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OXFORD New Syllabus Mathematics Book 2 7th Edition Teh Keng Seng, Loh Cheng Yee, Joseph Yeo, Ivy Chow - Solutions

Fig. 8.8 shows a square and a rhombus. P P S R S R Fig. 8.8
Fig. 8.7 shows two rectangles.(i) Are all the corresponding angles equal?(ii) Are all the ratios of the corresponding sides equal?(iii) Are the two rectangles similar? A B A B' D'E C Fig. 8.7
(a) Measure the lengths of each of the following pairs of sides.(6) AB, A' * B'(ii) BC. B' * C'(iii) CD, C' * D'(iv) DE, D' * E'(v) EF, E' * F'(vi) FA, F' A^ prime prime(b) Hence, find the value of each of the following ratios.What do you notice about the values of the ratios? A'B (i) B'C C'D'
Measure each of the following pairs of angles.(a) angle A , angle A'(b) angle B , angle B'(c) angle C , angle C(d) angle D , angle D'(e) angle E_{t} LE(f) angle F , LF What do you notice about the size of each of the above pairs of angles?
Discuss with your classmates other real-life examples of similarity.
In the figure, AABC is an isosceles triangle where ABAC, BC = 12cm and angle ABK = 58 deg . Given that ΔΑΒΚ = ΔΑCΗ and angle AKC = 90 deg find(1) the length of CH,(ii) ∠BAH. A B 58 K 12 cm C H
In the figure, Delta ABC equiv Delta*DEC . Given that angle ACB = 71 deg . angle CDE = 34 deg AC = 6.9cm and BC = 4cm find(i) angle ABC ,(ii) the length of BD. A D 6.9 cm 34" B 71 4 cm C E
In the figure, Delta ABK equiv Delta*ACK . Given that angle AKB = 90 deg , angle ACK =62^ * AB =1" cm and BK = 8cm find(i) angle BAC ,(ii) the length of BC. A B 17 cm 8 cm 62" K C
Are the following pairs of triangles congruent? If so, explain your answer and write down the statement of congruence. If not, explain your answer. (a) 36.9 4 cm 5 cm 4 cm P 36.9 3 cm 5 cm B 3 cm R (b) D S 18.8 cm 19.7 cm 80 18,8 cm 10 cm 80 70 30 E 10 cm F U 19.7 cm T
Given that EFGH LMNO, write down all the missing measurements. F65 E 3 cm H 120 G 5 cm N 2.4 cm 75 100 L M 3.4 cm
Given that PQRST VWXYZ, copy and complete each of the following. (i) PQ-VW- cm (ii) PT= = 2 cm (iii) QR = cm (iv) TS= cm (v) SR= cm (vi) LPQR = 2 cm P T V Z 2.1 cm 3.5 cm S 2 cm R W X 3.5 cm
Which pairs of shapes are congruent? G A B E F D H K L
In the figure, Delta ABC equiv Delta*CDE .(a) Given that angle ABC = 38 deg angle DCE = 114 deg . AC = 18cm and DE = 27cm find angle CDE ,(ii) angle CED ,(iii) angle ACB ,(iv) the length of BC,(v) the length of BE(b) What can we say about the lines AC and ED? D 27 cm C114 18 cm E 38 B A
In the figure, Delta ABC equiv Delta*CED(a) Given that angle BAC =20^ * , angle CDE = 60 deg , AB = 8.8cm and CD = 10cm calculate(i) angle ECD(ii) angle FCB(iii) angle ABC(iv) the length of AC,(v) the length of AE.(b) What can we say about the lines AB and DC? D 60 10 cm E 20 8.8 cm B
Are the following pairs of triangles congruent? If so, explain your answer and write down the statement of congruence. If not, explain your answer. (a) 4 cm A 60 B 80 6.1 cm 5.4 cm 40 R 40" 10.8 cm (b) D 4 cm 80 12.2 cm 60 80 90 8 cm E 60 S 6.13 cm 40' 6.13 cm 4 cm 5.39 cm 80 T 5.39 cm (c) 5 cm M
Are the following pairs of triangles congruent? If so, explain your answer and write down the statement of congruence.If not, explain your answer. (a) 3 cm B 60 70 3.68 cm 3 cm 3.39 cm 70 50 60 50 3.39 cm C 3.68 cm R (b) D S 5 cm 5 cm 80 U E F T
Given that ABCD = PQRS, copy and complete each of the following. (i) PQ AB= cm (i) SR= = 6 cm (iii) PS= (iv) QR = (v) LPQR= cm cm A 2 cm D 5 cm 6 cm R C B 5.3 cm S P e
Given that ABCD = WXYZ, copy and complete each of the following. A 2cm D B 80 (i) LABC= LWXY =ZXYZ = Z W 4 cm 60 X (ii) (iii) AD= cm (iv) = WX= cm
Discuss with your classmates other real-life applications of congruence.
