% tin by volume. (In other words, 0% of the total volume of the sample is tin and 90% of it is copper.) What percentage of the mass of the sample is tin? (ensity of tin = Y and density of copper = X.) X 00 9X Y X 00 9Y X Y 00 9X Y Y 00 9Y X X 00 9X + Y X F 00 9Y + X Y G 00 9X + Y Y H 00 9Y + X n Which one of the following epressions is equivalent to n 7 4 n? F 9 n n 4n 6 n 6 ULS 06 [Turn over

24 6 When a stationary uranium-8 nucleus decays by alpha emission it forms a nucleus of thorium-4. The total kinetic energy produced by the decay is. 4 Th-4 U-8 alpha-particle before decay after decay What is the kinetic energy of the alpha particle? ULS 06

25 5 7 In the diagram below, PQRS is part of a regular polygon. The polygon has n sides. The side PQ is etended to T such that PQT is a straight line. The length of RQ is the same as the length of RT. P [diagram not to scale] Q R S T Find an equation for n in terms of, where is the size of angle QRT in degrees. F G n = n = n = n = n = n n = = ULS 06 [Turn over

26 6 8 student carries out an eperiment to measure the speed of sound. loudspeaker that emits sound in all directions is placed between two buildings that are 8 m apart as shown. The student and loudspeaker are 48 m from one of the buildings. 8 m building building 48 m student and loudspeaker The loudspeaker is connected to a signal generator that causes it to emit regular clicks. The student notices that each click results in two echoes, one from each building. The rate at which the clicks are produced is gradually increased from zero until each echo coincides with a new click being emitted by the loudspeaker. What is the frequency of emission of clicks when this happens? (The speed of sound in air = 0 m s.) F G.0 Hz.5 Hz. Hz 4.0 Hz 5. Hz 6.7 Hz 0 Hz ULS 06

27 7 PRT dvanced Mathematics and dvanced Physics ULS 06 [Turn over

28 9 When = is substituted in the epression 8 p + q + + p the result is 0. When = is substituted into the same epression, the result is. 5. Find all possible value(s) of p. p = ± 6 p = or p = p = p = ± 7 there are no values for p ULS 06

29 0 parachutist is falling at terminal speed with his parachute open. The diagrams show, separately, the vertical forces acting on the parachute and the vertical forces acting on the parachutist. The letters L, M, N, P, Q and R represent the magnitude of each force as indicated. air resistance on parachute (L) 9 force from parachute (P) air resistance on parachutist (Q) weight of parachute (M) force from parachutist (N) weight of parachutist (R) onsider the following equations: quation : quation : quation : quation 4: quation 5: L = M + N R = P + Q L = Q N = P M + R = L + Q Which of these equations, if any, is/are the direct result of the application of Newton s Third Law to this situation? F G none of them only 4 only 5 only and only and 4 only, and 5 only H,,, 4 and 5 ULS 06 [Turn over

30 0 ULS 06 square PQRS is drawn above the -ais with the side PQ on the -ais. P is the point ( 5, 0) and Q is the point (, 0). circle is drawn inside the square with diameter equal in length to the side of the square. Which one of the following is an equation of the circle? = y y = y y = y y = y y = + + y y F = y y G = y y H = y y

31 crate has a total mass of 800 kg, including its contents. helicopter of mass 400 kg is carrying the crate using a light inetensible rope as shown: rope crate The helicopter and crate are accelerating upwards at.0 m s. What is the tension in the rope? (The gravitational field strength g is 0 N kg ; air resistance can be ignored.) F G H 6400 N 8000 N 9600 N N N N N N ULS 06 [Turn over

32 The first term of a convergent geometric series is 8. The fifth term is. The sith term is real and positive. What is the sum to infinity of this series? (The sum to infinity of a convergent geometric series is given by and r is the common ratio.) 8 ( + ) 8( ) 8 ( + ) 8( ) 6 a r, where a is the first term F G ULS 06

