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New Syllabus Mathematics Book 1 7th Edition Teh Keng Seng, Loh Cheng Yee, Joseph Yeo, Ivy Chow - Solutions

The figure shows AABC inscribed in a circle with centre O. If CBO is twice of CO and BO is one a half times of CBO, and find CO. A C B
In the figure, AC // ED and BE // CD. Find (i) DE, (ii) BDC. A 106 E 32 47 B
In the figure, ACE and BCD are straight lines. D 61-41 E 50 Find (i) ACB, (ii) ABC. B
In ∆ABC, B hat AC = 50 deg and B hat CA = 26 deg .(i) Find ABC.(ii) If AB is produced to D, find CBD.
If the sizes of the angles of a triangle are (x-35)°, (x-25)° and (1/2 x-10), find the value of x.
Given that AB // CD, find the values of the unknowns in each of the following figures. (a) A 108 B 71 C 37 b D E
Given that ABC, ADF and BDE are straight lines, find the value(s) of the unknown(s) in each of the following figures. (a) A 82 40 Bb F C (b) 57 D 51% B
Given that ABC and BED are straight lines, find the value(s) of the unknown(s) in each of the following figures. (a) E (b) A 115 B C89" E 27 B D 22 D 32
In the figure, ABC is a straight line. A B 20 C Given that ADB = BDC, find (i) BDC, (ii) CBD.
If the sizes of the angles of a triangle are 3x, 4x and 5x, find the smallest angle of the triangle.
Given that DAB is a straight line, find the value(s) of the unknown(s) in each of the following figures. (a) /55 D 47 (b) 35 (c) 110
Find the value of the unknown in each of the following figures. (a) 39 (b) B B 20 (c) C40 B (d) c (e) C A 62 B (f) 3d 68 B
For each of the following, the given angle is the base angle of an isosceles triangle. Find the third angle of the triangle.(a) 40°(c) 15(b) 87°(d) 79°
For each of the following, given the sizes of LA and LB, sketch ∆ABC. Find ∠C and hence classify each triangle according to the number of equal sides it has, and the types of angles it has, e.g. equilateral triangle and acute-angled triangle.(a) angle A = 20 deg angle B = 60 deg(b) angle A = 70
In the figure, AC = BC. Find the value of b. C 52 A B
Find the value of a in the figure. C 65 B A
In the figure, two rays OA and OB share a common vertex O. B 11-2 R-1 n A Find an expression, in terms of n, for the number of different angles in the figure if there are n rays between OA and OB.
When the minute hand of a 12-hour clock is at a right angle to the hour hand of the clock, a bell will sound once. Find the number of times the bell will sound from 9 a.m. on a particular day to 9 p.m. the next day.
Find the larger angle between the minute hand and the hour hand of a 12-hour clock at 7.20 p.m.
In each of the following figures, AB // CD. Find the value(s) of the unknown(s). (a) A. C- B 126 E 250 (b) P A 3 (6b 21) (5b-52) B
Given that AOB, COD and EOF are straight lines, find the value(s) of the unknown(s) in each of the following figures. (a) A 21 3 10 B 0 E +1 -17 (b) A 20 b 30 B 26 +15 D
For each of the following figures, find the value of the unknown. (a) 20 24 +4 (b) (46-211% (2b+1) (36 14) (+34)
Given that AOB and COD are straight lines, find the values of the unknowns in each of the following figures. (a) E 40 A 32 84 -B 2 (b) A 30 1/68 3d-5 E
In the figure, AB // CE and DF // AC. Find the value of x and of y. 7 B E C 41 58
In the figure, ABDE is a straight line and BC // EF. Find the value of x and of y. B 320 5D 147 E C F
In the figure, the lines AB and CD are cut by the transversals PQ and RS. If D hat YP = 46 deg , AS=104* and CR = 76", find BP. R C 0 W B 46 104 76% D Z S
In the figure, AC // EG, FD \\ GC, ABD = 46", DFE = 52 and FCG = 72". 46 D 52 E- Find (i) CGF, (ii) BCF, (iii) reflex BDF. B C 72 G
In the figure, AB // CD, BF || AD, EBF=68 and CDE = 58". B Find (i) AEB, (ii) ABE. 68 58
In the figure, HDF is a straight line, AB // CE / FG, ADH=47" and DFG=86". B H 47 Find (i) CDF, (ii) BAD. G E 86 D
In each of the following figures, AB || CD. Find the value of the unknown. (a) (b) 128 (4b-10) -B (c) A- 28 C 94 E B 19 -D (2-2) Q
Given that AB // CD, find the value of the unknown in each of the following figures. (a) (b) Ea 1420 B 1149 A 69 B 37 E D D