6. Given the functions f:x mapsto 4x - 3 and gx8-3x, find the value of x for which(i) f(x) = 13(ii) g(x) = 20(iii) g(x) = x(iv) f(x) = - 2x(v) f(x) = g(x)7. If f(x) = 10x - 3 and F(x) = 3/4 * x + 2 express (i) f(a), (a) + F(2a-4), in terms of a. (ii) F(8a+ 1),
Given the functions f(x) = x/4 + 5 and g(x) = 2/5 * x - 1(a) evaluate(i) f(8) + y * (5)(ii) f(- 1) - g(- 10)(iii) 2f(3) - 3g(5)(iv) 4f(- 3) - 7g(0)(b) What are the values of x for which f(x) = g(x) and f(x) =6?
Given the function g(x) = 5x - 9 evaluate each of the following. (i) g(2) (iii) g (ii) g(-5) (iv) g(0) + g(-3) (v) g S
3. Given the function f:x mapsto 12 - 5x , evaluate each of the following.(i) f(2)(ii) f(- 3)(iii) f(0)(iv) f(3) + f(- 5)
A function f is defined by f:x mapsto 1/2 * x + 2 for all real 1 values of x. What are the images of -20, 6, and 8 2 - under f? 3
Each of the following relations has the set of integers \{1, 2, 3, 4\} as its domain. State whether each of the following arrow diagrams defines a function. If the answer is no, state the reason. (a) 123+ (b) 10 4 13 1 2345 1234+ (c) (d) 123 4 10 30, 12 3 4. 8 14 17
Given the functions f(x) = 3/4 * x + 1/2 and g(x) = 1 - x, evaluate f(2), f(-2), (3) and g(-6). (i) Is it true that f(2) + f(3) = f(2+3)? (ii) Is it true that g(4)- g(2) = g(4-2)? (iii) Find the value of x for which f(x) = g(x). (iv) Find the value of f(a), f(24) and of g(3a). (v) Find the value of
Given the function f(x) = 4x + 9 evaluate f(1) f(2) and f(3) Is it true that(i) f(1) + f(2) = f(1 + 2) * i(ii) f(3) - f(2) = f * (3 - 2)!(iii) f(1) * f(2) = f(1 * 2)(iv) f(2) / f * (1) = f * (2/1)!
Given the functions fx 5x-9 and gx2-6x, find the value of x for which(i) f(x) = 16(ii) g(x) = 14(iii) g(x) = x(iv) f(x) = 2x(v) f(x) = g(x)(vi) 2f(x) = 3g(x)
5. Given the functions f(x) = x/2 + 3 and g(x) = 3/4 * x - 2(a) find the values(i) f(2) + g(2)(ii) f(- 1) - g(- 1)(iii) 2f(4) - 3g(6)(iv) 5f(- 2) - 7g(- 4)(b) What are the values of x for which f(x) = g(x) and f(x) = 17i
Given the function g(x) = 7v + 4 find the value of each of the following. (i) g(2) (iii) 20 (v) g 8(4)-8(-4) (ii) g(-3) (iv) g(0)+g(-1)
Given the function fx52x, evaluate each of the following.(i) f(1)(ii) f(-2)(iii) f(0)(iv) f(3) + f(- 3)
A function f is defined by f: x 6x-4 for all real 1 1 values of x. What are the images of 2, -4, and 2 under f?
