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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
Calculate each of the following, giving your answer in standard form, correct to 3 significant figures. (a) (1.35 x 10') (c) 1.21x10 (b) 6(3.4 x 10) (d) 9.261x10 2.3x102x4.7x10 8x10+2.510 (e) (f) 2x10 2x102-3.4x10
7. Calculate each of the following, giving your answer in standard form, correct to 3 significant figures. (a) (2.34 x 105) x (7.12 10-4) (b) (5.1 x 10)x(2.76 10-) (c) (13.4 x 10') (4 10) 3x104 (d) 9x10 (e) 2.54 x 10+ 3.11 x 10 (f) 3.1 x 10-6 105 4.37x10 +2.16x10 (g) 3x103 10 2.410 (h)
6. The mean distance from the Earth to the Sun is gigametres (Gm), where 150 and IGm = 10 deg * m . The mean distance from Pluto to the Sun is d terametres (Im), where d = 5.91 and 1 n = 10 ^ 12 . Express d as a percentage of c Give your answer in standard form.
5. (i) A nitrogen atom has an atomic radius of a picometres (pm), where a = 70 and 1 pm-10m. Express this radius in metres. Give your answer in standard form,(ii) An oxygen atom has an atomic radius of nanometres (nm), where b = 0.074 and nm = 10 ^ 4 * v . Express this radius in metres. Give your
Microwaves are a form of electromagnetic radiation with frequencies between 300 000 000 Hz and 300 GHz. Giving your answer in standard form, express(1) 300 000 000 Hz in MHz,(ii) 300 GHz in MHz.(1 MHz10 Hz and 1GHz = 10 ^ r * Hz )
A male African elephant can weigh as heavy as 7000 kilograms. Express this weight in grams, giving your answer in standard form.
Express each of the following in ordinary notation.(a) 9.6 * 10 ^ 3(b) 4 * 10 ^ 2(c) 2.8 * 10 ^ - 4(d) 1 * 10 ^ - 4
Express each of the following numbers in standard form.(a) 85.300(b) 52 700.000(c) 0.000 23(d) 0.000 000 0904
A Secure Digital (SD) memory card has a capacity of 512 megabytes. Each photograph has a size of 640 kilobytes. Assuming that 1 MB 10 bytes and 1 kB 10 bytes, how many photographs can this memory card store?
Calculate each of the following, giving your answer in standard form, correct to 3 significant figures. (a) (1.14 x 105) x (4.56 x 10') (c) (2.4 x 10%)+(6 x 10') (e) 1.14 x 105 +4.56 x 10' (g) 2.3710+3.2510* 4.110 6 (b) (4.2 x 10) x (2.6 10) 3.5105 (d) 1.410* (f) 2.6 x 10-4 x 10' (h) 6.310
Evaluate each of the following, giving your answer in standard form, correct to 3 significant figures. (a) (1.35 x 10 +4.5 x 10-1) x (2.37 x 10') 2.58x10-4.19x10* (b) 3.1710
4. For each of the following, give your answer in standard form.(a) An external hard drive has a capacity of 4.0 terabytes. Given that 1 terabyte = 10 bytes, express this capacity in bytes.(b) The diameter of a human hair is 25.4 micrometres. Given that 1 micrometre 10 metres, express this diameter
3. For each of the following, give your answer in standard form.(a) A steam power plant has a capacity of 250 megawatts. Given that 1 megawatt 10 watts, express this capacity in watts.(b) The average lifespan of a certain molecule is 0.5 nanoseconds. Given that 1 nanosecond 10 seconds, express this
2. Express each of the following in ordinary notation.(a) 1.325 x 10"(b) 4.4 x 10
1. Express each of the following numbers in standard form.(a) 5.300.000(b) 600 000 000(c) 0.000 048(d) 0.000 000 000 167
Express each of the following numbers in standard form.(a) 149 600 000(b) 0.000 038
In a particular study, the population of a town is observed to follow a cycle every 2 years in the first year, its population increases by 10%, and in the second year, its population decreases by 10%. If the current population is 50 000, what is the population after 40 years, correct to the nearest
In a particular experiment, the masa of a radioactive sample is halved every 1.5 hours. After 6 hours from the start of the experiment, it had a mass of 300 grams(i) Find the initial mass of the radioactive sample(ii) Calculate the man of the radioactive sample 24 hours after the start of the
In which year will there be 100 workers in the company!
