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cambridge international as & a level computer science
Think New Syllabus Mathematics Book 4 8th Edition Dr Yeap Ban Har, Dr Joseph B. W. Yeo, Dr Choy Ban Heng, Teh Keng Seng, Wong Lai Fong, Wong-Ng Slew Hiong - Solutions
1. Which of the following statements about Newton's third law pair of forces is correct?(a) the forces act on the same object(b) the forces act in the same direction(c) the forces are of different types(d) the forces have the same magnitude
An arrow of mass 0.05 kg is moving at a velocity of 60 m/s and is stopped when it hits a block of wood. The arrow comes to a complete stop in a time of 0.02 s.Calculate the average size of the impact force.
The tyres on a car produce a force of 250 N for 30 s.Calculate the change of momentum for the car.
A catapult with mass 0.25 kg is used to fire a stone of mass 0.05 kg with a velocity of 20 m/s.Calculate the recoil velocity of the catapult just after it has launched the stone.
3. A van of mass 2400 kg is moving at a velocity of 10 m/s. The van crashes into the back of a stationary car of mass 1000 kg and the two vehicles move off together. The impact lasts for 0.2 s.a) Calculate the velocity of the combined van and car immediately after the impact.b) Calculate the
2. What braking force is needed to bring a car of mass 900 kg travelling at 10 m/s to rest in a time of 6.0 s?
1. A ball of mass 0.12 kg moving at a velocity of 15 m/s is caught by a person. The ball comes to a stop in a time of 0.025 s. Calculate the impact force.
2. A 20 000 kg train carriage is moving along a track at a velocity of 2.0 m/s. The carriage collides with a second carriage of mass 10 000 kg and the two trolleys lock together, moving in the same direction. Calculate the velocity of the carriages after the collision.
1. A snooker ball of mass 0.15 kg travels towards a cushion at 2.2 m/s and bounces off in the opposite direction at 2.1 m/s. Calculate the change in momentum of the ball.
A trolley of mass 2.0 kg rolls down a ramp until it reaches a velocity of 3.0 m/s.The trolley collides with a stationary trolley of mass 1.0 kg and they join together.Calculate the velocity of the joined trolleys.
1. Copy and complete Fig. 10.26 to show the direction in which the Earth is accelerating.2. Explain what would happen to the Earth if the force of gravity was removed.3. Explain what would happen to the Earth's orbit if the force of gravity was greater. Fig. 1D.26 Sun Earth
3. What is the relationship between thinking distance and speed?
2. What would be the effects on thinking distance and braking distance of:a) wet roadsb) new tyresc) the driver drinking alcohol?
1. State what is meant by the following:a) thinking distanceb) braking distance.
2. At the start of a race, a sprinter's legs produce a force of 240 N. The sprinter's acceleration is 3.0 m/s².Calculate:a) the mass of the sprinterb) the time it takes the sprinter to reach his maximum speed of 10.5 m/s.
1. A motorbike engine can produce a maximum force of 6000 N. What is the maximum acceleration of the motorbike if the total mass of the motorbike and rider is 500 kg?
2. A car is accelerating at 4m / (s ^ 2) The force from the car's engine is 8000 N, and the mass of the car is 1500 kg. Calculate the air resistance acting on the car.
1. A speed boat has a mass of 2000 kg. The boat has two engines that each produce the same force. Calculate the force required from each engine to accelerate the boat at 10m / (s ^ 2)
15. Complete Table 1C.2 about regular blocks of six metals. Metal Mass Length Width Height Volume Density g cm cm cm cm g/cm Calcium 76.50 5.0 5.0 2.0 Magnesium 8.0 6.0 1.0 Nickel 213.6 4.0 3.0 1.73 8.90 Platinum 171.6 2.0 2.0 2.0 Silver 3.0 3.0 Tin 262.44 45.0 10.50 6.0 2.0 36.0 Table 1C.2
14. Describe how you would find the density of an irregularly-shaped pebble. Your account should give details of the apparatus used, units in which measurements are made and any necessary calculations.
