MTHEMTIS Unit Part of Relationships
ngles Eercise 1 opy the following diagrams into your jotter and fill in the sizes of all the angles:- 1) 50 ) 50 60 3) 4) 5) 85 6) 7) 7 54 7 8) 56 9) 70 Maths Department -- National 5
Eercise Make a copy of each diagram and fill in the sizes of all the angles Maths Department -3- National 5
Eercise 3 1) opy each of the following diagrams into your jotter, and mark the sizes of every angle in your diagram. (O is the centre of every circle) a b E F c 65º 56 O 0º O G D H W º 40º V O X Y Z d e f M H L K 110º 7º O N G O I 64º P J O 47º 63 S Q R g P h i Q F N 136º E 49 O 9º O 5º M G H X Y 134 O T Z ) In the diagram D is a semi-circle. is parallel to D and angle D = 68º. D a alculate the size of angle D. b Eplain why angle D is a right angle. 68º Maths Department -4- National 5
3) In the diagram PRQ is an isosceles triangle drawn inside a semi-circle. ST is parallel to PQ. Find the size of angle PST giving a reason for your answer. Eercise 3 1) opy each of the following diagrams into your jotter. In each diagram mark the size of every angle. O. is the centre of each circle. P S R T Q a) b)g W P X O 50º O R 35º Y Q Z Maths Department -5- National 5
c) d) 0º O O 5º E D X Y Z e) L M f) P Q K O 35º N O 4 R Maths Department -6- National 5
g) h) R S T K 70º L M O U O 17º i) V N H O E F 0º G j) L 139º J 144º O Maths Department -7- National 5 K
Eercise 5 1) The rectangle D below has angle = 7 o. State the size of the following angles: a) angle D b) angle D c) angle ED d) angle D e) angle E f) angle E g) angle E h) the refle angle E. E D ) This diagram shows two squares D and PQRS with a common centre Z. State the size of: a) angle PQ b) angle DPS c) angle QPS d) angle PS. Maths Department -8- National 5
3) The rhombus KLMN below has angle KNL = 3 o. State the size of the following angles: K a) angle MZL L b) angle NKZ c) angle ZLM d) angle KLM e) angle NML N f) angle refle angle KNM. 3 o Z M 4) The rhombus PQRS below has angle QPS = 8 o. State the size of the following angles: Q a) angle QZR. b) angle OPZ. c) angle PQZ. P d) angle PQR. e) angle PSZ. f) angle PSR. g) angle ZRS. 8 o Z S R Maths Department -9- National 5
5) The kite PQRS below has angle SPQ = 64 o. Notice carefully what you are told about triangle QZR! State the size of the following angles: a) angle PZS. b) angle SPZ. c) angle PQZ. d) angle ZRS. e) angle ZRQ. f) angle PQR. g) the refle angle PQR. h) the refle angle QPS. 6) D shown below is a parallelogram. State the following angle sizes: a) angle b) angle D c) angle D d) angle D e) angle Z f) angle Z g) angle Z h) angle DZ Maths Department -10- National 5
7) (HINT: Look carefully at triangle ZD) D is a parallelogram. State the following angle sizes: a) angle ZD. b) angle DZ. c) angle DZ. d) angle. e) angle Z. f) angle D. g) angle DZ. h) angle ZD. 8) State the sizes of the following angles: a) angle DE b) angle D c) angle D d) angle F g) angle ED Maths Department -11- National 5
Eercise 5 For each regular polygon calculate a) central angles b) internal angles c) eternal angles 1) ) 3) 4) 5) 6) Maths Department -1- National 5
hords and perpendicular bisectors 1) hord has length 18 cm and is 4 cm from the centre of the circle. a) Make a copy of this diagram and fill the above information on your sketch. b) alculate the length of the radius of the circle. c) Thus state the length of the diameter. d Write down the length of M. e alculate the area of triangle O. f What kind of shape is O? ) hord XY has length 1 cm. It is 10 cm from the centre O of the circle.. a) alculate the length of the diameter of the circle. b) alculate the area of triangle XOY. c) Write down the length of MZ. 3) chord of length 6 inches is 6 inches from the centre of a circle. a) Draw a diagram to illustrate the above information. b) alculate the lengths of the radius and diameter of the circle. 4) The diagram shows a circle of diameter 10" (radius 5"). hord PQ within this circle has length 8". a) alculate the distance of the chord from the centre. b) alculate the area of triangle POQ. Maths Department -13- National 5
