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Think! New Syllabus Mathematics 3 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
3 a Show that 20+2' +2+2'=24 - 1b Can you find a similar expression for 20 + 21 +23+23+ 2++ 25?c Read what Zara says:Is she correct? Give a reason for your answer. 30+31 +32+33-34-1
2 Write as a single power147× 144 b105×10ª63 ×6'36× 33 da€
1 Write as a single power 12×125 154×15 32× 3 b7X73 da C
11 Look at the following solution of the equation x = 64x6 = 64 ×3 = 8 so x=2 so There is an error in this solution. Write a corrected version.
10 a Write 64 as a product of its prime factors.b Show that 64 is a square number and a cube number.c Write 729 as a product of prime numbers.d Show that 729 is both a square number and a cube number.e Find another integer that is both a square number and a cube number.
9 Here is an equation: x3-x=120 a Is x =5 a solution? Give a reason for your answer.b Is x =- 5 a solution? Give a reason for your answer.
8 a. Copy and complete this table.xx-3-2-1012x2+xx2+x0x3+xx3+x0b. Use the table to solve these equations:i. x2+x=2ii. x3+x=2
7. Write whether each statement is true or false.a. 9 is a rational numberb. -9 is a natural numberc. 99 is an integerd. -999 is both an integer and a rational numbere. 9999 is both a natural number and a rational number
6. 232=529 and 233=12167Use these facts to solve the following equations.a. x2=529b. x2+529=0c. x3=12167d. x3+12167=0
5. Solve each equation.a. x3=216b. x3=−216c. x3+1000=0d. x3+8000=0
4. Solve each equation.a. x2=25b. x2=225c. x2−81=0d. x2+121=0
3. If possible, work outa. −64b. −6433c. −1253d. −72933
2. Work outa. 43b. (−6)3c. (−10)3d. (−1)2+(−1)3
1. Work outa. 142b. (−14)2c. (−20)2d. (−30)2
16 a b z-4=-8 -36z=9 b 2-2=20 d 30z=-6 Here is a statement: -3x(-6x-4)=(-3x-6)x-4 Is it true or false? Give a reason to support your answer. Here is a statement: -24+(-4-2)=(-24-4)-2 Is it true or false? Give a reason to support your answer.
15 Find the value of z. b PP yx-3=-36 d yx-5=-40 a C
14 Find the value of y. a C -8xy=48 -10xy=120
13 Copy and complete this multiplication pyramid. 15 270 -3 -3
12 Estimate the answers by rounding numbers to the nearest 10. a 92-28.5 b -41-18.9 C 83.8-11.6 d -7719
11 Work out a 42-7 b -50-10 c 27-3 d -52-4 e 60-5
10 a Find all the possible values of the two integers. The product of two integers is 6. Find all the possible values of the two integers. Here is a multiplication: -9x-7=63 Write it as a division in two different ways. b Here is a different multiplication: 12x-7=-84 Write it as a division in two
9 a The product of two integers is -6. b
8 This is a multiplication pyramid. Each number is the product of the two numbers below. For example, 3x-2=-6 a Copy and complete the pyramid. b Show that you can change the order of the numbers on the bottom row to make the top number 3456. -6 3 -2 -1 4
7 Show that (-6)+(-8)2-(-10)2=0
6 Estimate the answers by rounding numbers to the nearest integer. a -2.9x-8.15 b 10.8-6.1 C (-8.8) d (-4.09)
5 Work out a (3+4)5 b (3+-4)5 C (-3+-4)x-5 d (3+-4)x-5
4 Copy and complete this multiplication table. -4 -9 x -6 5 -45 -8 -16
3 Put these multiplications into two groups. A -12x-3 B (-6)2 C -4x9 D 182 E 9x-4 F -4x-9
2 Work out a -58 C 3 -9x-11 3x-4=-12 b -5x-8 d -20x-6
1 Copy this sequence of multiplications and add three more multiplications in the sequence. 7x-4=-28 5x-4=-20 1x-4=-4
17 The HCF of two numbers is 6. The LCM of the two numbers is 72. What are the two numbers?
16 a Show that the LCM of 48 and 25 is 1. d Find the LCM of 343 and 546. b Find the HCF of 48 and 25.
15 a Find the HCF of 168 and 264. b Find the LCM of 168 and 264.