Each of the following relations has the set of integers \{2, 4, 6, 8\} as its domain. State whether each of the following arrow diagrams defines a function. If the answer is no, state the reason. (a) - 2 2468 246 e. 8. (c) b d 9 2468 (d) 23 24 68 9 e 6 3 G 9 2468)
If f(x) = 7x - 4 and F(x) = 6x + 5, express(i) f(u)(ii) F(u + 2)(iii) f(3a) + F(2a + 1)in terms of a.
State, with reason, whether each of the following arrow diagrams defines a function. (a) Students (b) Scores Raj Ethan Ann Michael- Megan- B 4 D 3 5
State, with reason, whether each of the following arrow diagrams defines a function. (a) A B W X Hockey Soccer Tennis (b) 1. B Math Science History Geography
Given thatfind the value of n and of k. +233-k k2n+5 x"y" 13
Simplify (a+b)" (a+b)+3 + bc abc
The equation of a circle is given by the formula (x -a) ^ 2 + (y -b) ^ 2 = r ^ 2 where (a,b) are the coordinates of the centre of the circle and r is the radius.(i) Make y the subject of the formula (x -a) ^ 2 + (y -b) ^ 2 = r ^ 2(ii) Hence, find the y-coordinate(s) of the point(s) on the circle
In an electrical circuit, when two resistors are connected in parallel, the effective resistance, R ohms (2), of the two resistors is given by the formula 1/R = 1/R_{1} + 1/R_{2} where R_{1} and R_{2} are the resistances of the individual resistors in ohms.(i) Make R the subject of the 1/R =
Solve each of the following equations. (a) 12 5q 7 1= 5 7 (b)- y-3 10 3y-9 6-2y 3y-96-2y =3
Given that find V = pi * R ^ 2 * h + 2/3 * pi * r ^ 2(a) the value pi = 3.142 R = 12 h = 14 andr r = 9(b) the value of / when pi = 3.142 R = 8 V = 3800 and r =6 r(c) the values of R when pi = 3.142 V = 3500 h = 17 and r = 8.5(d) the value of r when pi = 3.142 R = 11 V = 4600 and 6.9.
Given that a ^ 2 + a ^ 2 * b = 320 find(a) the value of b when a = 8(b) the values of a when b = 2 1/5
Given that a * sqrt(b ^ 2 -c) = 5k find(a) the value of k when a = 3 b = 6 and c = 20(b) the value of c when a = 4 b = 7 and k = 11
In each of the following cases, make the letter in the brackets the subject of the formula. b (a) =2 2c 4 (c) a= 1- 1+1 (e) 3a-2= a 141 191 (b) A = P(1+100) IPL (d) k=h+ 2hk 5 14] (f) x + + z = k [y]
Express each of the following as a fraction in its simplest form. (a) 517 3 4a 8a 9 7 h (c) (d) + 2d-4f8f-4d (b) 5b b 3b+2c9b + 6c 2h+5 5 6 + 4 3 2 (e) (f) k-1 4k+5 3n 5 (g) (h) (2n-1) 211-1 + 2m-58+3m 1 1 p+3p-4 p+4
Simplify each of the following. (a) 3ab 4c ab 10A 3k-15k (c) x k-5 5k mn-4m+2n-8n 4-n (e) m+2n (g) 3.x x-2x+1 x 1 x" x(x-1) 27 6 (b) d-3f9f-3d 4x-1 (d) 4x-4y 1 9x-9y 3 (f) " pq (h) 7(p-q) 2p'q x 2-16 (p-q 2 22-12y+16-2
