Year 10 Practice Assessment Task 3 (Note: All hints except the cosine rule will not be in exam, so memorise)

Transcription

1 Year 10 Practice ssessment Task 3 (Note: ll hints except the cosine rule will not be in exam, so memorise) 1)! 5 m 35 6 m The area of this triangle is closest to () 8 6 m 2 () 12 3 m 2 () 17 2 m 2 (D) 24 6 m 2 rea = ½ ab sin 2)! x 7 alculate the value of x to the nearest degree. () 23 () 24 () 25 (D) 46 = 3)! P 7 cm Q 52 R Which expression gives the area of PQR in cm 2? 1 1 () 8 7 sin 52 () 8 8 sin () 8 7 cos 52 (D) 8 8 cos )! x m 10 m 20 10' 8 m a 2 = b 2 + c 2-2bc cos x 2 = () cos 20 10' () cos 20 10' () cos 20 10' (D) cos 20 10' 5)! 6 cm The value of x is () 52 () 76 () 124 (D) 148 x cm 120

2 6)!* 3 Hint: Use Pythagoras first to find hypotenuse. Then use SOH H TO sin =? 4 () () () (D) 5 4 7)! P R Q Which expression below gives the area of the triangle PQR? 1 1 () cos 70 () sin () sin 40 (D) cos 40 8)! In this triangle, to the nearest degree, =? () 13 () 14 () 16 (D) 29 4 cos = 9)! P 10)! 3 cm 60 R Q The area of the triangle PQR (in square centimetres) is closest to? () 6 0 () 10 4 () 12 0 (D) cos x =? () () 0 75 () (D) 0 6 x

3 11)!* x 66 Which of the following statements is true? x 50 x 50 () = () = sin 40 sin 66 sin 40 sin 26 x 50 x 50 () = (D) = sin 66 sin 40 sin 26 sin Hint: What s the size of the obtuse angle in the triangle to the right of the diagram? Then work out the remaining angle in the same triangle. Finally, use the sine rule in that triangle to finish the question. 12)! FIGURE NOT TO SLE 36 m 30 m 10 m The diagram shows a fun-park ride. The angle is closest to () 46 () 56 () 72 (D) 74 Use osine Rule 13)! 30 m 30 m 46 m The triangle is roped off to hold a shotput event at an athletics carnival. The area roped off is closest to () 444 m 2 () 450 m 2 () 529 m 2 (D) 887 m )! 410 cm Q: Why should you use SHOHTO for this? 313 cm : ecause the triangle is RIGHT NGLED! The diagram shows a large sloping advertising board. Find the angle, to the nearest degree, between the board and the ground. () 37 () 40 () 50 (D) 53

4 15)! 16)! Which congruence test shows that these two triangles are congruent? () SSS () SS () S (D) RHS 17)! Which congruence test shows that these two triangles are congruent? () S () SSS () SS (D) RHS Which congruence test shows that these two triangles are congruent? () SS () () S (D) SSS 18)! I II III 7 cm 65 7 cm cm 85 NOT TO SLE Which triangles are congruent? () I and II() II and III () III and I (D) ll are congruent 19)! I II III 10 cm 10 cm 6 cm 6 cm NOT TO SLE Which triangles are congruent? () I and II() II and III () III and I (D) ll are congruent 20)! The triangles below are congruent. 5x 60 3x x =? () 12 () 15 () 18 (D) 20

5 21)! The triangles below are congruent. The sum of their perimeters is 40 cm. x + 3 x =? () 14 cm () 4 cm () 2 (D) 16 cm x + 1 Q: What s an algebraic expression for the unknown side on the first triangle? : x + 3 (Why?) 22)! The triangles below are congruent. 73 z The values of x, y and z are: () x = 72, y = 73, z = 35 () x = 35, y = 73, z = 72 () x = 35, y = 72, z = 73 (D) x = 73, y = 35, z = 72 x 35 y 23)! The triangles below are congruent. c a b 47 d 53 The values of a, b, c, and, d are: () a = 47, b = 53, c = 80, d = 80 () a = 53, b = 47, c = 80, d = 80 () a = 80, b = 80, c = 47, d = 53 (D) a = 80, b = 80, c = 53, d = 47 24)! NOT TO SLE m P 375 m L is a searchlight on the ground. vertical beam from L hits a cloud at. n observer at, 300 m from L, observes the angle of elevation of to be 64. a. Find the height of the cloud above the ground. (Hint: Ignore the 375m and the P. Label L as x) b. plane is flying on a level course at a height of 375 m. The plane flies through the searchlight beam at P. alculate the angle of elevation of P from. Give your answer to the nearest degree. c. From P, the plane begins to climb, and its height increases at a rate of 12 metres per second. How long will it take to reach the height of the cloud? L

6 25)! Find the value of to the nearest minute NOT TO SLE Use the sine rule! 26)! 27)! 2 m wharf d m 5 m pontoon The diagram shows a wharf and a floating pontoon. 5-metre plank is positioned to reach the edge of the pontoon 2 metres below the top of the wharf. a. Find the angle, to the nearest degree. (Why is this a SOHHTO question?) b. Find the distance, d metres, of the pontoon from the wharf. Give your answer correct to one decimal place. c. The tide rises so that the plank makes an angle of 10 with the horizontal. Find how much (to the nearest centimetre) the tide has risen. Y X m 70 m Z Find the area of triangle XYZ to the nearest square metre. 28)! NOT TO SLE D 21 m m 52 river bank river bank The diagram shows a water-ski ramp at. Karen jumped from the ramp and landed at D. The points and are on the riverbank. ngles and lengths were measured at the time of the jump, as shown above. (Note: = 90, D = 90 ). a. Find the length of, correct to one decimal place. (Why is this a SOHHTO qn?) b. Find the length of D, correct to one decimal place. (Why is this a cosine rule question?) 29)! 2 4 m 5 m 3 m alculate the height of the building in metres. (Hint: Find the angle of elevation using the little triangle! Then use the entire triangle to find the height!)