A company was founded on January 2022. After years, its number of workers. N, is given by N-30x1.2(i) State the initial number of workers that the company started with(ii) How many workers are there after 3 years?
5. Yasir bought a car. After years, its value. $5is given by P = 25000 x 0.86t.(i) How much did Yasir pay for the cart(ii) Find the percentage decrease in the value of the car each year
The value of a painting, 50, years after 2020 is goon by P-2000 x 1.1"(1) What was the initial value of the painting! (i) Find the value of the painting in 2030.
3. Initially, the population of a species of insects in a colony is 1000. It increases by 1% daily(1) Write down a formula for the population, P after of days,(ii) What is the population after 30 days!
The number of tourists who visited a particular attraction in 2018 was 22000. Each year, the number declines by 12%. Find the number of tourists in 2030.
The number of bacteria in a petri dish doubles every hour. If the initial number of bacteria is 50 how many bacteria are there after 6 hours?
Waseem solved a quadratic equation with rational coefficients and found that the roots are 2 - sqrt(3) and 1 + sqrt(3) Explain why his answer is wrong.
Given that sqrt(a + b * sqrt(11)) = c/((sqrt(11) - 3) ^ 2) wherea, b and care rational numbers, find a possible set of values fora, b and c.
12 a = 1/(sqrt(2)) surd form, and b = (1 + a)/(1 -a) express in its simplest(i) b(ii) b - 1/b
11. A right circular cylinder has a volume of (6 + 2sqrt(3)) * pi*c * m ^ 3 and a base radius of (1 + sqrt(3)) cm. Find its height in the form (a + b * sqrt(3)) cm, where a and b are integers.
10. The area of a rectangle is 2sqrt(6) cm². If its breadth is (3 - sqrt(6)) cm, find its length in the form ( (a + b * sqrt(6)) * c , where a and b are integers.
9. Given that h = 3 + sqrt(2) express (h ^ 2 + 1)/(h - 2) in the form p + q * sqrt(2) where p and q are integers.
8. Express (9 - sqrt(3)) ^ 2 - 78/(sqrt(3 + 9)) in the form a + b * sqrt(3) where a and b are integers.
Without using a calculator, express each of the following in its simplest surd form. (a) 32 18 (b) 27 27 6 3 128 (c) + (d) 3
Simplify each of the following by rationalizing the denominator. (a) 13 (3+4) 3 5 (b) (2+6) (2-6) 48-50 32-6 (c) 6+32 (d) 27-8
Simplify each of the following by rationalizing the denominator. 3 8 4 (a) (b) 25+8 25+3 25-3
Simplify each of the following without using a calculator. (a) (5+2)(6-32) (c) (311-4) (e) (9-25)(9+25) (f) (27+35)(27-35) (b) (3+26) (d) (73-37)
Simplify each of the following without using a calculator. (a) 112+28 (b) 180-125 (c) 48+12-27 (d) 11-99+44 245-20 (e) 240 12x45 (f) 500
Simplify each of the following without using a calculator. (a) 2x32 (b) (c) 63 343 7 75x72 (d) 24
Simplify each of the following by rationalizing the denominator. (a) 10 (b) 310 7 9 (c) (d) 2+3 8-6 5 4 (e) (f) 43-2 27+3
Simplify each of the following by rationalizing the denominator. e 217 (b) 22 4+5 9 ST 5 5 (d) 26-3 + 7 4-33 33+4
Simplify each of the following by rationalizing the denominator. (a) (b) 7 2+3
Simplify each of the following without using a calculator. (a) (7+23)(5-3) (c) (3+25)(3-25) (b) (4-32) (d) (36+42)
Simplify each of the following without using a calculator. (a) 75+108 (c) 24+54-216 (b) 80-20
Simplify √32 + √50 without using a calculator.
