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Think New Syllabus Mathematics Book 4 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
15. The figure shows a quadrant of a circle of radice 12 cm.Given that B is the midpoint of the arc AC, find (i) the length of BD, (ii) the perimeter of the shaded region, (iii) the area of the shaded region. B C D 12 cm 0
14. In the figure, O is the centre of a circle with radius 16 cm.APYB, a sector of a circle with centre A and radius 32 cm, intersects the circle at A, B and Q. OX divides AOAQ into two congruent triangles.Given that ZOAQ = 66°, find(i) ZBOQ, (ii). the length of AQ, (iii) the perimeter of the
13. An ice cream seller makes a sign in the shape of an e cream cone, with a major segment ABCD of a andle, centre O and radius 0.4 m, on top of a riangle ABCE, such that EBOD is a straight line, as shown in the diagram.The sign is symmetrical bout DE, which is perpendicular to AC.The height of the
12. A rectangle, where BC-2AB. a semicircle, centre O, and are AD has Angle AFD-90 and F is the midpointGiven ure that is shaded. Take that AB-x units, find the fraction of the figure that is shaded. B F D C
11. Two circular discs of radii 4p cm and p cm touch each other externally and lie on a straight line AB as shown.Find an expression, in terms of p, for the area enclosed by the two discs and the line AB. 4p cm X A P cm B
10. The diagram shows two circular discs with centres A and B, of radii 11 cm and 7 cm respectively. They lie on a straight line MPQN and touch each other at R such that ARB is a straight line.(i) Show that PAB is approximately 77.2. (ii) Hence, find the area of the shaded region. Ar R B 11 cm 7 cm
9. David forms a sector of a circle of radius 12 cm.Find the area of the paper that he used, given that the perimeter of the sector formed is 38 cm.
8. In the figure, the area of the 5. shaded sector POQ is 18 of the area of the whole circle. (i) Find LPOQ.(ii) Given that the area of the shaded sector is 385 cm, find the diameter of the circle. P
7. The figure shows two sectors OAB and ODC with O as the common centre.Given that OAD and OBC are straight lines, OA = r cm, OC = R cm and ZAOB = mº, find the perimeter and the area of the shaded region ABCD for each of the following cases.(a) r=10, R = 20, m = 45 (b) r=5,R=8,m=120 (c) r=35,
6. The diameter of a circle is 18 cm. Find the angle subtended by the arc of a sector with each of the following areas. (a) 42.6 cm (c) 214.5 cm (b) 117.2 cm (d) 18.9 cm
5. Find the radius of each of the following circles.(a)(b)Area of major sector = 369 cm2 150
4. The diagram shows a circle with centre O and LPOQ = xº.The area of the circle is 3850 cm2.Find the area of sector OPSQ and the length of arc PSQ for each of the following values of x.(b) 84 (a) 36 (d) 198 (c) 108 Q S P to 0
3. The figure shows a circle with centre O and LAOB 0. The circumference of the circle is 88 cm.Find the length of arc ACB and the area of sector OACB for each of the following values of 0.(b) 99 (a) 60 (d) 216 (c) 126 0 B 0 C A
2. For each of the following circles with centre O, find (i) the perimeter, (ii) the area, of the minor sector. (a) 7 cm 030 (b) 0- 3.5 cm 340 (c) 140 6 cm
1. Copy and complete the table for each of the sectors of a circle. Radius Angle at Arc centre Area length Perimeter 7 cm 72 35 mm 136 mm 270 1848 mm a 150 220 cm 14 m 55 m 0 75 154 cm
19. The diagram shows a plot of land ABCD. B is due east of A and the bearing of C from A is 048°.AB = 36 m, BC = 58 m, BD = 72 m and CD = 95 m.(i) Find the bearing of C from B.A vertical control tower of height 35 m stands at B.Yasir cycles from C to D and reaches a point P where the angle of
18. Raju stands at a point B, due east of a vertical tower OT, and observes that the angle of elevation of the top of the tower T from B is 40. He walks 70 m due north and finds that the angle of elevation of T from his new position at C is 25.Find the height of the tower and hence distance OB. T N