14 Find the LCM of 42 and 90.
13 a b C Write 343 as a product of prime numbers. Write 546 as a product of prime numbers. Find the HCF of 343 and 546.
12a Write 135 as a product of prime numbers.b Write 180 as a product of prime numbers.c Find the HCF of 135 and 180.d Find the LCM of 135 and 180.
11a Write 104 as a product of its prime factors.b Write 130 as a product of its prime factors.c Find the HCF of 104 and 130.d Find the LCM of 104 and 130.
10 60 = 2² × 3 × 5 72 = 2³ × 3² 75 = 3 × 5²Use these facts to find the lowest common multiple ofa 60 and 72 b 60 and 75 c 72 and 75
9 315 = 3² × 5 × 7 252 = 2² × 3² × 7 660 = 2² × 3 × 5 × 11Use these facts to find the highest common factor ofa 315 and 252 b 315 and 660 c 252 and 660
8 a Write each square number as a product of its prime factors. i 9 ii 36 iii 81 iv 144 v 225 vi 576 vii 625 viii 2401b When
7 Write as a product of prime numbersa 70 b 70² c 70³
6 Write each of these numbers as a product of its prime factors.a. 96b. 97c. 98d. 99
5a. Draw a factor tree for 8712.b. Write 8712 as a product of prime numbers.
4 Work outa. 2×3×72 \times 3 \times 72×3×7b. 22×32×722^2 \times 3^2 \times 7^222×32×72c. 23×33×732^3 \times 3^3 \times 7^323×33×73
3a. Write as a product of prime numbers:i. 6 ii. 30 iii. 210b. What is the next number in this sequence? Why?
2a. Draw a factor tree for 300.b. Draw a different factor tree for 300.c. Write 300 as a product of prime numbers.
1a. Draw a factor tree for 250 that starts with 2×1252 \times 1252×125.b. Can you draw a different factor tree for 250 that starts with 2×1252 \times 1252×125? Give a reason for your answer.c. Draw a factor tree for 250 that starts with 25×1025 \times 1025×10.d. Write 250 as a product of its
17. The number of social networking accounts a group of students own is recorded.(a) If the mean number of social networking accounts the students own is 2.2, find the value of x.(b) If the median of the distribution is 2, find the greatest possible value of x.(c) If the modal number of social
16. The number of major hurricanes, which strike the Atlantic coast each year over a period of 50 years, was recorded.(i) If the mean of the distribution is 2.18, find the value of x and of y.(ii) Find(a) the median,(b) the mode, of the distribution.(iii) There are at most p major hurricanes
15. Raju has six money boxes.The modal, median and mean amounts of money in the money boxes are $50, $40 and $35 respectively. If he takes out $10 from each money box, find the new values of the modal, median and mean amounts of money in the money boxes.
14. The times taken for 12 students to solve a puzzle were recorded, to the nearest minute.The modal, median and mean timings were 13 min, 13 min and 15 min respectively. The students were given 3 min to read an insert before solving the puzzle, which was not included in the timings recorded. If
13. Imran has written down six numbers less than 15.OPEN The mean of these numbers is 7, the median and the mode are both 9.Half of the numbers are the same, and one of them is a single digit negative number. Two of the positive numbers are primes while the rest are multiples of 3.Find a possible
12. There are seven positive numbers in a data set. The mean of these numbers is 7, the median is 8 and the modes are 2 and 10.The largest number is a perfect square.Find the seven numbers.
11. The number of magazines read by a group of women in a week is recorded.(a) If the mean of the distribution is 2, find the value of x.OPEN(b) If the median of the distribution is 1, find a possible value of x. Number of magazines Number of women 0 1 2 3 5 2 1 x
10. The number of pets 40 students own is recorded.(a) (i) Show that x + y = 18.(ii) If the mean of the distribution is 6.4, show that x+3y=30.(iii) Hence, find the value of x and of y.(b) Using your answers to part (a)(iii), find(i) the median,(ii) the mode, of the distribution. Number of pets
9. Two classes, each with 21 students, took a physical fitness test. The number of pull-ups done by each student in 30 seconds was recorded.(i) Explain why we are unable to calculate the mean number of pull-ups done by the students in each class (ii) Find the median number of pull-ups done by the
8. Albert and Bernard were playing golf. Their scores on the first nine holes are shown in the table. In golf, the lower the score, the better it is.On the ninth hole, Albert hit his golf ball into a sand trap and lost the game.(i) Find the mean score on the nine holes for each player.(ii) Which
7. The median of eight numbers is 4.5. Given that seven of the numbers are 9, 2, 3, 4, 12, 13 and 1, find the eighth number.