In each of the following figures, AB // CD. Find the value(s) of the unknown(s). (a) (b) C- A- 30 E 140 2 7c D 38 B -D B
Given that AB // CD, find the values of the unknowns in each of the following figures. (a) P R (b) 117 78 A B C (c) (19 S -D APP (d) 150 31 " B D
In the figure, AB // CD.(a) List down(i) two pairs of equal corresponding angles,(ii) two pairs of equal alternate angles,(iii) two pairs of interior angles which are supplementary.(b) Is BWQAXR? Explain your answer.(c) Is the sum of DYP and CZR equal to 180°? Explain your answer. A H PR -B D Y Z
In the figure, AOB and COD are straight lines.(i) Find the value of x and of y.(ii). Find obtuse AOD and reflex COE. C 61 A 34 E (186-4x) 31 B D
Given that AOB and COD are straight lines, find the values of the unknowns in each of the following figures. (a) A. 2 -13 7a 103 (c) A 71 +5 5g" + 18 2 +35 (b) (d) 300 62 49 E B 104 G E h 32
In the figure, DOB is a straight line, If BỘC is twice of AÔB, CÔD is four times of AOB and DOA is five times of AÔB, find all the four angles. D B
x, y and z' are three angles lying on a straight line.(a) If y=x+z", find the value of y.(b) Ifx=y=", find the value of
9. Given that AOB and COD are straight lines, find the value(s) of the unknown's) in each of the following figures () (a) D (b) D B
In the figure, AOB and COD are straight lines. IÍ A hat OE = 90 deg and B hat OD = 48 deg , find A- E D 48. B
For each of the following figures, find the value of the unknown. (a) (c) 67 52" 135 (b) (d) 36 17d+27 139 5d
x, y and z' are three angles lying on a straight line.(a) If y=45" and "=86", find the value of x.(b) Ifx2y and=3y", find the value of y.
Given that AOB is a straight line, find the value of the unknown in each of the following figures.
Find the supplementary angle of each of the following angles.(a) 36°(b) 12"(c) 102°(d) 171
Find the complementary angle of each of the following angles.(a) 18(b) 46°(c) 53(d) 64°
Classify each of the following as an acute, obtuse or reflex angle. (a) (b) (c) (d) 181" (e) 89 (f) 124"
Using a protractor, measure and write down the value of each of the following unknowns. (a) (b) (c) (d)
In a 100-metre race, Vishal beats Jun Wei by 10 m. The two boys plan to have another race, where Vishal will start 10 m behind the starting point. Both boys run at the same rate as before. Will it be a draw? Or who will win the race and by how many metres?
Kate likes to walk down moving escalators and she takes one step at a time When she walks down at a rate of 2 steps per second, she reaches the bottom from the top after 18 steps. When she is exhausted, she will walk down at a rate of I step per second and she will reach the bottom from the top
The diameter of a wheel of a car is 48 cm. If the car travels at an average speed of 3.5 km/h, find the number of revolutions made by the wheel per minute, giving your answer correct to the nearest whole number. (Take a to be 3.142.)
Farhan cycles the first part of a 150-km journey at an average speed of 35 km/h and walks the remaining distance at an average speed of 5 km/h. If he takes 4.5 hours for his entire journey, find the distance that he cycles.
Two points, A and B, are x m apart. C lies on the straight line joining A and B such that the ratio of the length of AC to that of CB is 2: 3. An object travels from A to C in half a minute and then from C to B at an average speed of 30 m/s. Find an expression for(i) the time taken for the object
In a triathlon, an athlete swims 750 m in 15 minutes, cycles at an average speed of 40 km/h for 30 minutes and runs 5 km at an average speed of 3 m/s. Find his average speed for the entire competition, giving your answer in km/h.
A lorry leaves a factory on a journey of 195 km at 08 45, travelling at an average speed of 52 km/h.(1) Find the time at which the lorry arrives at its destination.(ii) On the return journey, the lorry leaves at 14 55 and arrives at the factory at 18 15.Calculate the time taken and the average
A car took 2 hours and 15 minutes to travel 198 km. If it arrived at its destination at 12 06, find(i) the time it started its journey,(ii) the average speed of the car, giving your answer in km/h.