5) EF is a chord 8 cm from the centre of a circle of radius 17 cm. a) alculate the length of the chord EF. E M 8 F b) MO is produced until it meets the circle at point G. O alculate the area of triangle EFG. G 6) chord 6 ins long is drawn in a circle of diameter 10 ins. alculate the distance of the chord from the centre. 7) chord is drawn in a circle of radius 5 cm at a distance of cm from the centre. alculate the length of the chord. 8) chord 6 ins long is at a distance of alculate the length of the diameter of the circle. 9) and D are parallel chords situated on opposite sides of the centre as shown in the diagram. has length 18 cm, D has length 4 cm and the radius of the circle is 13 cm. a) alculate the distance between the chords. b) What would their distance apart have been had they been situated on the same side of the centre? 3 1 ins from the centre of a circle. 5 10) The parallel chords and D are 14" apart. The chord has length 1", and the circle has radius 10". a) alculate the length of the chord D. b) alculate the area of the trapezium D. Maths Department -14- National 5
11) parallel chords of a circle of radius 14 cm are 15 cm and 18 cm in length. How far are the chords apart? (There are different answers) 1) In a circle of radius.5", two parallel chords are placed 3.1" apart. If the length of one chord is 4.8", find the length of the other. 13) Two equal and parallel chords in a circle of radius 6.5" are 7.8" apart. alculate the length of each chord. 14) The two circles shown in this diagram are concentric (same centre, O). The chord is 16 cm away from the centre and the radii are 0 cm and 4 cm. a) alculate the length of M. b) alculate the length of M. c) Write down the length of. d) alculate the area of triangle O. M D 16 O 15) and are the centres of the circles in the accompanying diagram. The circles have radii 7 cm and 1 cm. The common chord D has length 10 cm. a) alculate the length of the line joining the centres. b) What is the maimum possible distance between points which are on the circumferences of either circle? c) The line meets the circles at E and F. alculate the length of EF. Maths Department -15- National 5
v v 16) and D are two parallel chords of this circle whose radius is 13 cm. 10 4 If = 10 4 cm and D = 1 cm. calculate the distance between them. O (There are two possible answers another diagram may help) D 17) is a chord of a circle centre O. The perpendicular from O to the chord cuts the chord at and meets the circle at D. O If = 8 cm and D = 1 cm, find the radius of the circle. 1 D 18) PQ is a chord of a circle centre O. The perpendicular from O to the chord cuts the chord at S and meets the circle at T. If PQ = 1 cm and ST = cm, find the radius of the circle. P O S Q T Maths Department -16- National 5
O 19) JK is a chord of a circle centre O. The perpendicular from O to the chord cuts the chord at L and meets the circle at M. If JK = 14 cm and LM = 3 cm, find the diameter of the circle. O J L 3 M K 0) is a chord of a circle centre O. The perpendicular from O to the chord cuts the chord at and meets the circle at D. If = 0 cm and D = 6 cm, find 6 D a) the radius of the circle b) the area of triangle O. 1) sheep shelter is part of a cylinder as shown in Figure 1. It is 6 metres wide and metres high. The cross section of the shelter is a segment of a circle with centre O, as shown in Figure. O is the radius of the circle. alculate the length of O. Maths Department -17- National 5