For each of the following, state the mode(s) or modal class of the distribution. (a) Colour Frequency Red 28 Yellow 15 Green 28 Blue 35 Orange 19 Purple 35 Pink 28 Brown 20 Grey 11 (b) Temperature (x C) Frequency 0\x
5. For each of the following, state the mode(s) of the distribution. (a) x 6 7 8 6 10 (b) Frequency 1 1 1 1 1 Frequency 2 15 20 25 30 35
4. The temperatures, taken at midnight, of 6 consecutive nights in Singapore are given as follows:22 °C, 27 °C, 26 °C, 28 °C, 27 °C, 23 °C.(i) State the modal temperature.The temperature, taken at midnight, of the 7 day in Singapore was 22 °C.(ii) If 22 °C is added to the above set of data,
3. Find the mode(s) of each of the following sets of numbers.(a) 2,5,8,3,7,5,3,9,7,3(b) 8.1, 7.7, 7.8, 9.3, 6.4, 7.7, 9.3, 8.7(c) 11.3, 10, 21, 14.5, 26, 11, 20.1
2. For each of the following, find the median of the distribution or the class interval which contains the median. (a) h 100 200 300 400 500 600 Frequency 2 4 15 1 2
1. Find the median of each of the following sets of numbers.(a) 5, 6, 1,5,3,5,6(b) 1.2, 1.1, 4.1, 3.2, 4.1, 1.6, 2.8(c) 30, 33, 37, 28, 29, 25(d) 39.6, 12, 13.5, 22.6, 31.3, 8.4, 5.5, 4.7
13. The mean monthly wage of seven experienced and five inexperienced workers is $1000. If the mean monthly wage of the five inexperienced workers is $846, find the mean monthly wage of the seven experienced workers.
12. The heights of three plants A, B and C in a garden are in the ratio 2:3: 5. Their mean height is 30 cm.(i) Find the height of Plant B.(ii) If another Plant D is added to the garden such that the mean height of the four plants is now 33 cm, find the height of Plant D.
11. The mean of 10 numbers is 14. Three of the numbers have a mean of 4. The remaining seven numbers are 15, 18, 21, 5, m, 34 and 14. Find(i) the sum of the remaining seven numbers,(ii) the value of m.
The number of goals scored per match by a team during a soccer league season was recorded. Number of goals scored 0 1 2 per match 3 4 5 6 Number of matches 6 8 5 6 2 2 1 Find (i) the total number of matches played, (ii) the total number of goals scored, (iii) the mean number of goals scored per
7. The mean mass of 28 students in Class A is 50.5 kg. The mean mass of 35 students in Class B is 52.6 kg. Find the mean mass of the students in the two classes.
6. There are two buildings in a condominium. Building X has 60 units while Building Y has 80 units. The mean number of people living in each unit of Buildings X and Y are 3 and 4 respectively. Find the mean number of people living in each unit of the condominium.
5. The mean of eight numbers is 12. Five of the numbers are 6, 8, 5, 10 and 28. The remaining three numbers are each equal to k. Find(i) the sum of the eight numbers,(ii) the value of k.
4. The mean mass of five boys is 62 kg. When the mass of a boy is excluded, the mean mass of the remaining four boys becomes 64 kg. Find the mass of the boy that has been excluded.
3. The mean of 7 cm, 15 cm, 12 cm, 5 cm, h cm and 13 cm is 10 cm. Find the value of h.
2. Consider the prices, in $, of various computing books at a bookstore:19.90, 24.45, 34.65, 26.50, 44.05, 38.95, 56.40, 48.75, 29.30, 35.65.Find the mean price of the books.
The number of passengers on coaches travelling along 12 popular scenic routes are 29, 42, 45, 39, 36, 41, 38, 37, 43, 35, 32 and 40.Find the mean number of passengers on the coaches.
A solid consists of a cone and a hemisphere which share a common base. The cone has a base radius of 35 cm. Given that the volume of the cone is equal to of the volume of the hemisphere, find(i) the height of the cone,(ii) the total surface area of the solid, leaving your answer in terms of it.