The total cost of placing an advertisement in a newspaper comprises of a fixed cost of $3.50 and a variable cost that depends on the number of words. Each word costs 25 cents.(i) Find the total cost of placing an advertisement containing 22 words.(ii) If Michael does not want to spend more than $15
A box contains 36 books and some toys. The ratio of the number of books to the number of toys is 4: 5. After some toys are given away, the ratio of the number of books to the number of toys becomes 12:11. Find(i) the initial number of toys in the box,(ii) the number of toys that are given away.
Three types of coffee beans, A, B and C, are blended in the ratio 3:5:7 to make a bag of coffee powder.(i) Given that the bag contains 45 kg of coffee powder, find the mass of each type of coffee beans in the mixture.(ii) If A costs $7 per kg, B costs $10 per kg and C costs $13 per kg, find the
If a : b = 1/2 : 1/3 and b : c = 3 : 4 find a : c.
The diameter of a wheel of a car is 60 cm. If the car travels at an average speed of 13.2 m/s, find the number of revolutions made by the wheel per hour, giving your answer correct to the nearest whole number. (Take a to be 3.142.)
A car travels the first 50 km of its journey at an average speed of 25 m/s and the next 120 km at an average speed of 80 km/h. The car completes the last part of its journey at an average speed of 90 km/h in 35 minutes. Find the average speed for its entire journey, giving your answer in km/h.
Two points, & and N, are 160 m apart. M lies on the straight line joining L and N. An object travels from & to M at an average speed of 10 m/s in 6 seconds and then from M to N at an average speed of 25 m/s. Find the average speed of the object for its entire journey from L to N.
Nora leaves Town A and walks towards Town B at a speed of 100 m/min. At the same time, Kate and Lixin walk from Town B towards Town A at a speed of 80 m/min and 75 m/min respectively. If Nora meets Lixin 6 minutes after passing Kate, find the distance between Town A and Town B.
A passenger train travels at a speed of 72 km/h. A man on the passenger train observes a goods train travelling at a speed of 54 km/h in the opposite direction. If the goods train passes him in 8 seconds, find the length of the goods train.
Two points, X and Y, are 120 m apart. M is the midpoint of X and Y. An object travels from X to M in 12 seconds and then from M to Y at an average speed of 15 m/s. Find(i) the time taken for the object to travel from M to Y.(ii) the average speed of the object for its entire journey from X to Y.
A car travels the first 19 km of its journey at an average speed of 57 km/h and the remaining 55 km at an average speed of 110 km/h. Find the average speed of the car for its entire journey.
A bullet train travels at a speed of 365 km/h. In August 2001, Singapore's national record for the men's 100 m sprint was set at 10.37 seconds. How many times is a bullet train as fast as the fastest Singaporean sprinter?
Express each of the following in m/s.(a) 65 cm/s(b) 367 km/h(c) 1000X0 cm/min(d) 86 km/min
Express each of the following in km/h.(a) 8.4 km/min(b) 315 m/s(c) 242 m/min(d) 125 cm/s
A high-speed train travels at a speed of 200 km/h. If the train sets off from Station A at 12 24 and reaches Station B at 14 12, find the distance between the two stations, giving your answer in metres.
A particle travels 24.6 km in 30 minutes. Find the speed of the particle in(i) km/h,(ii) m/s.
The Singapore Flyer has a diameter of 150 m. If each capsule of the Singapore Flyer travels at an average speed of 0.262 m/s, calculate the number of revolutions made by a capsule per hour, giving your answer correct to the nearest whole number.
A car and a bus are travelling towards each other. They are 510 km apart at 13 20 and they pass each other at 16 20. If the car is travelling at a speed of 90 km/h, find the speed of the bus.
A car travels at a speed of 55 km/h. Find the distance travelled by the car in 12 minutes 30 seconds, giving your answer in metres.
A train travels 16.8 km in 25 minutes. Find the speed of the train in(i) km/h,(ii) m/s.
The distance from the southern tip of Singapore to Batam is 20 km. If a ferry starts on its journey from Singapore at 10.50 a.m. and reaches Batam at 11.30 a.m., calculate the speed of the ferry in (i) km/h, (ii) m/s.
The schedule of the arrival and departure times of a long-distance express overnight coach is shown below. Destination Arrival A Departure 21 30 B 22 15 22 30 C 02 25 02 30 D 03 50 04 20 E 07 50 08:00 F 09 20 09:30 G 10 45 Find the time taken for the coach to travel from (a) A to C (b) B to E (c) C
According to a timetable, a coach was due to leave a station at 22 55 and arrive at its destination at 06 05 the next day. Find(i) the time taken for the journey,(ii) the time when the coach reached its destination given that it reached 35 minutes before schedule.