13. (a) What is the difference between mass and weight?(b) A cylindrical-shaped piece of mahogany wood has a diameter of 20 cm and a length of 40 cm.Find the volume of the wood:(i) in cm³(ii) in m³.(c) The density of mahogany is 650 kg/m³.(i) Calculate the mass of the piece of wood in kg correct
12. Table 1C.1 gives the acceleration due to gravity on each of the planets in the Solar System. Use the data in this table to answer the questions that follow.(a) On which planet would an object weigh most?(b) On which planet would an object weigh least?(c) On which planet would an object weigh
11. The mass of a piece of granite is 15.6 g. When it is suspended in a displacement can, a mass of 55 of water is displaced. Find the density of the granite correct to two decimal places.
10. Fig. 10. 13 shows a reading on a force meter.What is the reading shown?(a) 3.8 N(b) 3.9 N(c) 4.1 N(d) 4.4 N 0 1 2 3 0123 scale in N 6 5 4 pointer 56 S object 7 7 8 8 9 9 10 -10 Fig. 1C.13 345
9. The density of sodium is 0,97 g/cm³. What would be the volume(a) 3.83 cm³(b) 4.75 cm³(c) 4.95 cm³(d) 5.73 cm³
8. The volume of the brass ball is 3.53 cm³.What is the density of the brass correct to one decimal place?(a) 3.5 g/cm³(b) 8.5 g/cm³(c) 26.547 g/cm³(d) 33.5 g/cm³ brass ball 20g S 58 Fig. 1C.12
7. What is the mass of the brass ball?(a) 20 g(b) 25 g(c) 30 g(d) 35 g brass ball 20g S 58 Fig. 1C.12
6. The density of brass is 8.5 g/cm³. What is the mass of a cube of brass of sides 2 cm?(a) 17.0 g(b) 34.0 g(c) 51.0 g(d) 68.0 g
5. The density of aluminium is 2.7 g/cm³, while the density of lead is 11.3 g/cm³. Approximately how many times heavier will a block of lead be than a similar-shaped block of aluminium?(a) 2 times(b) 3 times(c) 4 times(d) 5 times
4. What is the unit of weight?(a) joule(b) kilogram(c) metre(d) newton
3. The density of copper is 8.96 g/cm³. What is this expressed in kg/m²?(a) 89.6 kg/m³(b) 896.0 kg/m³(c) 8960 kg/m³(d) 89 600 kg/m³
2. Which of the following pieces of apparatus should be used to measure weight?(a) balance(b) force meter(c) metre ruler(d) thermometer
1. Which of the following is the symbol for a unit of mass?(a) cm³(b) °C(c) g(d) s
Fig. 1C.10 shows an aluminium block of dimensions 2.0 cm x 3.0 cm x 4.0 cm on an electronic balance.(a) Use the information in Fig 1C.10 to work out the density of aluminium in g/cm³.(b) Express the density of aluminium in kg/m². Fig. 1C.10 3.0 cm 2.0 cm 4.0 cm 64.80g
Find the volume of the cuboid shown in Fig. 1C.8. Fig. 1C.8 8 cm 10 cm 2 cm
15. A group of students want to investigate the speed of cars travelling along the road outside their school. In order to calculate the speed, the students must measure a distance and a time.(a) Suggest how the student should measure a distance and a time to make their values as accurate as
14 (a) What is meant by speed?(b) What is meant by velocity?(c) What is meant by acceleration?(d) A student standing on the ground drops a small steel ball from his head height. Describe the motion of the ball as it falls.
13. A car undergoes a uniform acceleration of 5 m/s² for 6 s, to reach a steady speed of 40 m/s.(a) Calculate the initial velocity of the car.(b) The car continues to travel at a steady speed of 40 m/s for 12 s.i) Calculate the distance travelled by the car during the 12 s.ii) The car decelerates
(a) A car takes 15 seconds to accelerate from rest to a speed of 30 m/s.i) Calculate the average acceleration of the car.ii) Explain why this is an average acceleration.(b) The car travels at 30 m/s for two minutes. It then decelerates steadily to rest during the next 12 seconds.i) On Fig. 18.19.