14. The figure shows a block of wood in the shape of a cuboid with dimensions 10 cm by 8 cm by 6 cm. Joyce cuts the block into two pieces such that the cutting tool passes through the points A, B and C as shown.Given that the triangular surface ACB on one piece of the block is to be coated with
13. In the diagram, XYZ is an equilateral triangle with des of length of 6 cm lying p rizontal plane.Plies vertically above Z, Ris the midpoint of XY and PX-PY = 10 cm. Find ZPYZ, (i) the angle which RZ P ZO 6 cm \10 cm Y R X
12. andi vertically at A on the S, KADC - 47 and AR - 240 m 24 m10 the distance between B and C, (i) the area of AABC, (ii) the shortest distance from A to BC. The boat at B sails in a straight line towards C. Find the greatest angle of depression of the boat from the top of the tree. 240 m 94 47
11. P is the centre of the upper face of the rectangular block with ABCD as its base.Find (i) /PAC, (ii) _PAB. P. D 5 cm A 12 cm B C 16 cm
10. The diagram shows a cuboid with a horizontal base EFGH where HG 15 cm, GF=8 cm and BF-7 cm.X is a point on AB such that XB = 4 cm. Find (i) the angle between CE and the plane ABEF, (ii) LGXF. A X4 cm B C D 7 cm E F 8 cm H 15 cm G
9. ABPQ is the rectangular sloping surface of a desk with ABCD lying on a horizontal plane. Q and P lie vertically above D and C.Given that AB = PQ = 90 cm, AQ=BP = 75 cm and LPBC= LQAD = 25, find (i) AC, (ii) PAC, (iii) the angle which BQ makes with the plane BCP. 75 cm D 25 A 90 cm B
8. ABCD is a pyramid. The square base ABCD has sides of length 20 cm and lies on a horizontal plane. Mis the point of intersection of the diagonals of the base and O is vertically above M.Given that OA=32 cm, find the length of AM, (i) the height of the pyramid, (iii) the angle between OA and the
7. In the figure, the angle of elevation of the top of a wrtical tower PQ from a point A is 30. The foot of the tower Q, is on the same horizontal plane a as A and B. Given that AB=60 m,LRAQ-45 and LABQ=75, find the height of the tower. 30 P A- 45 Q 60 m 75 B
6. The diagram shows a triangular stage ABC on horizontal ground, where AB 10 m, BC= 15 m and LABC is a right angle. The base of a vertical pole, OP, is at point P along the edge AC of the stage. The pole is held in place by two cables, OA and OC. Given that LAPB = 90 and OA = 12 m, find (i) LBAC, C
5. A rectangular block of sugar has a horizontal base EFGH. The corners C and D are vertically above E and H respectively. and H respectively.DH= 4 cm, GH= 6 cm and FG = 8 cm.Find(i) ZDGH,(ii) HF,(iii) the angle between DF and the plane EFGH. D 4 cm H C E 8 cm 6 cm G
4. The diagram shows a rectangular box. AB 3 cm, AD-4 cm, BD=5 cm and DH 12 cm. Find (i) the length of BH, (ii) the angle between BD and the plane CDHG, (iii) LHBD. H 12 cm D 5 cm 4 cm A
3. The figure shows AABC, right-angled at B and lying on a horizontal plane. P is a point P vertically above C.vertically above C Given that AB-7 cm, BC-6 cm and AP-11 cm, find (i) AC (ii) PC (iii) LPAC (iv) the angle between PB and the plane ABC. C P 11 cm A 6 cm 7 cm B
2. Given that the sides of the cube in Question 1 are of length 5 cm, calculate(a) the length of QV,(b) the angle which QV makes with the plane PQRS,(c) the length of PV,(d) the angle which PV makes with the plane PQRS.
1. With reference to the cobe below, name, in each case, the angle between the line and the plane.(a) PV and PQRS(b) QV and PQRS(c) SU and PQRS(d) PV and SRVW(e) TV and SRVW(f) QW and PQUT W U Q R
15. P, Q and R represent three ports. Q is 35 km from and on a bearing of 032° from P. R is 65 km from p and on a bearing of 108° from P.(a) Calculate(i) QR,(ii) the bearing of R from Q.A ship sets sail at 0930 hours from P directly to Rat an average speed of 30 km/h and reaches a point S due
14. Two cruise ships P and Q leave the port at the same time. P sails at 10 km/h on a bearing of 030 and sails at 12 km/h on a bearing of 300. Find their distance apart and the bearing of P from Qafter 2 hours.