33 4 shopper pushes a supermarket trolley a distance of 5 m in a straight line across a level, horizontal surface. The shopper applies a constant force of 50 N at an angle of 7 below the horizontal. The total weight of the trolley and its contents is 50 N. 50 N 7 o [diagram not to scale] RL What is the magnitude of the total vertical force that the surface eerts on the trolley and how much work is done by the pushing force? (You may use the approimations sin 7 = 0.60; cos 7 = 0.80.) vertical force / N work done / J F ULS 06 [Turn over

34 5 Tangents are drawn from a point P to a circle of radius 0 cm. 4 The centre of the circle is and the distance P is 0 cm. [diagram not to scale] P. Which one of the following is an epression for the shaded area in square centimetres? 00 ( π) 00 ( 5 π) 50 ( 6 π) 50 ( 6 5 π) 50 ( π) 50 F ( π ) ULS 06

35 5 6 plank of non-uniform density which has a mass of 5 kg is used to make a see-saw. pivot is placed under the centre of the plank as shown on the diagram m.0 m [diagram not to scale] pivot boy of mass 5 kg sits at one end of the plank with his centre of gravity.0 m from the pivot. The see-saw balances when a woman of mass 60 kg sits on the plank on the other side of the pivot. Her centre of gravity is 0.80 m from the pivot. Where is the centre of gravity of the plank and what is the magnitude of the force between the pivot and the plank? (The gravitational field strength g is 0 N kg.) distance from pivot force / N 0.40 m on left of pivot m on left of pivot 00 at the pivot 00 at the pivot m on right of pivot 00 F 0.0 m on right of pivot 00 G 0.40 m on right of pivot 00 H 0.40 m on right of pivot 00 7 Given that 7 cos θ tan θ sin θ =, which one of the following is true? cos θ = or 5 cos θ = or 5 cos θ = or 5 cos θ = or 5 ULS 06 [Turn over

36 6 8 car of mass 00 kg on a fairground ride travels at a speed of 5.0 m s at point X. The car is allowed to move down a sloping section of track without any energy input. The heights above the ground of points X and Y are shown. When the car reaches point Y its speed is 9.0 m s. 5.0 m s X car [diagram not to scale] 8.0 m Y.0 m How much energy is transferred in overcoming resistive forces as the car travels from X to Y? (The gravitational field strength g is 0 N kg.) 900 J 6400 J 7900 J J 00 J 9 The complete set of values of a for which the equation ( ) roots is = a + has two real distinct no values of a 4 < a < 4 a < 4, a > 4 4 < a < 8 a < 4, a > 8 F 8 < a < 4 G a < 8, a > 4 H all values of a ULS 06

37 7 40 The diagram shows a uniform, solid, heavy cube with side d. The cube rests with one of its edges in contact with a table that is perfectly level. horizontal force P acts on another edge of the cube, and the cube is stationary. d P [diagram not to scale] 0 o elow are four statements about the forces on the cube. It is possible that there is no frictional force between the cube and the table. There must be a frictional force acting to the left between the cube and the table. There must be a frictional force acting to the right between the cube and the table. 4 Force P has a clockwise moment about the edge in contact with the table equal to P d. Which of the statements is/are correct? F only only only and 4 only and 4 only and 4 only ULS 06 [Turn over

38 8 4 The straight line with equation y = m +, where m > 0, m, is perpendicular to the line with equation y = p + The lines cut the -ais at the points L and M respectively. The length of LM is 5 units. What is the value of m + p given that m >? y [diagram not to scale] (0, ) (0, ) L 5 M F ULS 06

39 4 The diagram shows two identical blocks, each of mass m, in two different arrangements. 9 a [diagram not to scale] b Which epression gives: arrangement arrangement gravitational potential energy gravitational potential energy of arrangement of arrangement? (g is the gravitational field strength.) mg(a b) mg(b a) mg(b + a) mg(a + b) F mg(a b) mg(a b) ULS 06 [Turn over