) Two equal circles cut each other at and. The line joining the two centres meets the circles at and D. D If = 14 cm and D = 4 cm, calculate the length of the radius. 3) Water is flowing through a pipe with a circular cross-section. If the pipe has a radius of metres and the width of the water surface is 3 5 metres, how deep is the water? ( possible answers) 4) The entrance to a tunnel is an arc of radius 5 metres. The width of the road is 7 6 metres. alculate the O 5 m a) distance OM b) height of the tunnel. M 7 6 m Maths Department -18- National 5
5) The curved part of a doorway is an arc of a circle with radius 500 mm and centre. The height of the doorway to the top of the arc is 000 mm. The vertical edge of the doorway is 1800 mm. alculate the width of the doorway. 6) badge is made from a circle of radius 5 cm. Segments are taken off the top and bottom of the circle as shown. The straight edges are parallel. The badge measures 7 cm from the top to the bottom. The top is 8 cm wide. alculate the width of the base. Maths Department -19- National 5
O M 7) n oil tanker has a circular cross-section of diameter 4 metres. The surface of the oil is 8 metres from the top of the tank. a) What is the height of OM? b) What is the width of the oil s surface? (see fig 1) c) The tanker is filled to a depth of 3 5 metres. What is now the width of the oil s surface? O M M fig 1 8 m 3 5 m fig 8) The design of a circular medallion is based on an equilateral triangle PQR. The sides of the triangle are 3 cm long. alculate the radius of the circle. P O Q R Maths Department -0- National 5
9 n oil tank has a circular cross-section of radius 1 m. It is filled to a depth of 3 4 metres. a) alculate, the width in metres of the oil surface. b) What other depth of oil would give the same surface width? Maths Department -1- National 5
Trigonometric Graphs Eercise 1 a) Draw a rough sketch of each of the following functions. b) State the period of the function. c) State the amplitude of the function 1) y sin ) y cos 3) y 3cos 4) y 10sin 5) 1 y cos 6) y sin 1 7) y cos 1 8) y sin 9) y cos 3 10) y sin 11) y cos 1) y sin3 13) y cos4 14) y 3sin 15) y cos 3 16) y 3cos 1 17) y sin 1 18) y 3cos 19) y 4sin 0) y sin 3 1) y sin 1 ) y cos 1 3) y sin3 4) y cos4 5) y 3cos 1 6) y sin 1 7) y 4cos 3 8) sin3 1 0 0 y 9) y sin 90 30) y cos 90 0 0 31) y sin 180 3) y sin 70 Maths Department -- National 5
Eercise Identification of Trigonometric graphs 1) The diagram shows the graph of y y k sin, 0 360. 360 a) Find the value of k b) State the period c) State the amplitude - ) The diagram shows the graph of y k sin, 0 360. a) Find the value of k b) State the period c) State the amplitude 4-4 y 360 3) The diagram shows the graph of y k sin, 0 360. a) Find the value of k b) State the period c) State the amplitude 5-5 y 360 4) The diagram shows the graph of y k cos, 0 360. Find the value of k. 3-3 y 360 5) The diagram shows the graph of y k cos, 0 360. a) Find the value of k b) State the period c) State the amplitude 4-4 y 360 Maths Department -3- National 5
6) The diagram shows the graph of y k cos, 0 360. a) Find the value of k b) State the period c) State the amplitude 7-7 y 360 7) The diagram shows the graph of y sin a, 0 360. a) Find the value of a b) State the period c) State the amplitude 8) The diagram shows the graph of y sin a, 0 360. a) Find the value of a b) State the period c) State the amplitude y 1-1 y 1-1 360 360 9) The diagram shows the graph of y cos a, 0 360. a) Find the value of a b) State the period c) State the amplitude 1-1 y 360 10) The diagram shows the graph of y cos a, 0 360. a) Find the value of a b) State the period c) State the amplitude 1-1 y 360 Maths Department -4- National 5