Simplify each of the following without using a calculator. 125 (a) 27x3 (b) (c) 12 (d) 80x12 (16)
Simplify each of the following without using a calculator. (a) 2x8 216 (b) 6 (c) 18
17. Simplify each of the following, expressing your answers in positive index form. (a) x'y'z x'y'z x xyz 5. 6 (xyz7 5 (b) x yz + x3y x'y ab" (c) "db12 bc cd "13 + (d) (a+b)" (a+b)**3 #13 bc abc
16. Simplify each of the following, expressing your answer in positive index form. (a) (a*b)(ab) (b) (cd) x ( a ) gh 212 S (c) (d) (e ) * 25 (e) (4j*k)+2hk (f) (mn ). +32m'n
15. Simplify each of the following, expressing your answer in positive index form. 3 (a) aa (c) c +c sxc (e) 23 45 32 (pa) 2357 (b) bs xb+b (d) mn (f) (mn 1) 81x 16xy
14. Simplify each of the following. (a) 3aa2+ axa- (b) (5p)-10px 7p + 2a P 6 1
13. Simplify each of the following, expressing your answer in positive index form where appropriate. (a) 5ax 3a + a (b) -24b(3b-) (c) (40*) 126 8e2f" (e) (k)x (d) (3gh)x(-4gh) (mn)x(m) *(*)* (f) (m 'n)
12. Simplify each of the following, expressing your answer in positive index form. (a) (b-sc)-1 (c) (3c)+(cd)-1 (b) 5f3f4
11. (a) Given that 1/256 = 4k, find k.(b) Given that 32 × 163/4 =2n, find n.(c) Find p if p2/3 = 4.
10. Solve each of the following equations. (a) 11-1331 (c) 9-243 (b) 2 128 (d) 10-0.01
9. Without using a calculator, evaluate (1000/27) ^ (9/3). Give your answer as a decimal.
8. Simplify each of the following, expressing your answer in index form. (a) Ja (c) (e) 2 (b) (6) (d) 1
Rewrite each of the following in the radical form and hence evaluate the result without using a calculator. (a) 81 (b) (-27) (c) 32 (d) (-343)
7. Evaluate each of the following without using a calculator. (a) 216 (b) 8 (c) 16's (d) (-1000) (e) 81-9 (f) 625075+10025
5. Evaluate each of the following without using a calculator. (a) 196 (b) 125 (c) 16 32 (d) 81
4. Evaluate each of the following without using a calculator. (a) (72) 274 (c) (2.50+(3) (b) 50-5-2 (d) x 32+2015
3. Evaluate each of the following without using a calculator. (a) 2 (c) (b) (-5) (d) 513
2. Find the value of each of the following without using a calculator. (a) 2 x 24 (c) (-8)-82 (b) 72 x 7+7 (d) 3+3-3
1. Evaluate each of the following without using a calculator. (a) 17 (b) (c) 4a (d) -86 (e) (72cd) (f) 7(e)
solve each of the following equations (a) 5x=125 (b) 7-- (c) 8-16 49
solve each of the following equations (a) 2-32 (b) 3 61 (c) 9=27
Simplify each of the following, leaving your answer in positive index form. (a) (m)m (c) (mn) (b) m+m x'y (d) 1000y12 h k (e) hk (f) (25pq (25pq) (p'q)
Simplify each of the following, leaving your answer in positive index form. (a) mxm (b) b) (pq) + (pq) 10 32x (c) 15
What happens if you are not careful about the conditions of the bases? The following shows a ridiculous proof that concludes that 1 - -1.Explain what is wrong with the proof. = I -(-1)x(-1) zx(1-)= (L-A)= EXEN- =(-1)' -1
Simplify each of the following, leaving your answer in positive index form. (a) a (b)
Evaluate each of the following without using a calculator. (a) 643 (c) 10015 (b) 32 3 (d) 425 +273
What is 5 2/3 equal to? (a) 53 =(53) = (b) 5-52 Law 3 of Indices -(s) Law 3 of Indices =(5)
Rewrite each of the following in the radical form and hence evaluate the result without using a calculator. (a) 164 (b) (-27)}
Rewrite each of the following in the radical form and hence evaluate the result without using a calculator. (a) 362 (c) 243 15 (b) 6254 (d) (-1000)
Evaluate each of the following without using a calculator. (a) 256 (b) $1024 64 64 (c) (d) 125 729
Evaluate each of the following without using a calculator. (a) 625 243 (b) 32
Simplify each of the following, leaving your answer in positive index form. (a) axaa 16d2e (b) (2d 'e) (c) 18g3(g)
Simplify each of the following, leaving your answer in positive index form where appropriate. (a) axa a (b) 8bc3(2bc)
(i) What happens if m = n in Law 2?(ii) What happens if m < n in Law 2?(iii) Why is it no longer necessary for m > n in Law 2?(iv) What happens if m = 0 in Law 2?