8. A solid metal ball of radius 3 cm is melted and recast to form a solid circular cone of radius 4 cm. Find the height of the cone.A solid consists of a cone and a hemisphere which share a common base. The cone has a base radius of 35 cm. Given that the volume of the cone is equal to of the volume
7. A storage tank consists of a hemisphere and a cylinder which share a common base. The tank has a height of 16.5 m and the cylinder has a base diameter of 4.7 m. Find the capacity of the tank. 4.7 m 16.5 m
6. Find(i) the total surface area,(ii) the volume, of the solid cylinder with conical ends as shown. 6 m 6 m -8m- 8 m
5. A container is made up of a hollow cone with an internal base radius of r cm and a hollow cylinder with the same base radius and an internal height of 4r cm. Given that the height of the cone is three-fifths of the height of the cylinder and 7 litres of water are needed to fill the conical part
4. A solid consists of a hemisphere and a cone which share a common base. The cone has a base radius of 21 cm, a height of 28 cm and a slant height of 35 cm. Find(i) the volume,(ii) the total surface area, of the solid. 21 cm 28 cm 35 cm
A solid consists of a hemisphere and a cylinder which share a common base. The cylinder has a base radius of 7 cm and a height of 10 cm. Find L(i) the volume,(ii) the total surface area, of the solid. 10 cm 7 cm
2. A cylinder has a radius of 6 cm and a height of 15 cm. A hole in the shape of a cone is bored into one of its ends. If the cone has a radius of 3 cm, find the volume of the remaining solid. 3 cm 6 cm 15 cm
1. A rocket is in the shape of a cone attached to a cylinder with the same base radius. The cone has a slant height of 15 m. The cylinder has a base diameter of 12 m and a height of 42 m. Find the total surface area of the rocket. 12 m 15 m 42 m
15. There are 20 identical solid hemispheres. The curved surface and the flat surface of each hemisphere are to be painted red and yellow respectively. Find the ratio of the amount of red paint needed to the amount of yellow paint needed.
14 A cylindrical can has a base radius of 3.4 cm. It contains a certain amount of water such that when a sphere is placed inside the can, the water just covers the sphere. If the sphere fits exactly inside the can, find(i) the surface area of the can that is in contact with the water when the
13. A basketball has a surface area of 1810 cm³. Find its volume.
12. A sphere has a volume of 850 m³. Find its surface area.
11. A cylindrical tin has an internal diameter of 18 cm. It contains water to a depth of 13.2 cm. A heavy spherical ball bearing of diameter 9.3 cm is dropped into the tin. Find the new height of water in the tin, leaving your answer correct to 2 decimal places.
10. A sphere of diameter 26.4 cm is half-filled with acid. The acid is drained into a cylindrical beaker of diameter 16 cm. Find the depth of the acid in the beaker.
9. 54 solid hemispheres, each of diameter 2 cm, are melted to form a single sphere. Find the radius of the sphere.
8. A hollow aluminium sphere has an internal radius of 20 cm and an external radius of 30 cm. Given that the density of aluminium is 2.7 g/cm³, find the mass of the sphere in kg. 30 cm 20 cm
7. Find the number of steel ball bearings, each of diameter 0.7 cm, which can be made from 1 kg of steel, given that 1 cm³ of steel has a mass of 7.85 g.
6. A hemisphere has a curved surface area of 364.5 cm². Find its radius.
Find the radius of each of the following spheres with the given surface area.(a) 210 cm²(b) 7230 mm²(c) 3163 m²(d) 647 cm²(e) 911 mm²(f) 49 m²
4. Find the total surface area of a solid hemisphere of radius 7 cm. (Take it to be 3.142.)
3. Find the surface area of each of the following spheres.(a) radius 12 cm(b) radius9 mm(c) diameter6m
2. Find the radius of each of the following spheres with the given volume.(a) 1416 cm³(b) 12 345 mm³(c) 780 m³(d) 972 cm³(e) 498 mm²(1) 15m² 16
Find the volume of each of the following spheres with the given radius.(a) 8 cm(c) 4 m(b) 14 mm
20. A cone has a circular base of radius 13.5 m. Given that the total surface area of the cone is 1240 m², find its volume.
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