11) The diagram shows the graph of y k sin a, 0 360. a) Find the values of a and k b) State the period c) State the amplitude - y 360 1) The diagram shows the graph of y k cos a, 0 360. a) Find the values of a and k b) State the period c) State the amplitude 4-4 y 360 13 )The diagram shows the graph of y k sin a, 0 360. a) Find the values of a and k b) State the period c) State the amplitude 5-5 y 360 14) The diagram shows the graph of y k cos a, 0 360. a) Find the values of a and k b) State the period c) State the amplitude 15) The diagram shows the graph of y k sin a, 0 360. a) Find the values of a and k b) State the period c) State the amplitude y 4-4 y - 360 360 Maths Department -5- National 5
16)The diagram shows the graph of y k cos a, 0 360. 4 y a) Find the values of a and k b) State the period c) State the amplitude 17) The diagram shows the graph of y k sin, 0 360. -4 y 1 360 a) Find the value of k b) State the period c) State the amplitude -1 360 y 18) The diagram shows the graph of 1 y k cos, 0 360. 0 360 a) Find the value of k b) State the period c) State the amplitude y -1 - -3 19) The diagram shows the graph of y k cos a, 0 360. a) Find the values of a and k b) State the period c) State the amplitude 1 0-1 - 360 0) The diagram shows the graph of y 3 y k sin a, 0 360. a) Find the values of a and k b) State the period c) State the amplitude 1 0 360-1 Maths Department -6- National 5
1) The diagram shows the graph of y k sin a, 0 360. a) Find the values of a and k b) State the period c) State the amplitude ) The diagram shows the graph of y k cos a, 0 360. a) Find the values of a and k b) State the period c) State the amplitude y 3-3 y 9-9 360 360 Eercise 3 For each function, find a) the maimum and minimum values of the function. b) a corresponding replacement for for each. 1) y 3 sin ) y cos 7 3) y sin 4) y 4cos 5) y 5cos 6) y sin 3 7) y cos 1 8) y sin 4 9) y 3cos 5 10) y cos 11) y 8 3sin 1) y cos3 13) y sin 14) y 1 sin 15) y 1 sin 16) y 5 cos 17) y 4 sin 18) y 1 cos 19) y 1 cos 0) y 4cos 3 1) y cos4 3 ) y 3cos 4 3) y 4cos3 Maths Department -7- National 5
4) On a certain day the depth, D metres, of water in an estuary, t hours after midnight, is given by the formula: t 0 D 15 7 8sin 30 a) find the depth of the water at.00 pm. b) what is the time after midnight when the water is 0 m? c) find the maimum depth of the estuary and at what time after midnight it first occurs. d) find the minimum depth of the estuary and at what time after midnight this first occurs. e) how long does it take for the depth to change from maimum to minimum depth? 5) Repeat question 4 with formula: t 0 D 1 8 6cos 30 6) toy is hanging by a spring from the ceiling. Once the toy is set moving, the height H metres at time t seconds, of the toy above the floor is given by the formula: t 0 H 1 7 0 cos 30 a) state the minimum value of H. b) find the height of the toy above the floor after 10 seconds. c) find when the toy is first 1.6 m above the floor. 7) The number of hours of daylight h, in a ritish city is given by the formula; 360 h 11 7 3sin 365 where is the number of days after 1 pril. a) what is the maimum number of hours of daylight? b) what is the least number of hours of daylight, and by how many days after 1 pril does this occur? 0 Maths Department -8- National 5
