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

Find the value of the unknown in each of the following right-angled triangles. (a) 19 cm 11 cm (c) 29.2 cm 18.8 cm (b) 9.1 cm 21 cm
If y is inversely proportional to (tan x) and y = 2 when x = 30 deg find the value of y when this value of x is doubled.
A figure VWXYZ is made up of three right-angled triangles. Given that VW 154 m. VY 88 m.ZVXW=ZVYZ=90°, ZVWX=63", ZVZY=46", find(i) the perimeter,(ii) the area, of the figure. W63 154 m. 88 m X 46 Z Y
Find the value of the unknown in each of the following right-angled triangles. (a) (b) (cm 12 cm bem 34 16 cm, 43" (c) 7 cm dcm 44.2 fem e em e cm
Find the value of the unknown in each of the following right-angled triangles. (a) a cm 14 cm 28" (b) 13 cm 62.5 bcm
Find the value of the unknown in each of the following right-angled triangles. (a) 13.5 m 36 am (b) 17 m 61" bm
Find the value of the unknown in each of the following right-angled triangles. (a) em 15 cm 67 (b) 15 9.7 cm bcm
In AXYZ, LZ=90. Given that LX-35" and YZ = 12 cm, find the length of XZ. X 351 Z 12 cm
Find the value of the unknown in each of the following right-angled triangles. (a) B x cm 11 cm (b) R 67 30 cm 8.7 cm
use a calculator to evaluate each of the following. 5 tan 61.4" 4(sin 22.5") (a) (b) 2 cos 10.3 cos 67.5 tan 15" + cos 33 tan 47.9 (c) sin 78.4 (d) cos 84 - sin 63 cos 67' + sin 89 sin 24.6" + cos 62.1 (e) (f) tan 63.4" x cos 15.5* tan 21+ cos 14 sin 57' - cos 73 cos 24.7 x sin 35.1" tan 15.3" x
use a calculator to evaluate each of the following. (a) tan 47" (c) cos 30.19 (b) sin 75.3 (d) sin 35+ cos 49" (e) 2 cos 42.3+3 sin 16.8* (f) sin 71.6x tan 16.7"
For each of the following right-angled triangles write down an expression for (i) sin P. (iii) tan P, (v) cos Q. in terms of x, y and/or z. (a) p xem 2 cm (b) y cm P A cm (ii) cos P, (iv) sin Q, (vi) tan Q. R R y em cm
For each of the following right-angled triangles, name state of the value (i) sin A, (iii) tan A, (v) cos B. (a) B. 5 cm 13 cm (b) B (ii) cos A, (iv) sin B, (vi) tan B. A 12 cm 24 m C 7 m 25 m A
For each of the following right-angled triangles, name(i) the hypotenuse,(ii) the side opposite angle a_{1}(iii) the side adjacent to angle (a) Q R a (b) Y- Ja N. -P -X
Use a calculator to evaluate each of the following. (a) cos 24 (c) sin 72.15 5 (b) tan 74.6" (d) 3 sin 48 + 2 cos 39 tan 48.3 sin 28.7" (e) tan 18.3 (f) cos 15+ cos 35
Use a calculator to evaluate each of the following. (a) sin 32" (c) tan 25.96 3 (b) cos 15.3 (d) 2 sin 37 +5 tan 56" cos 57 (e) (f) cos 48.1 in 46.5' + tan 26.4
In AXYZ, XY = cm, YZ = am, XZ = bm and Z = 90. Write down an expression for (i) sin X, (iv) sin Y, (ii) cos X, (v) cos Y. (iii) tan X. (vi) tan Y. in terms of a, b and/or c am em hm
In APQR, PR 4 cm, RQ=3 cm, PQ-5 cm and LR 90. State the value of (i) sin P, (iv) sin Q. (ii) cos P, (v) cos Q. R 4 cm (iii) tan P. (vi) tan Q. 3 cm 5 cm
Congruent figures have exactly the same shape and size. Similar figures have the same shape but not necessarily the same size. What about figures with the same size but of different shapes? An interesting example is the Haberdasher's Puzzle: how do we cut an equilateral triangle into 4 pieces and
Pythagoras Theorem is usually stated in terms of the lengths of the sides of a right-angled triangle. c ^ 2 = a ^ 2 + b ^ 2 However, it can also be stated in terms of the areas of squares. i.e. A_{1} = A_{1} + A_{r} A A If the areas refer to the areas of semicircles instead of the areas of squares,
Given a triangle ABC where BC = 370 units, AB116 units and AC = 74 units, find the area of the triangle.