Simplify each of the following. 24.x x(c-d)(c+3d) (a) (b) 6x'y 5x(c-d) 5a+10b 3/+4d (c) (d) 10ac +20bc (6f+8d) p2-4p+4 (e) (f) p2-2p 3r-qs+3s-gr 9+q-6q (8) 3w+8w+4 3-12 +7 +6 (h) 3: +9:+6
The resistance of a wire, R ohms (2), is directly proportional to its length, I m, and inversely proportional to the square of its radius, r m.(a) Express & in terms of I, r and a constant k.(b) Maker the subject of the formula in (a).(c) (i) Given that a wire with a length of 2 m and a radius of
Given that y = 3x + root(a + b ^ 2, 3) find(a) the value of y when a = 13 b = 15 and x = 3.8(b) the value of a when h = 13 x = 8.5 and y = 35(c) the values of b when a = 23 15.6 and y = 56
Given thatfind the value of (1/x + 1/y)/(2/x) = 4/3 2
The amount of energy, E joules (J), stored in an object with a mass of m kg is given by the formula E = mgh + 1/2 * m * v ^ 2 where I m is the height of the object above the ground, ms is the velocity of the object and g is taken to be 10 ms.(i) Given that 20, make the subject of the formula E =
The time taken, T seconds, for a pendulum to complete one oscillation is given by the formula 7=2 where I m is the length of the pendulum and g is taken to be 10 m s.(i) Make / the subject of the formula 7=2(ii) Hence, find the length of the pendulum if it takes 12 seconds to complete 20
In optics, the focal length, fcm, of a lens, can be calculated using the formula where.cm and em are the object distance and the image distance from the centre of the lens respectively.(i) Make v the subject of the formula 11(ii) Hence, find the image distance when the focal length of the lens is
Solved each of the following equations. 5 (a) 2 (b) x+2 =1. 7x-4x-3x-1 7+x + 15 3 5 10 1 + 3+1 (c) 5x-1 5 (d) 2x-4x-2 4 3 6x-3 3 5 1 (e) =4 2- 4-2x-2
Given that A = 1/3 * pi * r ^ 2 * h + 4/3 * pi * r ^ 3 find(a) the value of A when pi = 3.142 h = 15 and r = 7(b) the value of / when pi = 3.142 A = 15.4 and 14.
Given that (m(nx - y ^ 2))/p = 3n_{j} find(a) the value of p when m = 5 n = 7 x = 4 and x = - 2(b) the value of when m = 14 p = 9 x = 2 and x = 3(c) the values of y when m = 5 n = 4 p = 15 and x = 42
Given that a = sqrt((3b + c)/(b - c))(i) make b the subject of the formula,(ii) find the value of when a = 2 and c = 5
Given that V = pi * r ^ 2 * h + 2/3 * pi * r ^ 3(i) make the subject of the formula,(ii) find the value of li when V = 245 and r = 7
Solved each of the following equations. (a) (c) a+2 +4 c+3 6 10 375 3 (b) c+2=0 (d) =2 (2) -- f 3f b 2 5 1 2 -2b-1 2 =0 d+4 d-2 5 6 9 (f) + =4 6h 7h 14h 3 (g) k+1 1 2k+2
Given that find a = sqrt((3b + c)/(b - c))(a) the value of a when b = 7 and c = 2(b) the value of when a = 4 and b = 9
Given that sqrt(a * x ^ 7 -b) = c find the values of x when a = 2 b = 7 and c = 5