8) The depth d metres, of water in a harbour entrance over a 4 hour period starting at midnight is given by: h 0 d 6 sin 30 where h is the number of hours after midnight. a) find the maimum depth of the harbour and the first time after midnight this occurred. b) a fishing boat needing a depth of 5 metres wants to dock in the harbour. If the depth of the harbour at midnight is 6 metres, how long is it before the depth reaches 5 metres and it becomes too shallow for the boat to dock? c) what is the first time that the depth again goes above 5 metres and it becomes deep enough for the boat to leave the dock? Eercise 4 0 0 Solve the following equations where 0 360. 1) 3cos 1 0 ) 5cos 0 3) 6sin 1 0 4) 9sin 0 5) 8sin 3 0 6) 4tan 3 0 7) 3tan 9 0 8) 4cos 1 0 9) 7cos 3 0 10) 1sin 1 0 11) 8tan 1 0 1) 9tan 5 0 13) 4 3tan 5 14) 7 cos 15) 3sin 1 16) cos 75 3sin 1 17) tan35 cos 1 18) 8sin 3 19) 11sin 5 0) 3(sin 1) 4 Eercise 5 0 0 Solve the following equations where 0 360. 1) sin 1 0 ) cos 1 0 3) cos 3 0 4) cos 1 0 5) 3 tan 1 0 6) tan 1 0 Maths Department -9- National 5
7) cos 3 0 8) tan 3 0 9) sin 3 0 10) tan 3 4 11) sin 1 1) sin 1 0 13) tan 3 0 14) cos 1 15) 3 sin 4 16) 1 sin 3 Eercise 6 alculate where the following trigonometric graphs cut: a) the -ais b) the y-ais 1) y cos 1 ) y 4sin 3 3) y cos 3 4) y 4tan 1 5) y sin 1 6) y 6sin 5 7) y cos 4 8) y tan 3 9) y 3 7cos 10) y 3 tan 1 11) y 4cos 3 1) y 5sin Eercise 7 Prove the following identities: 1) 3cos 1 3sin ) (cos sin )(cos sin ) cos 1 sin 1 cos 3) ( 1 sin )tan sin 4) 1 cos sin sin 5) 3cos 3sin 3 6) (cos sin ) cos sin 1 7) ( 1 sin )(1 sin ) cos 8) 3 3sin 3cos 9) 5cos 5 5sin 10) (cos sin )(cos sin ) 1 sin Maths Department -30- National 5
11) cos tan sin 1) 1 cos 13) tan cos 14) tan 1 cos sin cos sin cos 1 cos sin cos sin 15) 4sin 3 1 4cos 16) cos 1 1 sin 17) (cos sin ) 1 sin cos 4 4 18) cos sin cos sin 19) cos sin 0 0) 1 1 1 sin 1 sin cos 1) cos (1 tan ) 1 ) (cos sin ) 1 sin cos 3) sin 3cos cos 4 4) cos cos sin cos 3 sin sin 5) tan 3 cos cos 7) 1 sin 1 3tan 8) cos 4 4 6) sin 1 cos cos tan sin 1 9) 1 sin.tan cos cos cos 4 sin sin cos 30) 3sin cos 3cos 31) sin cos tan 1 cos 3) 1 1 tan 33) tan sin cos cos 1 sin 1 sin cos cos Maths Department -31- National 5
Similar Triangles Eercise 1 1) Find the length of the side PQ. Q 90 90 4 cm 1 cm 16 cm 60 30 60 30 P R ) Find the length of the side PQ. 4 90 8 Q 90 10 60 30 P 60 30 R 3) Find the length of the side XY. 65 Y 9cm E 65 X 40 3 cm 75 Z D 40 1 cm 75 F Maths Department -3- National 5
4) Find the length of the side RT. M S 75 1 cm 75 0 cm L 84 15 cm 1 N R 84 1 T 5) Find the length of the side JL. X 5 7.5 m Y 100 5.1 m 55 Z J 5 K 100 55 6.8 m L 6) Find the length of the side KL. 110 Y 3 m 110 K X 30 8 m 40 Z J 30 40 1 m L Maths Department -33- National 5
7) Find the length of side PQ Q cm 95 95 65 6 cm 0 P 65 0 1 cm R 8) Find the length of PR. M Q 40 40 10 cm 15 cm 110 30 L 18 cm N P 110 30 R 9) Find the length of EF. 0 F 4.5 cm 0 Y E 5 9 cm 135 G 135 5 X 1 cm Z Maths Department -34- National 5
10) Find the length of the side S 70 4 m 70 6.4 m. 5 85 R 5 10 m 85 T 11) Find the length of the side ST. S 6.3 cm M 75 14 cm 8.1 cm 75 L 84 1 N R 84 1 T 1) Find the length of side PQ. Q 65 95 15.5 cm 65.5 cm 0 P 0 18.6 cm 95 R Maths Department -35- National 5
13) Find the length of QR. M Q 110 40 4 cm.4 cm 30 40 P 110 L 30 6 cm N R 14) Find the length of side EF. F 5 Y 135 8.1 m E 0 7.5 m 135 G X 5 10.8 m 0 Z 15) a) Find the length of side QR. b) Find the ratio area of triangle : area of triangle PQR. cm 85 Q 4.5 cm 3 cm 85 60 35 P 60 35 Maths Department -36- National 5 R
16) a) Find the length of DF. b) Find the ratio of area of triangle DEF : area of triangle. E 5 cm 30 D 50 50 7.5 cm 100 F 3.6 cm 100 30 17) a) Find the length of RQ. b) Find the ratio of area of triangle PQR : area of triangle. P 10.5 cm 110 5 0 cm 45 15 cm 5 110 45 Q R Maths Department -37- National 5