Three positive integers, where a
Farhan runs diagonally across a rectangular field 80 m by 60 m, from one corner to the opposite in a straight line at a speed of 7.5 m/s. Find the time taken for him to complete his run.
A vertical pole 47 casts a shadow Hl at a certain time in a day. It casts a shadow AT at another time on the same day. Given that FK 18 m.KT12.5 m and KH: HT=3:2. find(8) the height of the pole,(ii) the distance FH. 18 m K H 12.5 m F T
In the figure, ABCD is a rectangle of sides 28 m and 15 m. PBRQ is a square of sides 6 m.6) Find the area of the shaded region DPQR.(ii) Calculate the length of DP.(iii) Given that X is a point on DP such that AX is perpendicular to DP, find the length of AX. A B R 6 m 15 m C 28 m
In the figure, angle BAD = 90 deg(i) Given that AB = 36cm and AD = 48cm find the length of BD.(ii) Given further that BC = 87cm and CD = 63cin show that ABCD is a right-angled triangle. 36 cm A B 48 cm D 87 cm 63 cm C
A floor tile in the shape of a rhombus has sides of length 52 cm and a diagonal of length 48 cm. Find(1) the length of the other diagonal,(ii) the area, of the floor tile.
A piece of stained glass in the shape of a parallelogram LMNO is such that the diagonal LN is at a right angle to LM. Given that l. M = 12cm and MN = 1.5cm find the area of the piece of stained glass.
A rare stamp in the shape of an equilateral triangle FGH has sides 2 em. Find the perpendicular distance from F to GH.
Khairul's briefcase has a rectangular cross section.The length and the diagonal of the briefcase are 30 cm and 37 cm respectively. Find the height of the briefcase. 37 cm 30 cm
If the diagonal of a square is 42.5 cm long, find(i) the perimeter,(ii) the area, of the square.
Find the value of the unknown in each of the following figures. (a) (b) 8.7 m a cm 13.5 m 3 cm 9.6 cm (c) 4 cm 5 cm cem +3 cm++ 6 cm (d) bm dm 10 m - 11 m 6 m
The lengths of the sides,a, b andc, of a triangle are given by a = m ^ 2 - n ^ 2 b = 2mn and c = m ^ 2 + n ^ 2 where m and in are positive integers and m > n Show that the triangle is a right-angled triangle.
A rectangular grass patch, PQRS, has sicles 40 m and 30 m. A straight path which cuts through the grass patch joins S and Q. Lamppost X is located on SQ such that SX / X * Q = 16/9 and RX = 24m Jun Wei walks along the path and stops at a point which is nearest to R. Show that he stops at X. S 40 m
In ASTU, ST = 7/12 * cm TU = 5/6 * cr and SU = 1/3 * cm Is ASTU a triangle?
In APQR, PQ = 19cm QR = 24cm and PR = 30cm Show that APQR is not a right-angled triangle.
