MATHEMATICS. S2 Level 3/4 Course -1- Larkhall Maths Department Academy

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1 MTHEMTIS S2 Level 3/4 ourse -1- Larkhall Maths Department cademy

2 17 cm The ircle Eercise 1() Find the circumference ( 1) 2) ) of the following circles 3) 4) 1 12 cm 5 cm 28 m 5) 6) 7) 3 2 cm 8) 15 m 22 m 9) 10) 11) 12) 52 cm 5 cm 34 m Eercise 1() Find the circumference ( ) of the following circles 1) d = 2 m 2) d = 20 m 3) d = 54 cm 4) d = 4 2 m 5) d = 12 6 cm 6) d = 6 3 cm 7) r = 2cm 8) r = 6 m 9) r = 50 m 10) r = 3 2 cm 11) r = 8 4 m 12) r = 12 6 cm 13) d = 28 m 14) d = 7 4 cm 15) r = 19 m 16) r = 264 cm Maths Department -2- S2 Level 3/4 ourse

3 17 cm Eercise 2() Find the area ( ) of the following circles 1) 2) 3) 3 2 cm 4) 15 m 22 m 5) 6) 7) 8) 1 12 cm 5 cm 28 m 9) 10) 11) 12) 24 cm 5 cm 12 m Eercise 1() Find the area ( ) of the following circles 1) r = 2 m 2) r = 10 m 3) r = 14 cm 4) r = 4 2 m 5) d = 6) d = 10 cm 7) d = 20 cm 8) d = 6 m 9) r = 50 m 10) r = 3 2 cm 11) d = 8 4 m 12) r = 12 6 cm 13) d = 28 m 14) d = 7 4 cm 15) r = 19 m 16) d = 264 cm S2 Level 3/4 ourse -3- Maths Department

4 6 cm Eercise 3() Find the area of the following shapes 2) 1) 3) 12 cm 4) 1 m 5) 9 m 6) 2 m 7) 5 cm 8) 11 m 9) 0 7 m 10) 20 m 11) 12) 13 m 12 cm Eercise 3() Find the area of the following shapes 1) 45 6 cm 2) 10 cm 45 3) 14 cm 4) 9 m 5) 3 m 120 6) 23 m 60 7) 72 8) m Maths Department -4- S2 Level 3/4 ourse

5 6 cm Eercise 4() Find the perimeter of the following shapes 2) 1) 3) 12 cm 4) 1 m 5) 9 m 6) 2 m 7) 5 cm 8) 11 m 9) 0 7 m 10) 20 m 11) 12 cm 12) 13 m Eercise 4() Find the perimeter of the following shapes 1) 45 6 cm 2) 10 cm 45 3) 14 cm 4) 9 m 5) 3 m 120 6) 23 m 60 7) 72 8) m S2 Level 3/4 ourse -5- Maths Department

6 7 m 7 m 12 cm 2 m 5 cm 10 m Eercise 5() Find the area of the following shapes 2) 1) 3) 4 cm 6 cm 4 cm 18cm 4) 9 m 8 m 5) 6) 30 m 3 m 20 m Eercise 5() Find the area of the following shapes 1) 3) 4 cm 2) 11 m 4 cm 4) 5) 12 m 6 m 6) 4 m 4 m Maths Department -6- S2 Level 3/4 ourse

7 7 m 7 m 12 cm 2 m 5 cm 10 m Eercise 6() Find the perimeter of the following shapes 2) 1) 3) 4 cm 6 cm 4 cm 18cm 4) 9 m 8 m 5) 6) 30 m 3 m 20 m Eercise 6() Find the perimeter of the following shapes 1) 3) 4 cm 2) 11 m 4 cm 4) 5) 12 m 6 m 6) 4 m 4 m S2 Level 3/4 ourse -7- Maths Department

8 Eercise 7() Find the total shaded area in each of the following diagrams Maths Department -8- S2 Level 3/4 ourse

9 Eercise 8() 1 wheel has diameter 80 cm. How far does the wheel travel in one revolution? 2 Repeat Question 1 for the following wheels: a) Diameter = 1 2 m b) Diameter = 2 6 m c) Radius = 3 m d) Radius = 54 cm. 3 alculate the diameter of a circle with circumference 40cm 4 Repeat Question 3 for the following circles: a) ircumference = 82 cm b) ircumference = 160 cm c) ircumference = 29m. 5 alculate the diameter of a circle with area 40 cm². 6 Repeat Question 5 for the following circles: a) rea = 76 cm² b) rea = 15 m² c) rea = 10km² (d) rea = 300 m² 7 alculate the area of a circle whose circumference is 70 cm. 8 alculate the area of a circle whose circumference is 25 m. 9 alculate the circumference of a circle whose area is 50 cm². 10 alculate the circumference of a circle whose area is 90m². S2 Level 3/4 ourse -9- Maths Department