13. A, B and C are three points on level ground. The bearing of B from A is 068 and the bearing of C from A is 144. AB=370 m and AC 510 m. ==Find (i) the distance between B and C, (ii) ZACB, (iii) the bearing of C from B, (iv) the shortest distance from A to BC. N 68 370 m A 144 510 m C B
12. The diagram shows a park, ABCD, and a path BD. A is due north of D, B is due east of D and LDBC= 37. AD 34 m, AB=57 m and BC = 28 m.(i) Calculate the bearing of B from A. (ii) A path of the shortest distance possible is to be constructed from C to BD. Find the length of the path. (iii)
11. Points P, Q and R are on level ground.R is 600 m from Q on a bearing of 305°.Q is 950 m from Pon a bearing of 078°.(i) Calculate PR.(ii) Find the bearing of R from P. Z R 600 m N Q 78 950 m 305 P
10. A helicopter flies 30 km from a point P to another point Q on a bearing of 128. It then flies another 25 km to a point R on a bearing of 295. Find the distance between P and R.
9. A bookshop is 250 m due north of a supermarket. Sara walks from the supermarket in the direction 055. Calculate how far she has to walk before she is (a) equidistant from the bookshop and the supermarket, (b) due east of the bookshop.
8. A, B and C are three points on level ground. Given that the bearing of B from A is 122, LCAB=32 and LABC=86, find the possible bearing(s) of C from B.
7. P, Q and R are three points on level ground. Given that the bearing of R from P is 135, LPQR = 55 and LPRQ=48, find the bearing of (i) P from R, (iii) P from Q. (ii) Q from R,
6. A, B, C and D are the four corners of a rectangular plot marked out on level ground. The bearing of B from A is 040 and the bearing of C from A is 090. Find the bearing of (i) B from C, (ii) A from C, (iii) D from C.
5. A petrol kiosk P is 12 km due north of another petrol kiosk Q. The bearing of a police station R from P is 135 and that from Q is 120. Find the distance between P and R.
4. A point Q is 24 km from P and on a bearing of 072 from P. From Q, Waseem walks at a bearing of 320 to a point R, located directly north of P. Find (i) the distance between P and R, (ii) the distance between Q and R.
3. The figure shows the positions of P, Q and R.Find the bearing of (b) Pfrom Q.(a) Q from P.(d) P from R.(c) R from P.(f) R from Q.e) Q from R. N Z4 Q P 36% 100 43 R 37
2. The figure shows the positions of P, A, B and C.Find the bearing of (a) A from P, (b) B from P, (c) C from P, (d) P from A. (e) P from B, (f) P from C. C 47 N 35 A P B 15
1. The figure shows the positions of O, A, B, C and D.Find the bearing of (a) A from O, (b) B from O, (c) C from O, (d) D from O. C D N 4 39 33 A 44 0 28 B
13. A flagpole of height 12.2 m is placed on top of a building of height h metres. From a point T on level ground, the angle of elevation to the base of the flagpole B is 26 and the angle of elevation to the top of the flagpole C is 35.Find the value of h. 12.2 m C B hm 26 35 T
12. A satellite dish stands at the top of a cliff. The angle of depression of a ship, which is 80 m away from the base of the cliff, from the top of the satellite dish is 37. The angle of depression of the same ship from the foot of the satellite dish is 32. Find the height of the satellite dish.
11. The angles of depression of two boats due west of a cliff from the top of the cliff are 23 and 18 respectively. Given that the cliff is 88 m high, calculate the distance between the two boats.
10. The Eiffel Tower in Paris is 320 m tall. The angle of elevation from where Vasi stands at point A to the top of the tower is 38. Vasi walks x metres to point B and observes that the angle of elevation from B to the top of the tower is now 58. 38 58 A xm B C 320 m
9. An overhead bridge has a height of 5.5 m. The angles of elevation of the top of the bridge from two points P and Q on the ground are x and 23 respectively. 5.5 m af 23 P45.1 mQ
8. A castle is located on top of a mountain. Ali stands 55 m away from the foot of the mountain, on level ground. The angles of elevation of the top of the castle and the top of the mountain from Ali's line of sight are 60° and 45° respectively. Find the height of the castle.
6. Exercis astle has a height of 218 m. A bird stands on vel ground 85 m away from the foot of the castle. Calculate the angle of depression of the bird from the top of the castle.7. A clock tower, MT, has a height of 45 m. The angles of elevation of the top of the clock tower from two points A and
5. A boat is 65.7 m away from the base of the dif The angle of depression of the boat from the top d the cliff is 28.9. Find the height of the cliff. Exercis astle has a height of 218 m. A bird stands on vel ground 85 m away from the foot of the castle. Calculate the angle of depression of the bird
4. A building is 41 m high. The angle of depress a fire hydrant from the top of the building is 33 Find the distance between the fire hydrant and the foot of the building.