Determine if each of the following triangles is a right-angled triangle. For each right-angled triangle, state the right angle.(a) AABC, given that AB = 16cm BC = 63cm and AC = 65cm(b) ADEF, given that DE = 24cm EF = 27cm and DF = 21cm(c) AGHI, given that GH = 7.5m HI = 7.1m and GI=24 m(d) AMNO,
XYZ is a plot of land such that XY = 45m YZ = 24m and XZ = 51m(i) Show that angle XYZ = 90 deg .(ii) A tree 7 is located on ZY such that ZT = 14m Find 7X, the distance of the tree from X. X 51 m 45 m Z T +14 m Y -24 m - ->
Determine if each of the following triangles is a right-angled triangle. For each right-angled triangle, state the right angle.(a) AABC, given that AB = 12cm BC = 10cm and AC = 8cm(b) APQR, given that PQ = 34m QR = 16m and PR = 30m
Determine if each of the following triangles is a right-angled triangle. For each right-angled triangle, state the right angle.(a) AABC, given that AB = 39cm RC = 15 cm and AC = 36cm(b) APQR, given that PQ = 28m QR = 20 m and PR = 19m
A designer is tasked to design two tables for children such that the tabletops are of different shapes as shown, and that the perimeter of each tabletop is 132 cm. Square Tabletop (a) Find Round Tabletop (i) the length of each side of the square tabletop, (ii) the radius of the round tabletop. (b)
A courier travels due North at an average speed of 40 km/h for 6 minutes to collect a parcel, before travelling 10 km due East to deliver it. He then travels due South at an average speed of 30 km/h for 12 minutes to collect another parcel. Find the shortest distance between the courier and his
The top surface of a pouch is in the shape of a rectangle LMNO with siles 9 cm and 6 cm.(i) A zip is to be sewn along OH such that H is a point on LM and HM = 2 cm. Find the length of the zip.(ii) A second zip is to be sewn along NK such that NK is the perpendicular from N to OH. Calculate the
A folded napkin has a triangular cross section of sirles x cm, (x + 1) cm and (x + 2) cm. lf one of the angles of the triangle is 90", find the value of x.
A campsite in the shape of a rectangle FGHI has sides (3x + +)m and (x + 1)m, and the length of the diagonal FH is (4x + 1)m. Find the area of the campsite. (x + 1) m (3x+6) m (4x + 1) m G H
A straight pole PR is leaning against a vertical wall MQ.(i) Given that PQ = 4.2 m and RQ = 1.1 m, tind the length of the pole.(ii) The upper end of the pole. P. slicles down 0.9 m to a point on the wall, X. Calculate YR. the distance the lower end of the pole has slid away from its original
Two spotlights, P and Q, are mounted on a vertical pole AB. Light beams from P and Q shine to two points on the ground, H and K, respectively. Given that PQ = 12.7m KB = 172m PH = 39 m and QK = 21m find(i) BQ, the height above the ground at which the spotlight Q is mounted,(ii) HK, the distance
8. A table coaster in the shape of a rhombus has diagonals of lengths 10 cm and 24 cm. Find the length of each side of the coaster.
Devi folded a sheet of paper into an envelope, as shown in the figure. In the figure, angle AED = angle ADB = angle BCD = 90 deg . To seal the envelope, she has to apply glue along AD and DB. Given that AE = ED = 8 cm and DC = BC = 14cm find the total length of the sides along which the glue has to
Two vertical buildings of heights 30 m and 37 m are 16 m apart. A cable is pulled taut and attached from the top of one building to the top of the other building. Find the length of the cable. 30 m 37 m 16 m
Mr Lee huys a 30-inch television. The height of the screen is 18 inches. Given that television screens are measured across the diagonal, i.e. the length of the diagonal is 30 inches, how wide is the screen?
A ladder of length 5 m is placed against a vertical wall with its foot 1.8 m away from the base of the wall. How far up the wall does the ladder reach?
A rectangular swimming pool has a length of 50 m and a breadth of 30 m. During a swimming proficiency test, Ethan has to swim from one corner of the pool to the opposite corner. Find the distance Ethan has to swim.
Each side of a square field is 50 m long. A barricade is to be placed along the diagonal of the field. Find the length of the barricade.
Some cables are supported by a vertical post of height 47 m. The cables are attached from the top of the post to a point on level ground, 18 m from the foot of the post. Find the length of each cable.