In each of the following cases, make the letter in the brackets the subject of the formula. (a) V=r (b)=u+2as (c) y=(x-p)+q 14 [u] [x] 4 (d) = / m-3
In each of the following cases, make the letter in the brackets the subject of the formula. (a) +2=k 141 h+1 (b) z= px (c) Px (d) y(z-y) =p+q 1 1 a b 1:1 x lpl =1 |b|
In each of the following cases, make the letter in the brackets the subject of the formula. 9 (a) F=C+32 5 IC (b) A 20+ url [/I 1 (c) s=ut+ [u] (d) S=12a+ (n-1)dl Idl
In each of the following cases, make the letter in the brackets the subject of the formula. (a) h-k=m [h] (b) b=D+4ac [DI V (c) P= [VI R 8 (d) A= * 101 360
In each of the following cases, make the letter in the brackets the subject of the formula. (a)=b+c m (b) 54-r 2P [a] [p] 3 k+a (c) =3k [k] 5 (d) A = (a + b)h [b]
In each of the following cases, make the letter in the brackets the subject of the formula. (a) ax + by=k [y] (b) PV=RT In] (c) 5b-2d 30 [d] (d) R=m(a+g) [a]
Solve each of the following equations. a-3 (a) 5+2=1=4 2a- 3 5 (b) 3 2b+3 3b-4
Solve each of the following equations. a-2 a-1 (a) = 1 5 3 6 4 (b) = 0 2b-5 b-3
Given that find the value of x when x = 4 and z = 3 root((x + y)/(x - y), 3) = z_{t}
Given that find the value of b when alpha = 3 a = root((5b + 16)/(2b - 23), 3)
Given that find y = sqrt((x + 7)/(x - 2))(a) the value of y when x = 5(b) the value of r when y = 4
Given that v = sqrt(64/(3.4 + 1)) calculate(a) the value of y when x = 1(b) the value of x when x = 2
(i) Make the subject of the formula p = a + (b * x ^ 2)/(3k)(ii) Hence, find the value of when a = - 1 b = 2 k = 1 and p = 5
(i) Make the subject of the formula 3y = sqrt(b ^ 2 - 4ax)(ii) Hence, find the value of x when a = - 5 b = 4 and y = 2
(i) Make k the subject of the formula p = a + (b * x ^ 2)/(3k)(ii) Hence, find the value of k when a = 1 b = - 2 p = 3 and x = 9
(i) Make x the subject of the formula y = (2x + 5)/(3x - 7)(ii) Hence, find the value of x when y = - 3
The simple interest S/ payable on an investment is given by where $P is the principal, R% is the interest rate on the investment per annum and 7 is the number of years that the investment is held. I = (PRT)/100(i) Make 7 the subject of the formula I = (PRT)/100(ii) Hence, find the number of years
(i) Make a the subject of the formula v = u + al.(ii) Hence, find the value of a when 14, 10 and v = 50
Expressas a fraction in its simplest form. 1 22 3x y 2x
Express each of the following as a fraction in its simplest form. (a) + 5 2(a b) 3(b-a) - 4 (b) - c-l 1 3c 7 14-6c 4f 2d u+1 11+2 (c) (d) 10f-5d 6f-3d 2u-8 12-3u 2m-5 m+3 h+k 3h+k (e) (f) + 9n-6 4-6n P-q 8q-8p 5x2 2x 3x 2x (g) (h) 6x-6y 3y-3x + 4y-2z z-2y 3z-6y