3. At a certain time in a day, a tree PQ, 44 m high, casts an 84-m long shadow RQ. Find the angle of elevation of P from the point R. P R Q 84 m 44 D
2. Two buildings on level ground are 120 m and 85 m tall respectively. The angle of elevation of the top of the taller building from the top of the shorter building is 33.9. Find the distance between the two buildings.
1. Li Ting standing at P. is flying a kite attached to a string of length 140 m. The angle of elevation of the kite K from her hand is 58°, Assuming that the string is taut, determine the vertical distance between her hand and the kite. 140 m P 58 Q
Find the length of PQ 5 cm A 6 cm 3 cm P B 7 cm 14 cm C
17. In the figure, the point Plies on AB such that AP=5 cm and PB-3 cm. The point Q lies on AC such that AQ=6 cm and QC-7 cm f#!#
16. In AABC, AB=8 cm, BC-5 cm and CA-6 cm. BC is produced to R so that CR=3 cm. (i) Express cos LBCA in the form q are integers. (ii) Hence, find the length of AR.
15. The figure shows two triangles ABC and ADE.Determine if AADE is an enlargement of LABC. Find the value of cos 0. Hence, find the value of x. D 2 cm 3 cm B 3.5 cm x cm C 5 cm E 6 cm
14. petium ABCD, AB is parallel to DC, 45 cm, BC=5 cm, CD=7.5 cm and 6cm. The point X lies on CD such that BX is to AD. Find LBCX and the length of BD. triangles ABC and ADE pure shows two triangles ABC and ADE. D 2 cm x cm B 3.5 cm 3cm C 5 cm E 6 cm Determine if AADE is an enlargement of AABC Find
13. A shown as a a triangle XYZ on a map with 2cm to 5 km. Given that XY-9 cm, he length, in km, which is represented by XZ, om and XZ-8 cm, find the area of the farm, in km. RCD. AB is parallel to DC,
12. In the figure, D is a point on CB such that AD=2 cm, AC = 4.5 cm, CD=3.5 cm and LABD = 50.Find (i) LADB, (ii) the shortest distance from A to CR (iii) the length of BD. 4.5 cm 2 cm 50 C 3.5 cm D
11. The figure shows a quadrilateral with the dimensions as shown.Find (i) the value ofa, (ii) 0. A 5 cm 92 6 cm a cm 7 cm 5 cm
10. The diagram shows the support structured roof of a building. ADC is a straight li AD CD 12 m, BQ-7 m and LPDAFind (i) ZBAD, (ii) the length of the support PD, (iii) the length of the support DQ. B 7 m P 5 m 0 50 A 12 m D 12 m C
9. In AABC, BC = 4 cm. M is the midpoint of BC such that AM = 4 cm and LAMB = 120°. Find(i) the length of AC,(ii) the length of AB,(iii) ZACB.
8. The diagram shows the cross section of the roof of an old cottage. It is given that AP = 5 m, PC = 8 m, LAPC 60 and LABC = 45.Find (i) the length of AB, (ii) the length of AC. B 45 P 60 5 m A 8 m C
7. In the figure, the point B lies on AC such that AB-8 m, BD-9 m, LABD=125 and LBCD-55Find (i) the length of CD, (ii) the length of AD. D 9 m 125 55% C A 8 m B
6. In APQR, PQ=7.8 cm, QR = 9.1 cm and PR=4.9 cm. Find the size of the largest angle.
5. In AABC, AB = 6.7 cm, BC= 3.8 cm and AC 5.3 cm. Find the size of the smallest angle.
4. In AXYZ, x=7 m, y=8 m and z = 9 m. Find all the unknown angles.
3. MNO, m = 4.2 cm, n = 5.8 cm and 141.4. Find o.
2. dh CHI, g=9 cm, i=7 cm and LH = 30.\
1. BLANC, a=5 cm, b = 7 cm and _C=60°.
16. In AABC, LA = 35, BC=5 cm and sin B (i) Given that B is obtuse, find B. (ii) Find the length of AC. G F
15. A map has a scale of 8 cm to 1 km. An plot of land is shown as a quadrilateral A the map. The length of the diagonal AC LBAC 55, LBCA 77, LDAC-% LDCA 40. Find = (i) the length, in cm, of the side AB on the (ii) the length, in km, which is represente (iii) the area, in km, which is represented
14. Three buildings on a plot of land form a AMNO in which buildings M and O are the furthest apart, with a distance of 80 m between them. Building N is 67 m away from building M. It is given that L.MON = 43º. Find the distance between buildings O and N. 80 m 43 N M 67 m