A ship travels due South from Port A for 1.2 hours to reach Port B and then travels due East for another 1.7 hours to reach jetty C. It then travels due South to Buoy D which is 18 km away from Jetty C. From Buoy D. it travels 38 km due West to reach Island E. If the average speed of the ship is 10
Boat A travels due East from Port P for 3 hours to reach Port and then travels due South for another 2 hours to reach Port R. Boat B travels due North from Port P for 2 hours to reach Port S and then travels due East for 3 hours to reach Port 7. If the average speeds of Boat A and Boat B are 12
A school field in the shape of a rectangle ABCD has sides (x+7) m and x m, and the length of the diagonal BD is (x+9) m. Calculate the value of x. A D (x+9) m B xm C (x+7) m
In the figure, angle DGF= angle EPF = 90 deg . Given that DE = 31m EF = 23m_{e} DG = 32m and PF = 13m_{e} find the area of the figure. D 31 m 32 m E G P 13 m F 23 m
In Delta*ABC AC = 43cm and angle B = 90 deg H lies on AB such that HB = 15cm and K lies on CB such that CK = I * 9cm Given that HK = 22c*m_{e} find the length of AH. 43 cm 22 cm 19 cm H 15 cm B
In triangle WXY , WY = 24m and angle Y = 90 deg P lies on WX such that YP is perpendicular to WX WP = 18 m and PX = 14m Q lies on YX such that QX = 9.8m Find(i) the length of YQ.(ii) the area of triangle XPY . 24 m W 18 m 14 m Y X +9.8 m-
Find the value of the unknown in each of the following figures. (a) b cm 60 cm 2a cm a cm 27 cm 36 cm
Find the value of the unknown in each of the following figures. (a) a cm 34 cm 30 cm
The figure shows an isosceles triangle TUV where TU = TV = 9.6m and UV = 15.4m Find the height, 7H, of the triangle. 9.6 m T U H 15.4 m
In the figure, angle PQS= angle QSR = 90 deg . Given that PQ = 45cm QR = 30cm and PS = 53cm find the length of(i) QS(ii) SR. P 45 cm 53 cm 30 cm S R
A triangle MNO is right-angled at N, with NO = 11m and MO = 14.2m Find the length of MN.
In AGHI, CH = 33cm Gl = 65cm and angle H = 90 deg Find the length of HI.
A triangle DEF is right-angled at E, with DE = 6.7m and EF = 5.5m Find the length of DF.
In AABC, AB = 8cm BC = 15cm and angle B = 90 deg , Find the length of AC.
Find the value of the unknown in each of the tollowing right-angled triangles. (a) 15 m 39 m am (b) (c) 9.8 m 6.5 m cm (d) 14 m bm 19 m 24.7 m dm 14.5 m
Find the value of the unknown in each of the following right-angled triangles. (a) 20 cm a em 21 cm (c) 10 cm (b) (d) 35 cm 12 cm bcm dem 12 cm 23 cm 29 cm
T, is the translation to (5, 9). and T_{2} is a translation that will move the point (2, 5) [[3], [- 7]](1) Find the image of the point A(2, 4) under T_{c}(ii) Find the translation vector represented by T_{x}(iii) What is the image of the point B(4, - 8) under T_{2} ?
Find the equation of the image of the line y = 2x - 5 under an anticlockwise rotation of 90° about the origin.
A model of the Port of Singapore Authority Building is made to a scale of 1 cm to 7.5 m. The height of the model building is 24.4 cm. Find(i) the actual height of the building,(ii) the height of the model building if it is made to a scale of 1 cm to 12 m.
The cross section of a blade of a paper cutter is in the shape of a triangle APQ. with parallel grooves CB and QP. Given that triangle ABC is similar to triangle APQ , AB = 6cm BP = CB = S cm and CQ = 6.5cm find the length of (i) QP (ii) AC. A- 6 cm B 5 cm 5 cm C 6.5 cm Q
Given the function :x 13-9x, evaluate each of the following. (i) f(2) (ii) (iii) 2f(0) + f(1) (iv) f(3)-f
The centripetal force, F Newtons, acting on an object of mass kg, moving at a velocity 'ms along a path with radius rm, is given by the formula F = (m * v ^ 2)/r(i) Given that v >= 0 make v the subject of the formula F = (m * v ^ 2)/r(ii) Hence, find the tangential velocity of a motorcycle 225 kg
Simplify each of the following. (a) 4a b-8a'b-14ab3 4ab (b) 6cd+12c'd-9cd' -30-d
In the figure, the curve y = x ^ 2 + 5x + 4 cuts the x-axis at two points A and B, and the v-axis at the point C. Find the coordinates of A, B and C. y= r+5x+4 C A BO
(i) x = 3 is a solution of the equation x ^ 2 + px + 15 = 0 find the value of p.(ii) Hence, find the other solution of the equation.