Notice that some conditions for the bases a and b are now different.(i) Why is it necessary for a ≠ 0 in Law 1?(ii) Why is it necessary fora, b ≠ 0 in Law 4?
1. If bases a and b are real numbers, and indices m and n are integers, then Law 1 of Indices: amxa if a 0 Law 2 of Indices: a"a" if a 0 Law 3 of Indices: (am)- if Law 4 of Indices: ax = if a, b 0 Law 5 of Indices: a+b= if
Simplify (2d)0 + (d2 e-4)-1.
Evaluate each of the following without using a calculator. (a) 62 (c) 45 (b) (-8)-1 (d) 9
Evaluate each of the following without using a calculator. (a) 43 (b) (-7) (c) 35 2
2. Find the value of each of the following without using a calculator.(a) 3 ^ 0 * 3 ^ 3 / (3 ^ 2)(b) 3 deg + 3 ^ 2
1. Evaluate each of the following without using a calculator.(a) 2022 deg(b) (- 8) deg(c) 3 * y deg(d) (3y) deg
Evaluate each of the following without using a calculator.(a) 38 deg(b) 2x ^ 0(c) (2x) ^ 0(d) - 7 deg * (- 7) deg + 16 deg
Given thatform a pair of simultaneous hence find the value of a and of b. (2p'q')* (4pq) (-39) 9 P
Given that x ^ 9 * (x ^ 3) ^ (2n) / ((- x deg) ^ 2) = x ^ 23 find the value of n.
Simplify each of the following. (a) (2xy) (5xy) (10xy) (b) 8x*y (4x) 4xy X- (2xy) (3xy) (2xy)* (c) (d) 4xy8x*y (4xy)*(xy) (4xy)
Simplify each of the following. (a) (c) 2a2 ()) 27e9 AA (b) (d) 2d h -3g 2h2 (9)+(5)
Simplify each of the following. (a) (ab) x (2ab) (c) (8e)=(ef) (b) cdx(-5c'd) (d) 16gh (-2gh)
Simplify each of the following. (a) (a) a (c) (c)+(-c) (e) (ef2)5(-ef)+ (b) (b)7 x (b) (d) (-3d) (2d) (f) (4k)+(-2k)
Simplify each of the following. (a) hkxh"k (c) 11pqx 2pq (e) 15mn 3mn (b) (-m'n) x 4m"n" (d) hk+hk (f) (-10xy) (-2xy)
(a) Express 33 * 34 / 3 in the form 3n.(b) Write 28 * 23/27 as a single power of 2.
Simplify each of the following, leaving your answer in index notation where appropriate. (a) 1413713 (b) (95)320 (c) m (e) 9 (d) (f) ( (
Simplify each of the following, leaving your answer in index notation where appropriate. (a) (92)* (c) 2 9 (e) (2k6) (b) (h)5 (d) 34 x (52) (f) (-3x)
Simplify each of the following, leaving your answer in index notation where appropriate. (a) 5+55 (b) (-7)"(-7)* (c) 6x+x (d) (-15y")+5y
Simplify each of the following, leaving your answer in index notation where appropriate. (a) 23 x 27 (c) xxx (b) (-4)x(-4)5 (d) (3y) x (8y)
Simplify each of the following, leaving your answer in index notation where appropriate. (a) 217 (b) (4) (+ (d) (457) 64% 64x7 21
Simplify each of the following, leaving your answer in index notation where appropriate. (a) 10% +28 (b) 20 (c) 27 p pq 16
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