11. (a) On the given axes, sketch the distance-time graph for a body that is:i) moving at a low constant speed ii) moving at a higher constant speed iii) accelerating.(b) On the given axes, sketch the speed-time graph for a body that is:i) moving at a constant speed ii) moving with a uniform
10. Which one of the following statements about velocity and acceleration is correct?(a) Velocity and acceleration are both scalars.(b) Velocity and acceleration are both vectors.(c) Velocity is a scalar and acceleration is a vector.(d) Velocity is a vector and acceleration is a scalar.
9. A car is travelling at 24 m/s along a straight road. The driver applies the brakes and the car undergoes a uniform deceleration of 6m / (s ^ 2)How long does the car take to come to rest?(a) 0.25 s(b) 4.0 s(c) 30 s(d) 144 5
Which of the following speed-time graphs, (a), (b), (c) or (d), represents a body moving with a non-uniform deceleration? Pads Fig. 18.16 time (b) speed time (c) (d) paads time speed time
7. Which of the following distance-time graphs, (a), (b), (c) or (d), represents a stationary body? distance time (b) (a) distance time () distance time distance (d) time
6. A body decreases its speed from 50 m/s to 10 m/s in 10 s. What is its acceleration?(a) 4.0 m/s²(b) -4.0 m/s²(c) 6.0 m/s²(d) -6.0 m/s²
5. On a speed-time graph, which of the following represents distance travelled?(a) area under the graph(b) gradient(c) intercept on the x-axis(d) intercept on the y-axis
4. On a distance-time graph, which of the following represents speed?(a) area under the graph(c) intercept on the x-axis(b) gradient(d) intercept on the y-axis
3. A car starts from rest and moves with a uniform acceleration in a straight line for 3 s. It reaches a speed of 6 m/s What is the acceleration of the car?(a) 0.2 m/s²(b) 2.0 m/s²(c) 18 m/s²(d) 20 m/s²
2. A motorcycle moves at a steady speed of 25 m/s for 120 s. What distance does it travel?(a) 21 m(b) 48 m(c) 145 m(d) 3000 m
1. A boy takes 300 s to walk 450 m. What is his average speed?(a) 0.67 m/s(b) 1.5 m/s(c) 750 m/s(d) 1350 m/s
A car accelerates uniformly from rest to a speed of 10 m/s in 4 s. The car continues at this speed for 10 s, then decelerates uniformly to rest in a further 5 s.1. Draw a graph of the car's motion on the axes in Fig. 18.13.2. What is the total time taken for the journey?3. What is the initial
2. A car moves at a uniform speed of 30 m/s for two minutes. Calculate the distance it travels.3. During a journey, the average speed of a bus is 20 m/s. What is the average speed of the bus in kilometres per hour?!!~!!~!!~!!
1. Sophie walks 800 m to school. She takes four minutes to walk the first 300 m, then seven minutes to walk the remaining 500 m.Calculate:a) her average speed during the first 300 m.b) her average speed for the whole journey.