Solve the equation (2x - 1)(3 - 4x) = 2(1 - 2x)
If R represents an clockwise rotation of 187 about the origin, describe R and R
State the coordinates of the reflection of the point (4, 5) in the line x = 2
A map has a scale of 1 cm to 8 km.(i) Express the scale of the map in the form, where is an integer.(ii) If two towns are 72 km apart, find the corresponding distance on the map.(iii) If the actual area of a forest is 496 km², calculate its area on the map.
It is given that AABC is congruent to APQR, angle A = 70 deg angle B = 60 deg and AB = 8 cm(i) Write down the length of PQ.(ii) Find ZR.
If f(x) = 7x - 2 and F(x)=1+6+6 , find an expression, in terms ofa, for each of the following.(i) f(a)(ii) F(16a-8)(iii) f(1/7 * a + 1) + F(4a - 3)
(1) Make x the subject of the formula 5a = (3x - 4)/(2y - 3x)(ii) Hence, find the value of x when a = 1 and y = 5
4. Express each of the following as a fraction in its simplest form. x-1 5-2x 2x+3 7 (a) (b) 4x-2 3-6.x 9x-1 3x-1
The variables x and y are connected by the equation y = 3x - 2x ^ 2 Some values of and the corresponding values of y are given in the table.(a) Find the value of p and of y.(b) On a sheet of graph paper, using a scale of 2 cm to represent I unit on the x-axis and I em to represent I unit on the
The length of a rectangle is 5 m longer than its breadth and its aren is 66 m². Let the breadth of the rectangle bex m. Formulate an equation in terms of t Hence, find the perimeter of the rectangle.
1. Solve each of the following equations.(a) 16a - a ^ 2 - 64 = 0(b) b ^ 2 - 16/25 = 0(c) 1 + 3c = 10r ^ 2(d) d ^ 2 + d ^ 2 - 132d = 0
R is an anticlockwise rotation of 90° about the origin.(a) Find the coordinates of the image of each of the following points under R.(1) (3,5)(ii) (7,-4)(b) Find the coordinates of the image of each of the following point under R.(1) (3,4)(ii) (-2, -3)(c) Find the coordinates of the image of (2,
10. M is a reflection in the line =x. Find the coordinates of the image of T=(a) (1.3) under M.(b) (25) under M(c) (3,7) under M
Given that the line y=2x+3 is mapped onto the line y=mx+c by a translation represented by find the values of m and c.
Find the image of the point P(2, 1) under(a) a reflection in the line x+y=4,(b) a 180° rotation about the point (-5, 3),(c) a translation represented by(3).(d) a reflection in the line y=x+2.
Find the equation of the image of the line y=x+4 under(a) a reflection in the line x=2,(b) a translation representation by the column vector).(c) a 90 clockwise rotation about the origin O
Find the equation of the image of the line ya under an anticlockwise rotation of 90 about the point (2, 0).
Mis a reflection in the line y=-x. Find the coordinates of the image of the point (5, 2) under(a) M.(b) M²,(c) M
The figure above shows two squares ABCD and PQRS. In each of the following cases, describe completely the single transformation that will map(a) PQRS onto ABCD,(b) ABCD onto QPSR,(c) PORS onto CDAB,(d) ABCD onto SPOR,(e) PORS onto DABC. 6- D C S R 2 0 A 2 B P 6 8 10 12
The figure above shows the point A(1, 3) and B(6, 1).(a) The line AB is rotated through 90° clockwise about B. Find the equation of the image of the line AB.(b) The line y = 1 is the line of symmetry of AABC. Find the coordinates of the point C. 0 A(1, 3) B(6, 1)

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