Express each of the following as a fraction in its simplest form. 4a 5 2b (a) (b) 3a-5 4a-1 2b+1 (2b+1) h+5 3 (c) (d) + 2 3 h2-6h h-6 m m-4 m-3 (e) x+y x r-4y 4y x-3y + x-y x-y2 x+y 1 2 18 (f) 2z-3 3-2z 9-4z 2
Express each of the following as a fraction in its simplest form. 7 4 3 5 (a) (b) 6a 9a 2b 3b 6h 1 I (c) (d) f-4h 2f-5h 3c 3d 3k 8k 4a (e) (f) P+3 +3 p-1 P-1 2p+1 + x-3y 3x-9y 2z 6z 3z
Express each of the following as a fraction in its simplest form. + 4 3 a+4 2 I 3 (b) 2b b+c 2 3 (c) + d-5 2d+3 (d) f+5 J-1 11 2 3 2 (e) (f) 3h-7 6-5h k-1 k-1 3 5 2 3 (g) (h) + 4m 1 2m+1 n-2 (n (n-2)
Express each of the following as a fraction in its simplest form. (a) (b) (c) (d) 2 + 3 a+3 a+4a+3 b -5b-6 b-6 1 2p 2p-8p-10 p-5 x x + y + 4 3x +3xy+2y2x+2y
Express each of the following as a fraction in its simplest form. (a) 2 - 3 x+1 2x-5 1 1 2: (b) (c) 9 5+5 -5-25
Express each of the following as a fraction in its simplest form. (a) 5v 2 (b) 4 1-2
Express each of the following as a fraction in its simplest form. 2m+ 3n 3m m-11 2n 3p Sp-2q 5x 7 y (b) 4p-4q3p-3q 4x-3y 6y-8x @
Express each of the following as a fraction in its simplest form. 6 3 4 7 h 3h (a) (b) 5a 8a 2b+3c 6b+9c (c) 2-3k 3k-2
Express each of the following as a fraction in its simplest form. (a) 27 3 3 2 (b) 5a 2b-4c 3b-6c 2h 3k (c) h-2k 2k-h
Simplify -2xy -2-2-2yz
Simplify each of the following. ac 5a (a) x 9b 2b (b) 8b 6df 3f8df2 9f16d 27d (c) 2y+ 4y 64.xy x (d) 3ps 3pq 14s 5xy 100xy 4 par 12pq 7qr 3w-7 21-9w 6xy 12x-24y (e) + (f) 5w 27w 16y-8x 4.xy h-h-6 c-d (g) (h) h2-9 h + 2h -2cd+d cd+d2 m-4 (i) m m - 3m+2 m 32-22 (1)-4+2-5:+6 (k) (a-4b)+ a +2ab (1)
Simplify each of the following. 15a 4c (a) X (b) 3(c+d) 2c-2d 8ab'c 5ab x c-d 8c+8d (c) a-2b 4a-8b (d) 8c 2c 16 24 6(c+d) 3c + 3d
Simplify each of the following. 2a+b (a) (b) 4a-b c + 2cd-15d 4c + 20cd 3a-6 (c) (d) a+a-6 x+6x-7 r (e) k-9 k-7k+12 mk + 8k m +4m-32
Simplify each of the following. xy+ 3y 8a+ 4b (a) (b) 4x+12 bc + 2ac a +2ab (c) (d) 6a 2-cd (e) (m-n) 5pq (f) m mn 15p-10pq
Simplify each of the following. 9.x(a-b) (a) (b) 27x (a-b) 7a (a-3b) 21ab(a-3b) Sab (2a + 3b) 8an (b+c) (c) (d) 32ab(3b+2a) 96an(c + b) 2-2y-15 8-2m-m (e) (f) -3y-10 2m-3m-2 9x-2 3x+5xy-2y (h) 3 -2xy-3x 4x+7xy-2y b-a 2-6y-7 2a + ab-3b (j) 2y-17y+21 3x-3y a-ab-ac+bc (k) (1) ax-ay-x+y a+ab-ac-bc
Simplify each of the following. 4x (a) (b) 12xy 16a'b 24ab 23q'r (c) (d) 3mn p 2 3 69gr's 18m'np 6 (e) 15ac' 16.xyz (f) 75abc 64.xyz
Simplify 3m-n 2n-6m +m 111 +11
Simplify each of the following. 2a 15c (a) (b) 5c 8a 2x-6 3 3p 35gr 5 15q 12pr 6pq h-6h+9h-2 (c) (d) 5x+5y 7y+7x h-2h h-3

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