A student uses a pendulum to obtain a value for the acceleration of free fall g. Fig. 2.1 shows the pendulum hanging from a fixed support.(a) The length / of the pendulum is measured from the support to the centre of mass of the bob(i) On Fig. 2.1, mark and label the length I of the pendulum.(ii)
3 A student uses a 30 cm ruler graduated in millimetres to estimate the thickness of a sheet of paper by two different methods.(a) Method 1 The student:• takes 1 sheet of paper from a pack of 500 sheets and folds it in half• folds the paper in half again• repeats this process until the paper
Describe how the student checks that the two strings are equal distances from the centre of metre rule B.(c) B is made to rotate backwards and forwards through a small angle in a horizontal plane about its centre, as shown in Fig. 1.3.The student determines the time T for B to rotate once, forwards
2 A student investigates the movement of a suspended metre rule.Metre rule A is clamped horizontally above the bench, as shown in Fig. 1.1.(a) Describe how the student checks that A is horizontal. You may draw on Fig. 1.1.(b) A second metre rule B is suspended horizontally from A by two strings of
(a) (i) State the difference between a scalar quantity and a vector quantity.(ii) State two examples of each type of quantity.(b) Fig. 1.1 shows the direction and size of two vectors P and Q.In the space next to Fig. 1.1, draw a labelled vector diagram to show the resultant vector obtained by
A student carried out an investigation to determine the time period of a simple pendulum. She set up the apparatus shown on the right.The student used a digital stopwatch to measure the time taken for ten complete oscillations of the pendulum.She repeated this measurement twice then calculated the
(a) State what is meant by the resultant of two vectors.(b) A man can row a boat through still water at 1.5 m/s. He wants to row due north across a river. The river is flowing due west at 1 m/s. Use a scale drawing to determine his resultant velocity.(c) A force of 6.0 N and a force of 3.0 N act at
Complete the table to show which quantities are scalars and which are vectors. The first one has been done for you. Quantity mass force displacement acceleration distance speed Table 1A.5 Scalar Vector
Give the quantity measured in each of the following S.I. units.(a) kilogram(b) newton(c) metre(d) metre squared(e) metre cubed(f) metre per second
Which of these pieces of apparatus:(a) is used to measure lengths between one metre and several metres(b) is used to measure lengths between several centimetres and 1 metre(c) can measure lengths to the nearest 0.001 cm?
9. Here are pictures of some instruments used to measure length.Which of these pieces of apparatus:(a) is used to measure lengths between one metre and several metres(b) is used to measure lengths between several centimetres and 1 metre(c) can measure lengths to the nearest 0.001 cm? TTTTTTTTT (b)
The time taken for one complete oscillation of a pendulum is called the:(a) amplitude(b) frequency(c) length(d) period
Human reaction time is normally considered to be about:(a) 0.002 s(b) 0.02 s(c) 0.2 s(d) 2.0 s
What prefix is used to indicate x 10?(a) kilo(b) mega(c) micro(d) milli
Which of the following is a vector quantity?(a) displacement(b) mass(c) speed(d) time
Which of the following is a scalar quantity?(a) acceleration(b) force(c) mass(d) velocity
5.6 us is equivalent to:(a) 0.0000056 seconds(b) 0.0056 seconds(c) 560 000 seconds(d) 56 00000 seconds
Which of the following is a correct unit for velocity?(a) m(b) m²(c) m/s(d) ms
Which of the following is the S.1. unit of mass?(a) gram(b) kilogram(c) ounce(d) pound
2. A student walks 12 km north then 12 km east. Calculate the student's resultant displacement?
1. A 7.0 N force and a 3.0 N force act at right angles to each other. Determine the resultant of the two forces by scale drawing?
A student carried out the experiment described in Experiment 1A.1. She obtained the results shown in Table 1A.3.(a) Complete the table to show the mean values of 10t and the period, t.(b) Plot a graph of the length. I, of the pendulum on the x-axis against the mean period, t, on the y-axis.(c)
2. 4.8 cm³ of the solution are run out of the burette. What is the reading on the burette now?
1. What is the level of aqueous solution in the burette shown in Fig. 1A.7. You may assume the unit is cm³. 39 38 37 Fig. 1A.7
5. Express a force of 2 900 000 newtons in mega newtons, using the correct symbol for the unit?
4. An electric current is measured as 0.0024 amperes. Write this in milliamperes using the correct symbol for the unit.
3. Write the S.I. unit for speed in symbols.
2. What quantity is measured in m³?
1. What is the S.I. unit for time?
21. A game is such that a fair die is rolled repeatedly until a '6' is obtained. Find the probability that(i) (a) the game ends on the third roll,(b) the game ends on the fourth roll,(c) the game ends by the fourth roll.(ii) Suppose now that the game is such that the same die is rolled repeatedly
20. A box contains 7 electrical components. The box was dropped in transit and one of the components became defective, but not visibly. The components are taken out from the box at random and tested until the defective component is obtained.What is the probability that the defective component is
19. Bag A contains 20 potatoes, 4 of which are rotten.Bag B contains 12 potatoes, 3 of which are rotten.David selects one potato at random from each bag.(i) Complete the tree diagram below to show the possible outcomes of David's selections.(ii) David wants to find out the probability of selecting
18. A box contains n marbles. 8 of the marbles are blue and the rest are red. Ken takes two marbles from the box, at random, without replacement. (0) Complete the tree diagram.(ii) The probability that Ken takes two blue marbles is Write down an equation to 13 represent this information and show
17. A bag contains 10 red balls, 9 blue bal 7 yellow balls. Three balls are drawn in at random, without replacement. By tree diagram or otherwise, find the pri obtaining S (i) a red and two blue balls in that o (ii) a red, a yellow and a blue ball int (iii) three balls of different colours.