Maths Department -38- National 5 Eercise (ll sizes in centimetres) 1) Find D ) Find PR 3) Find JL 4) Find 5) Find 6) Find LK D E 6 9 4 P S Q T R 9 1 6 D E 6 8 3 J M K N L 8 1 J M L N K 18 9 1 D E 7 11 14
Maths Department -39- National 5 7) Find 8) Find QR 9) Find PR 10) Find 11) Find PR 1) Find JL P Q S R S 8 11 14 D E 9 1 3 D E 4 P Q S R T 9 1 J K M L N 6 8 1 P Q S R T 9 1
Eercise 3 (ll sizes in centimetres) 1) Find RS ) Find D 1 P Q 7 R 3 S 6 T D 14 E 3) Find E 4) Find GH 1 D 15 E E 1 F 10 0 15 D G H Maths Department -40- National 5
v v 5) Find 6) Find E 7 7 1 1 D 18 E D 31.5 E 7) If E = 3, find 8) If E = 1, find a) a) b) E b) E 15 18 D 5 E D 4 E Maths Department -41- National 5
9) If E = 55, find 10) If DE = 30, find a) a) FE b) E b) DF 8 D 3 E F D 36 E G 7 H 11) If PT = 55, find a) PR b) RT 1 P Q R S 1 T Maths Department -4- National 5
Eercise 4 (ll sizes in centimetres) 1) a) Find D b) Find 4 7 8 E 5 D ) Find SR P 7 Q 6 R S 4 T 3) a) Find XY b) Find WX 4 X W 6 3 V 4 Z 7 Y 4) a) Find QT b) Find PQ Q 4 R 7 P 11 T 3 Maths Department -43- National 5 S
5) T = 0 T a) Find K b) Find KT K c) Find TQ 3 5 Y 1 Q 6) alculate a) D 5 8 7 b) E D 14 E 7) alculate a) PQ b) RS P 9 R 8 7 Q S 6 T 8) alculate a) FE b) ES F E 13 S 4 3 Z R Maths Department -44- National 5
9) W =14 a) alculate L b) alculate LW M 5 L 4 R W 10) KN =1 a) Find KS and KN b) If YN is cm longer than TK, find the lengths of YN and TK. K T 3 S 4 Y N Maths Department -45- National 5
Eercise 5 1) Triangles E and D with some of their measurements, are shown opposite. 6 cm Triangle E is similar to triangle D. 10 cm E cm D alculate the length of E. ) is the diameter of the circle with centre O and radius 1 cm. D is a chord of the circle. OE is parallel to D. ngle D = 58 0. E 1 cm O D 58 alculate the length of ED. 3) In triangle, = 8 cm, = 6 cm and PQ is parallel to. M is the midpoint of. Q lies on, cm from M as shown in the diagram. a) Write down an epression for the length of Q. 4 b) Show that PQ = 4 3 centimetres. P 8 cm 6 cm M Q Maths Department -46- National 5
4) vertical flagpole 1 metres high stands at the centre of the roof of a tower. The tower is cuboid shaped with a square base of side 10 metres. t a point P on the ground, 0 metres from the base of the tower, the top of the flagpole is just visible as shown. alculate the height of the tower. P 0 m 1 m 10 m 5) metal beam is 6 metres long. It is hinged at the top, P, of a vertical post 1 metre high. When touches the ground, is 1 5 metres above the ground as shown. When comes down to the ground, rises as shown. 1 5 m P 1 m 6 m y calculating the length of P, or otherwise, find the height of above the ground. P 6 m 1 m Maths Department -47- National 5
Eercise 6 In each question the shapes are similar. Find the ratio of their areas. 1) 18 cm 1 cm ) 10 cm 5 cm 3) 16 cm 1 cm Maths Department -48- National 5
4) 5) 14 cm 35 cm 6) 3 cm 40 cm 11 cm 44 cm Maths Department -49- National 5
7) 0 cm 60 cm 8) 50 cm 300 cm 9) 140 cm 10 cm 10) 300 cm 500 cm Maths Department -50- National 5
Eercise 7 In each question the shapes are similar. Find the ratio of their volumes. 1) 10cm 0cm ) 3 inche s 5 inches 3) 6cm 9cm 4) m 5m Maths Department -51- National 5
5) 7cm 1cm 6) 50cm 15cm 7) 7cm 1cm Maths Department -5- National 5
8) 40cm 16cm 9) 8cm 1cm 10) 33cm cm Maths Department -53- National 5