A car arrived at a town at 15 06 after travelling for hours. Find the time the car started the journey. 4
An overnight train left at 21 55 on a journey that took 9 h 18 min. Given that the train departed on a Monday, find the day and time at which it arrived at its destination.
A train left a station at 8.35 a.m. and arrived at its destination at 3.12 p.m. How long did the journey take?
Copy and complete the following table: Departure Time Journey Time Arrival Time (a) 02 40 55 minutes (b) 22 35 8 hours (c) 15 45 17 50 (d) 09:48 22 16 20 35 (e) (Tuesday) 07 15 (Wednesday) 3 (f) 1 hour 23.50
Convert the following times to 12-hour clock notation.(a) 03 30(b) 23 12(c) 19 15(d) 00 00
Convert the following times to 24-hour clock notation.(a) 8.00 a.m.(b) 9.42 p.m.(c) midnight(d) 2.42 a.m.
A train left Singapore at 07 35 and arrived at Seremban at 13 05 on the same day. How long was the train journey?
A car leaves Town A at 21 15 on Wednesday and arrives at Town B5 hours later. At what time and day does the car arrive at Town B?
10 chefs can prepare a meal for 536 people in 8 hours. Assuming that the chefs cook at the same rate and that the rate at which they cook remains constant throughout the preparation, find the number of people 22 chefs can prepare a meal for in 5 hours.
224 hours are required to complete a project.4 men are employed for this project.(1) The hourly rate of each man is $7.50. If the 4 men do not work overtime, find the total amount to be paid to the men.(ii) Their normal working hours are from 9 a.m. to 6 p.m., with a one-hour lunch break. Given
A cook uses fifteen 2-litre bottles of cooking oil in 4 weeks. If he decides to buy 5-litre tins of cooking oil instead, how many tins of cooking oil will he use over a 10-week period if the rate at which he uses it remains unchanged?
A cook uses fifteen 2-litre bottles of cooking oil in 4 weeks. If he decides to buy 5-litre tins of cooking oil instead, how many tins of cooking oil will he use over a 10-week period if the rate at which he uses it remains unchanged?
A piece of metal is heated to 428 °C before it is left to cool. The temperature of the metal falls at a rate of 23 °C per minute for the first 3 minutes, at a rate of 15 °C per minute for the next 15 minutes and then at a rate of 8 °C per minute until it reaches room temperature of 25 °C.
200 g of fertiliser is required for a plot of land that has an area of 8 m². Find(i) the amount of fertiliser needed for a plot of land that has an area of 14 m²,(ii) the area of land that can be fertilised by 450 g of fertiliser.
A car requires 22 litres of petrol to travel a distance of 259.6 km. Find(i) the distance that the car can travel on 63 litres of petrol,(ii) the amount that the car owner has to pay to travel a distance of 2013.2 km if a litre of petrol costs $1.99.
Michael has to pay $39 for 650 minutes of outgoing calls made using his handphone. Find(i) the amount he is charged for each minute of outgoing calls,(ii) the amount he has to pay if he makes 460 minutes of outgoing calls.
For each ornament that a worker makes, he is paid $1.15. He makes 4 ornaments every 15 minutes. Find the amount earned by the worker if he works for 3 hours.
Ethan can blow 15 balloons in 20 minutes, Jun Wei can blow 18 balloons in 25 minutes and Vishal can blow 16 balloons in 21 minutes. Assuming that all balloons are blown to the same size, who can blow balloons at the fastest rate?
(a) A typist types 1800 words in 1 hour. Find the number of words that she can type per minute.(b) If $120.99 is charged for 654 units of electricity used, find the cost of one unit of electricity.(c) A man pays a total of $4800 in flat rental for 3 months. Find his monthly rental rate.(d) If the
In a competition, 5 people can finish 20 steamed buns in 3 minutes 20 seconds. Assuming that everyone consumes steamed buns at the same rate and that the rate of consumption remains constant throughout the competition, find the number of steamed buns 10 people can finish in 5 minutes.
(a) A school bus company charges $2.70 per kilometre to ferry 36 children for an outing. How much does each child have to pay if the distance travelled for the trip is 32.5 km²(b) A car requires 25 litres of petrol to travel a distance of 265 km. Find(i) the distance that the car can travel on 58
(a) Khairul pays 56 for parking his car in a shopping centre for 2.5 hours. Calculate(I) the parking charges per minute,(ii) the amount that he will have to pay if he parks his car in the shopping centre for 12 hours. 4(b) On another occasion, Khairul drives from Singapore to Malaysia. His car

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