40 40 4 f () = a where a is a positive constant. Find the complete set of values of for which f () is an increasing function. a, a a a a, 0 a a 0, a F G H a a, a a a, a a a 44 n object is fired vertically upwards from the ground at time t = 0 s in still air at a speed of 8.0 m s. On the way up, what is the height of the object above the ground when it has a speed of.0 m s, and at what time does it reach this height on the way down? (The gravitational field strength g is 0 N kg. ir resistance can be ignored.) height / m time / s F G.0.0 H.0.0 ULS 06

41 4 45 The curve y = is translated by the vector 4 and then reflected in the line y = Which one of the following is an equation of the resulting curve? y = 4 ( ) y = ( ) y = + 4 ( ) y = + 4 ( ) y = 5 4 ( ) y = F ( ) y = G ( ) y = H ( ) 46 The diagram shows a ball P, of mass 4.0 kg, moving to the right at 0 m s directly towards a stationary ball Q, of mass.0 kg. 0 m / s P 4.0 kg stationary Q.0 kg The balls collide but do not join together. Immediately after the collision ball Q moves at 0 m s to the right. What is the velocity of ball P immediately after the collision, and how much kinetic energy in total is lost during the collision? velocity of ball P after collision kinetic energy lost during collision / J m s to the left 50 0 m s to the left m s to the right 50 F 5.0 m s to the right 50 ULS 06 [Turn over

42 4 47 The complete set of values of for which > 0 is <, > 4 < < 4 <, < <, > 4 < <, < < < < 48 point object of mass.0 kg is at rest on a level, horizontal surface. The coefficient of friction between the object and the surface is 0.5. Two horizontal forces at right-angles to each other, with magnitudes 9.0 N and.0 N, are applied simultaneously to the object. What is the magnitude of the acceleration of the object as it begins to move? (The gravitational field strength g is 0 N kg.) 5.0 m s 7.5 m s 7.5 m s 8.0 m s 0 m s F 0.5 m s ULS 06

43 4 49 cursor starts at the point (0, 0) and moves parallel to the -ais in the negative direction. What is the minimum distance parallel to the y-ais between the cursor and the graph of y = 4 6 5? n object of mass 0 kg is pulled up a rough plane inclined at 0 to the horizontal by a light, inetensible cable attached via a frictionless pulley to a freely-falling 0 kg mass. The acceleration of the object along the plane is.5 m s. cos 0 = sin 60 = sin 0 = cos 60 = 0 o 0 kg 0 kg [diagram not to scale] frictionless pulley What is the frictional force between the object and the plane? (ir resistance and the mass of the pulley can be ignored. The gravitational field strength g is 0 N kg.) F G 5 N 50 N 75 N 00 N 50 N 75 N 50 N ULS 06 [Turn over

44 5 What is the area enclosed by the line = 7 44 and the curve = ( y ) + 4? F 0 5 spacecraft of initial total mass 4000 kg is travelling relative to the arth at a constant speed of 745 m s. It ejects some fuel backwards in a sudden burst at a speed relative to the spacecraft of 45 m s. s a result of this, the speed of the spacecraft immediately after the fuel is ejected increases to 7500 m s. What is the mass of fuel ejected? F kg 4 kg 40 kg 50 kg 00 kg 0 kg ULS 06

45 curve has equation y = What is the complete set of values of the constant k for which the equation = k has eactly four distinct real roots? no values of k < k < 5 5 < k < 0 k > 0 7 < k < 0 F all values of k 54 n object of weight 40 N hangs from the end of a light inetensible string of length 0.5 m, which is attached to the ceiling. constant horizontal force of 0 N is applied to the object, causing it to move to a new equilibrium position with the string no longer vertical. y how much has the gravitational potential energy of the object increased as a result of its change of position? F. J.8 J.5 J 4. J 4.9 J 5.6 J ULS 06

46 46 LNK PG ULS 06

47 47 LNK PG ULS 06

48 48 LNK PG ULS 06