8 cm 18 cm Eercise 8 1) These picture frames are similar. The costs are directly related to their areas. 30 cm 40 cm a) What is the breadth of the larger picture frame? b) If the smaller frame costs 88, what is the cost of the larger frame? c) If the larger frame costs 4 50, what is the cost of the smaller frame? ) These triangular boes of chocolates are similar. The costs are directly related to their areas. a) What is the height of the larger bo? b) If the smaller bo costs 8, what is the cost of the larger bo? c) If the larger bo costs 18 50, what is the cost of the smaller bo? 3) The costs of these circular jigsaws are directly related to their areas. 4 cm 30 cm a) If the cost of the larger jigsaw is 6, what is the cost of the smaller one? 5 cm 10 cm b) If the cost of the smaller jigsaw is 1 40, what is the cost of the larger one? 4) These mirrors are similar. The heights are 80 cm and 48 cm respectively. The width of the larger mirror is 56 cm. The costs of the mirrors are directly related to their areas. a) What is the width of the smaller mirror? b) If the cost of the larger mirror is 36, find the cost of the smaller one. c) The cost of the smaller mirror is 18 50, find the cost of the larger one. Maths Department -54- National 5
49.5 cm 15.4 cm 5) These pentagonal tiles are similar. The costs are directly related to their areas. a) What is the length of the dotted line in the larger pentagon? 10 cm 1 cm b) If the cost of the smaller tile is 1 50, what is the cost of the larger one? c) If the cost of the larger tile is 3 50, find the cost of the smaller one. 6) These chopping boards are similar. The costs are directly related to their areas. a) alculate. 35 cm b) If the cost of the large chopping board is 14, what is the cost of the smaller one? 5 cm c) If the cost of the small chopping board is 14, what is the cost of the large one? 7) bottles are similar in shape. The heights of the bottles are 8 cm and 35 cm respectively. The width of the smaller bottle is 9 cm. The costs of the bottles are directly related to the volumes of the contents. a) What is the width of the larger bottle? b) If the cost of the smaller bottle is 1 40, what is the cost of the larger one? c) If the cost of the large bottle is 1 83, find the cost of the small one. 8) The cost of balls are directly related to their volumes. The diameters of the balls are 10 cm and 15 cm. a) If the cost of the smaller ball is 1 0, what is the cost of the larger one? b) If the cost of the larger ball is 6 50, find the cost of the smaller one. Maths Department -55- National 5
15 cm 9) jars are similar in shape. The heights of the jars are 15 cm and 1 cm. The width of the larger jar is 6 cm. The costs of the jars are directly related to their contents. a) What is the width of the smaller jar? b) If the cost of the larger jar is 1 10, what is the cost of the smaller one? c) If the cost of the smaller jar is 68p, what is the cost of the larger one? 10) These boes of biscuits are similar in shape. The costs of the boes are directly related to their volumes. a) What is the height of the smaller bo? 7 cm 7 cm 1 cm 1 cm b) If the cost of the larger bo is 9 54, find the cost of the smaller one. c) If the cost of the smaller bo is 3 5, find the cost of the larger one. 11) The ice cream cones are similar in shape. The diameter of the smaller cone is 4 cm. The costs of the cones are directly related to their volumes. a) What is the diameter of the larger cone? 10 cm 1 cm b) If the cost of the smaller cone is 48p, what is the cost of the larger one? c) If the cost of the larger cone is 1, what is the cost of the smaller one? 1) Drinking chocolate is sold in different sizes of cylindrical tins which are similar in shape. The diameters are 9 cm and 15 cm respectively. The height of the smaller cylinder is 1 cm. The costs are directly related to their volumes. a) What is the height of the larger cylinder? b) If the cost of the smaller tin is 1 0, what is the cost of the larger one? c) If the cost of the larger tin is 8 60, what is the cost of the smaller one? Maths Department -56- National 5