13. In A/KL.11- 15 mm, KL = 19 mm and /JKL = 39°.Find the obtuse _KJL and the length of /K0.
12. In the figure, LPQR = LPSR 90, LQPR = 27.6, LPTS 64.2, PR = 5.7 cm, PS 3.2 cm and = PT=2.7 cm.Find (i) the length of QR, (ii) /SPR, (iii) _PST. S R Q 5.7 cm 3.2 cm 27.6 64.2 T 2.7 cm P
11. In the figure, PQRS is a nature reserve. A 5.7-km long walkway connects Q to S. It is given that ZQRS = 90°, /SQR = 73°, PQS = 48° and LPSQ=55°.Find the area of the nature reserve. P Q 48 5.7 km 73 55% R S
10. In the figure, RST is a straight line, /PST = 90°, ZSPR= 63°, ZPSQ = 54°, PS = 4.3 cm and ST = 5.7 cm.(i) Determine if QS is parallel to PT.(ii) Find the length of PR.(iii) Find the length of QS. R 63 54 4.3 cm S 5.7 cm T
9. An experiment is carried out to determine the extension of springs. Springs are attached to a horizontal bar at A, B and C and are joined to a mass DGiven that LACD=40, LCAD = 30, LABD = 80 and BD=5 cm, find(i) the distance between A and B, (ii) the distance between B and C, (iii) the vertical
8. In the figure, A, C and D are three points along a straight road where _ABC = 62°, ZACB = 68°, pc = 6 m and CD = 7.5 m.Find the distance AC, the area of the region enclosed by AB, BD and DA B 62 6 m 68 C 7.5 m D
7. june shows a metal framework in which AD m. CBAD - 25%,-46, 208C - 103' and the height of B'Find the length of the metal bar AB, the angle that BD makes with BN, the length of the metal bar CD. C 103 B 7.1 m 5.3 m 46 25 D N
6. In AABC, LABC=91, BC=7.4 cm and AC 11.6 cm. Find (i) LBAC, (ii) LACB, (iii) the length of AB.
5. In APQR, LP = 101, PQ = 13.4 cm and QR = 20.8 cm.Find (i) ZR.(ii) _Q, (iii) the length of PR. 20.8 cm R Q 101 13.4 cm P
4. For each of the following triangles ABC unknown angles and sides.(a) LA=92.0, b = 6.93 cm and a=153(b) LB 98.0, a = 14.5 m and b=17Am(c) LC 35.0, b = 8.7 cm and c=9.5 C b a A4 C B
3. In APQR, LP 75, LQ=60 and q = 14 cm. Find the length of the longest side.
2. In APQR, QR-7 cm, LPQR=47 and PRQ=97, Find the length of PQ.
1. For each of the following triangles, find the unknown angles and sides. (b) (a) C 7.4 cm 76 42 A4 B F 6.25 m 62 38.7 D E
13. In quadrilateral ABCD, AB = 3.2 cm, BC = 5.1 cm.4CBD = 34.4º and the length of the diagonal BD is 7.5 cm. Given further that the area of AABD is 11.62 cm2 and Z.ABD is obtuse, find(i) the area of ABCD,(ii) ZABD.
12. The diagonals of a parallelogram have lengths x cm OPEN and y cm. They intersect at 150". Given that the area of the parallelogram is 100 cm2, find a possible value of x and the corresponding value of y.
11. The length of each side of a rhombus is 15 cm.Given that the rhombus has an area of 40 cm3, find the angles of the rhombus.
10. In AXYZ, XY = 13.cm and YZ = 16,2 cm. Given that the area of AXYZ is 59.5 cm2, find the two possible values of /XYZ.
9. In APQR is 158 cm APOR, LPRQ=55, 3QR = 4PR and the area ofFind the length of QR. P Q 55% R
8. AABC. AB = 5x cm, AC = 4x cm and CGiven that the area of AABC is 97 cm, find the ale of x - 4PR and the area c C 4x cm A 68 5x cm B
7. In the figure, LADC= LACB=90, LEAD LCAB 40.4, AE = 4.1 cm, AD=3.7 cm AC = 8.0 cm.Find (i) LACD, (ii) the length of AB, (iii) the area of AAED. 4.1 cm A 55.1 E 40.4 8.0 cm 3.7 cm D C
6. The diagram shows the plan of two neighb estates in the form of two triangles.Calculate the total area of the two estates. 112 m 30% 202 m 60.5 197 m
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