10 Trigonometry Eercise 1() 1 opy each of the triangles below into your jotter. On each triangle mark H for the hypotenuse and by looking at the 'marked' angle write O on the opposite side and on the adjacent side. 2 For the following angles find correct to 3 decimal places (i) the sine (ii) the cosine (iii) the tangent a) 20 b) 61 c) 9 d) 76.4 e) 27.5 f) 54.9 g) 5.6 h) 84.3 i) 7.8 j) 29.4 k) 43.1 l) 36.8 m) 59.2 n) 48.1 o) 71.9 p) 34.5 q) 89.1 r) 2.5 s) 18.2 t) Find the angle (correct to 1 decimal place) which has a tangent of a) b) c) d) e) f) g) h) i) j) Maths Department -10- S2 Level 3/4 ourse

11 4 Find the angle (correct to 1 decimal place) which has a cosine of a) b) c) d) e) f) g) h) i) j) Find the angle (correct to 1 decimal place) which has a sine of a) b) c) d) e) f) g) h) i) j) Eercise 2() 1 Find the length of the side marked. (TNGENT) 2 Find the length of the side marked. (SINE) S2 Level 3/4 ourse -11- Maths Department

12 3 Find the length of the side marked. (OSINE) Eercise 2() Find the length of the side marked. (MIXED) Maths Department -12- S2 Level 3/4 ourse

13 Eercise 2() alculate the length of the side marked in each triangle Q 65 P X 14 cm cm cm 53 Z R X 58 Y 22 cm 19 cm X km Q 27 Y P X 69 R 24 cm Z Y 9 cm Z Y E m F G Z K 20 m 64 3 cm R L L K 4 km M E 40 F 9 m G U 17 V 18 P cm 63 R W 5 cm 30 L 75 V 42 m D H V R mls 21 K m N G Y 86 m N K 15 km D 30 km E S2 Level 3/4 ourse -13- Maths Department F

14 H mls 7 K G m 29 cm y cm m y 21 P cm cm Q 70 R y Eercise 3() Find the size of the angle marked in each triangle Maths Department -14- S2 Level 3/4 ourse

15 4 11 m Eercise 3() Find the size of the angle marked in each triangle 1) 2) 3) 4) 17 mls alculate < 4 mls R P 4 cm L 9 cm V 18 m alculate <RPV alculate <DLH D 14 m 12 km H V alculate <VR R 5 km 5) 6) 7) 17 m 8) N K 12 km alculate <KNG 3 km G K 6 7 m Y 3 6 m N alculate <YKN L D 21 m alculate <DHL H 5 72 m alculate < S2 Level 3/4 ourse -15- Maths Department

16 Eercise 4() Find the size of in each triangle. Maths Department -16- S2 Level 3/4 ourse

17 Eercise 4() X m 5 m P 7 5 m m Y Z Q R Find YZ Find QR 3 Triangle STV is isosceles 4 Triangle is isosceles ST = SV = Find the lengths of ST and SV. S 50 T Find the lengths of and m V 2 5 cm 5 Find the length of and the length of the altitude of triangle X through X. Hence, find the area of triangle X. X 7 m Find the length of PR and the length of the altitude of triangle PQR through Q. Hence, find the area of triangle PQR. P Q 18 2 m R 7 8 Q 10 cm cm D P S R alculate the length of D alculate the length of PS S2 Level 3/4 ourse -17- Maths Department

18 km E Q 21 D G F P T 53 R alculate the length of EF alculate the length of TR L m D Find the distance from to 9 m K N M Find the length of KM P = S m D Q = 40 4 cm R 9 cm alculate the length of Find the size of <PRS Eercise 5() 1) ramp is fitted at a school to allow disabled access to the second floor of the building. The ramp is 48 m long and is at an angle of 11 to the horizontal. What is the height of the second floor above the ground? Maths Department -18- S2 Level 3/4 ourse

19 2) The diagram shows a shop s ramp for customers who are wheelchair users. It connects the pavement to the level of the shopping mall. The ramp is 14 metres long and slopes at an angle of 9, as shown. alculate the difference in height, h metres between the pavement and the shopping mall. Give your answer correct to the nearest metre. 3) The diagram shows a flagpole which is supported by a wire which is fied to the ground 8 2 metres from the base of the flagpole. The wire is 15 3 metres long. alculate the angle between the wire and the ground m 8.2 m 4) Sam is flying a kite. The string is 48 metres long. How high is the kite above the ground? (marked in the diagram) 5) triangular bracket is designed to support a shelf. Its length is 10 cm and its height is 7 5 cm. 10 cm alculate the angle at the base of the bracket, angle. 7 5 cm S2 Level 3/4 ourse -19- Maths Department