16. Class A has 18 boys and 17 girls and 14 boys and 22 girls. A student from selected at random and transferred to A teacher then selects a student at rai) S the extended Class B. Find the probably) student selected is (i) the student who was initially from) (ii) a boy.
15. Box A contains 7 blue balls and 5 end th Box B contains 3 blue balls and 7, ball is removed at random from Bo into Box B. After thoroughly mixing is drawn at random from Box Ba into Box A. and the (i) Draw a tree diagram to show th probabilities of the possible of (ii) Find the probability that
14. In a wardrobe, there are 16 shirts, of which 8 are black, 6 are white and 2 are blue. The shirts are identical except for their colour.(i). If two shirts are taken out of the wardrobe at random, find the probability that(a) both are black,(b) one shirt is black and the other is white,(c) the
13. Bernard has three pairs of headphones - A, B and C. In a year, the probabilities of Headphones A, B and C malfunctioning are 0.03, 0.12 and 0.3 respectively. Find the probability that, in a year,(i) all three pairs of headphones malfunction,(ii) all three pairs of headphones function
12. The table below shows the number of male and female employees working in the front office, Back middle office and back office of an investment bank.Three representatives, one from each department, are selected at random to attend a seminar. What is the probability that (i) all three
11. The diagram below shows two discs, each with four equal sectors. Each disc has a spinning pointer which, when spun, is equally likely to come to rest in any of the four equal sectors.In a game, the player spins each pointer once. His score is the sum of the numbers shown by the pointers.(i)
10. A red die has the number 1 on one face, the number 2 on two faces and the number 3 on three faces.Two green dice each has the number 6 on one face and the number 5 on five faces. All the dice are fair.The three dice are rolled together.(i) Copy and complete the tree diagram by writing the
9. Five balls numbered 1. 2. 5, 8 and 9 are put in a bag.(D) One ball is selected at random from the bag.Write down the probability that it is numbered(1) On another occasion, two balls are selected at random from the bag. By drawing a tree diagram, find the probability that(a) the number on each
8. A class has 30 girls and 15 boys. Two rep are to be selected at random from the da (i) Draw a tree diagram to show the probabilities of the possible outcom (ii) Albert said that the probability tha a girl are selected as representatives Explain what he has done incorrec (iii) Find the
7. Ten cards are marked with the letter'y(a)P. O. R. T. T. O' and 'N' respecte are placed in a box. Two cards are dran(c)random, without replacement.(1) Draw a tree diagram to show the(đ"of the possible outcomes.(ii) Joyce said that the probability that red 9bear the letter 'O' is.Explain gro gr
6. A bag contains 6 green cards and mixing the cards thoroughly, Yast cards at random from the bag, one(i) Draw a tree diagram to show probabilities of the possible out(ii) Yasir said that the probability are blue is . Explain what he incorrectly.(iii) Calculate the probability that Ya(a) two green
5. In a group of 8 boys, 3 are left-handed. The remaining 5 boys are right-handed. 2 boys are chosen at random from the same group of 8 boys.(i) Copy and complete the tree diagram.Second boy First boy(ii) By using the tree diagram, find the probability that (a) the first boy chosen is right-handed
4. Li Ting has two laptops, laptop X and laptop Y. In any one year, the probability of laptop X breaking down is 0.1 and the probability of laptop Y breaking down is 0.35. In any one year, what is the probability that(i) both laptops break down,(ii) laptop X breaks down but laptop Y does not,(iii)
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