7 30)! Draw a right angled triangle for which it is true that 31)! Find to the nearest degree. 11 cm 45 Why is the sine rule the right choice? 32)! 37 Find the value of y correct to one decimal place. 4 9 m 68 y m 75 Why is the sine rule the right choice? Which angle don t you need? 33)! 34)! 35)! 11 m Hint: Draw a diagonal 7 m that breaks it into 2 identical triangles. Then 40 use rea rule! alculate the area of this parallelogram. Give your answer in m 2 correct to one decimal place. O 2 5 m 70 is a chord of a circle centre O, with radius 2 5 m. O = 70. Find in metres, correct to one decimal place. Why is the cosine rule used for this question? 7 m 2 m 16 D The diagram shows a building standing on a slope inclined at 16 to the horizontal (D). From point, 2 metres down the slope, a 7 metre ladder,, is placed against the wall. i. Use the triangle D to find D. Give your answer correct to 2 decimal places. ii. Hence, or otherwise, find the angle. (Hint: Use triangle D and SOHHTO)

8 36)! From the triangles below, select the triangle which is congruent to: ii. iii. iv. D v. E 17 cm 10 cm 4 cm 9 cm 7 cm 6 cm F 2 cm 70 D 6 cm 17 cm 100 E 40 G 4 cm 1 7 cm 9 cm H 2 cm 70 J 100 I 40 37)! The triangles below are congruent. List the pairs of equal sides and equal angles. D E F 38)! re the two triangles below congruent? Give a reason for your answer. (SSS,SS,RHS,S) 39)! re the two triangles below congruent? Give a reason for your answer. (SSS,SS,RHS,S) 40)! Prove these two triangles below congruent? Put letters on each vertex and then do a 5 line proof!

9 41)! re the two triangles below congruent? Give a reason for your answer. (SSS,SS,RHS,S) 42)! re the two triangles below congruent? Give a reason for your answer. (SSS,SS,RHS,S) 43)! re the two triangles below congruent? Give a reason for your answer. (SSS,SS,RHS,S) 44)! re the two triangles below congruent? Give a reason for your answer. (SSS,SS,RHS,S) 45)! re the two triangles below congruent? Give a reason for your answer. (SSS,SS,RHS,S) 46)! re the two triangles below congruent? Give a reason for your answer. (SSS,SS,RHS,S) 47)! re the two triangles below congruent? Give a reason for your answer. (SSS,SS,RHS,S) 48)! re the two triangles below congruent? Give a reason for your answer. (SSS,SS,RHS,S)

10 49)! Explain why the two triangles below are not congruent. 50)! re the two quadrilaterals below congruent? Give a reason for your answer. 51)! Prove that FEG. E 3 cm 6 cm G 6 cm F 3 cm 52)! Prove that MNO QRP. P 2 cm M N R 2 cm Q O 53)! Prove that KLM NPO. K L O M 20 P 120 N 54)! Prove that GKI. G 3 cm I 3 cm K

11 55)! Prove that D. D 56)! Use Pythagoras' Theorem to calculate the length of. Hence prove that DEF. D 170 mm 154 mm 72 mm F 72 mm E 57)! Use Pythagoras' Theorem to calculate the lengths of and DE. Hence prove that DFE. State the condition(s) of congruency. D 63 mm 65 mm 16 mm E 16 mm F [[End Of Qns]]

12 «1)» «2)» «3)» «4) D» «5) D» «6) D» «7)» «8)» «9)» «10)» «11)» «12)» «13)» «14)» «15)» «16) D» «17)» «18)» «19) D» «20)» «21)» «22)» «23)» «24) a) 615m b) 51 c) 20 seconds» «25) 38 11» «26) a) 24 b) 4 6 m c) 1 13 m» «27) 2367 m 2» «28) a) 47 4 m b) 61 8 m» «29) 6 4 m» «30) m 2 (to 1 dp)» «31) 31» «32) 3 1» «33) 49 5 m 2» «34) 2 9 m» «35) i) 1 92 m ii) 58 4' (to the nearest minute)» «36) i) G ii) F iii) H iv) J v) I» «37) = EF, = FD, = ED, = E, = F, = D» «38) Yes, SSS» «39) Yes, SS» «40) Yes, S» «41) Yes, RHS» «42) Yes, SS» «43) Yes, RHS» «44) Yes, RHS» «45) Yes, RHS» «46) No. The angle is not the included angle.» «47) No. orresponding sides are not equal.» «48) No. orresponding sides are not equal.» «49) No. orresponding sides are not equal.» [nswers] «50) No. orresponding sides are not equal.» «51) Proof, SSS» «52) Proof, SS» «53) Proof, S» «54) Proof, SS» «55) Proof, RHS» «56) = 170 mm, Proof, RHS or SSS» «57) = 65 mm, DE = 63 mm, Proof, RHS or SSS or SS»