20 6) ramp has been constructed at a bowling club. It is 3 5metres long and rises through 0 3metres. alculate the angle,, that the ramp makes with the horizontal. VITORI OWLING LU 0 3m 3 5m o 7) boy flying a kite lets out 200 m of string which makes an angle of 72 with the horizontal. What is the height of the kite? 8) ladder is 15 m long. The top rests against the wall of a house, and the foot rests on level ground 2 m from the wall. alculate the angle between the ladder and the ground. 9) ladder 12 m long is set against the wall of a house and makes an angle of 75 with the ground. a) How far up the wall will the ladder reach? b) How far is the foot of the ladder from the wall? 10) telegraph pole standing on horizontal ground is 9 m high, and is supported by a wire 10 m long fied to the top of the pole and to the ground. alculate: a) the angle between the wire and the ground. b) the distance of the point on the ground from the foot of the pole. Maths Department -20- S2 Level 3/4 ourse

21 Eercise 5() 1) The front of the tent shown below is an isosceles triangle. The size of the angle between the side and the bottom of the tent is. alculate. 2) television mast is supported by wires. The diagram below shows one of the wires which is 80 metres long. The wire is attached to the mast 20 metres from the top and makes an angle of 59 with the ground. alculate the height of the mast. Give your answer to the nearest metre. 3) lan is standing 30 metres from a tree. lan s height is 150 centimetres. He measures the angle to the top of the tree to be 32. alculate the height of the tree. S2 Level 3/4 ourse -21- Maths Department

22 4) The frame of a child s swing is in the shape of an isosceles triangle. If the base of the triangle is 1 9 metres and the sides are at an angle of 65 o to the ground, calculate the height of the swing, h. h 65 o 1 9 m 5) PQRS is a rhombus. It s diagonals PR and QS are 16 cm and 10 cm long respectively. alculate the sizes of the angle of the rhombus. S P Q 6) straight road 350 m long rises 10 m vertically from one end to another. R alculate the angle between road and the horizontal. 7) horizontal concrete floor is 30 cm thick. small hole is bored through it at an angle of 35 o to the horizontal. alculate the length of the hole to the nearest cm. 8) The diagram shows a cross section of a valley. How much higher is than? y D 125 m 190 m E 9) In this figure calculate 7 cm a) the angle. b) the angle D. 3 cm D Maths Department -22- S2 Level 3/4 ourse 5 cm

23 10) O is the centre of a circle of radius. PM = 7 cm, angle POQ = 72 o. alculate the length of QN. P Q M O N 11) It is intended to build a room (DEFG) in a loft of a bungalow. The roof of the room must not be lower than 2 4 m. If the house roof slopes at 40 o what is the maimum width of the room? 12) The diagram shows part of the support of a roof. 2 4 m 40 E D 10 m Find the slope of the roof and the length of the support D. F D G 2 m 3 m S2 Level 3/4 ourse -23- Maths Department

24 hanging the Subject of a Formula Eercise 1(/) Make the subject of these formulas. 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) Eercise 1() Make the subject of these formulas. 1) 2) 3) 4) 5) 6) 7) 8) 9) Maths Department -24- S2 Level 3/4 ourse

25 10) 11) 12) 13) 14) 15) 16) 17) 18) Eercise 2(/) Make the subject of these formulas. 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) hange the subject of each of the following formulae to the variable indicated. 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) S2 Level 3/4 ourse -25- Maths Department

26 32) 33) 34) 35) 36) 37) The perimeter of a square is. hange the subject to. 38) The area of a rectangle is. hange the subject to. 39) The volume of a cuboid is. hange the subject to. 40) The speed of a train is. hange the subject to a) b). 41) The current in a circuit is. hange the subject to a) b). 42) The area of a triangle is. hange the subject to. 43) The area of a metal plate is. hange the subject to. 44) The equation of a straight line is. hange the subject to. 45) The illumination of a lamp is. hange the subject to. 46) The perimeter of a rectangle is. a) hange the subject of the formula to. b) alculate when. 47) The sum of the numbers in a series cab be given by. a) hange the subject of the formula to. b) alculate when. Maths Department -26- S2 Level 3/4 ourse

27 48) The sum of the angles of a polygon with sides is right angles, where. a) hange the subject to, and find how many sides a polygon has if its angle-sum is 10 right angles. b) an a polygon have an angle-sum of 15 right angles? S2 Level 3/4 ourse -27- Maths Department