10MA 10 2 Sem2 Solutions

8/3/2019 10MA 10 2 Sem2 Solutions

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Teacher's Name: BOH CAM FAR GAV

Jl1HN MONA LSHSCIENCE SCHOOL

Year 10 Core MathematicsExamination Paper 2 - Tech Enhanced

Thursday ia" November 2010NAME: .

Reading Time: 10minutesWriting Time: 60minutesMarks: 40Pages: This exam consists of 11 pages (including this page)Permitted materials:Pens, pencils, rulers, erasers, CASCalculator or any scientific Calculator and 1 A4 double sided page of handwritten notes.

**Please note that the use of whiteout is strictly prohibited**

Instructions:This paper is in two sections.Section A, worth 15 marks, is multiple choice. All answers to multiple choice questions should be recordedon the included multiple choice answer sheet.Section B, worth 25 marks, is made up of 2 analysis questions. All working and answers to the analysisquestions should be recorded in the space provided within this booklet.


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[This page has been left blank intentionally as there were no x-intercepts]


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Section AEach multiple choice question is worth 1 mark. Record all answers to these questions on the multiple choicesheet provided.

1. The value of8 in the following diagram is closest to:Q

A. 45B. 90c. 180 I Answer is B ID. 270E. 360

2. The value of a in the following diagram is closest to:B

A. 10B. 20c. 40 I Answer is C ID. 80E. 160

3. Luck Bunny has a box of 50 coloured Lego blocks, 14 of which are green. If Luck Bunny removesone block at random, what is the probability that it is not green?

A. 1B. 1-2c. 14 I Answer is E I50D. 725E. 18-25


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4. A group of 25 students were surveyed to see what they had for breakfast. The information from thissurvey is represented in the Venn Diagram shown below;

If a student was selected at random, what is the chance that they would have had cereal forbreakfast?

A. 8-25B. 13-25 IAnswer is B Ic. 1323D. 8-23E. 8-13

5. Luck Bunny has a drawer full of different coloured ear warmers. In the drawer he has 3 green earwarmers, 2 blue ear warmers and 1 red ear warmer. If Luck Bunny randomly selects ear warmersfrom this drawer, what is the probability that Luck Bunny pulls out a green ear warmer for his firstchoice followed by a red ear warmer for the second?

A. 4,-6B. 3-6

3 3 1 3c. - -x-=-30 6 5 30D. 21 So answer is C30E. 3-36

6. Which of the following shows 0.0000005382 written in correct scientific notation?A. 5.382 x 107B. 5.382 X 10-7 IAnswer is B Ic. 5382 X 10-7D. 53.82 X 10-8E. 5382 X 10-10


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27. (64)3 when simplified is equal to:A.lB. 2c. 4D.8E. 16

IAnswer is E I

8. When simplified, 3a 3bs x 8a2b becomes:A. 13asbsB. 13asb6c. 24a6bsD. 24asbsE. 24asb6

9. The solution of23p-2 = 128 is:

IAnswer is E I

A. P = 7B. P = 5c. p= 3D. 5P =-3E. 7P =-3

IAnswer is C I

10. For the formula y = 5 X 4 t, the completed table of values for t = {O, 1, 2, 3} is:A.

B. t 0 1 2 3y 1 20 400 8000IAnswer is A I

I ~ I 0 I 1 I 2 I 3 Ic. 5 9 13 17I ~ I

0I

1I

2I

3ID. 0 20 80 320

I ~ I 0 I 1 I 2 I 3 I. 6 9 21 69


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11. The expansion of ( X - 5 ) 2 is:A. X 2 -IOx-25B. x2 - 25x + 10C. x2 -25x-IOD. x2 +IOx+25

=(x-5)(x-5)=x2 -IOx+25SoanswerD

E. x2 -IOx+25

12. The simplest form of ( a + 8)( a -7) is:

A. (a-8)(a-7) (a-8)(a+8)B.

a-8(a+8)(a-7)a-7 a-8

C. a+8 a-7--a-7 Soanswer BD. (a+8)(a-7)E. aI

. 3(x-3)(x+2)=O13. The solutions to are:A. x=2,x=3B. x=3,x=-2C. x =O,x = 2D. x = 9,x =-6E. x =9,x =-2

x=3,x=-2So answer B

14. For two triangles, which of the following is not a valid test for congruenceA. Angle Side SideB. Angle Side Angle There is an ambiguous situationC. Side Side Side for ASSD. Angle Angle Side So answer is AE. Side Angle Side


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15. A beetle on the ground looks up at bird in a tree with an angle of elevation, a .The bird looks downat the beetle at an angle of depression, jJ . Which of the following statements is true?

A. a and jJ sum to 90B. a and jJ sum to 180c. a is half jJD. a is double jJE. a and jJ are the same

So answer is EBy drawing a diagram


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Section BAnswer all questions in the space provided in this booklet. Appropriate working must be shown in order toobtain full marks

1.Tess' Tents Limited has been producing a standard pyramid-shaped tent called the Ramses for 30years. It has a centre pole, AM, which pitches up a canvas to form a rectangular based pyramid aspictured below.

A

,/1.8 m 'E ' 0 I, I.>-------1----

Io D

M 2.4 mBoC---------------------V C0m

A problem with the Ramses is that the centre pole gets in the way of the people sleeping and movingwithin the tent. A new design proposes 4 poles that run up the edges and meeting at the apex. Anexample is AD.a) What is the length of these new poles? Give your answer correct to 1 decimal place.

M C .JI . 5 2 + I .2 2M C .J3I9= 1.9209372712299 ... [ A I ]A C .J 3 .6 9 + I .8 2A C ~A C 2 .6 3 2 4 9A C ~ 2.6T hep o le sw illbe2.6m long ... [ A I ]

[2 marks]Pegs are placed in the four comers of the test to stabilise the tent. If it is windy, the tent will nowinclude 5 m guy ropes that extend from the Apex, A to the ground. If the angle formed with groundis 25 or less, then the Ramses will be guaranteed for strong winds.b) Is the Ramses guaranteed for strong winds?

. . . [A I]

. () I .8Sill =-5( ) . _ 1 ( 1 . 8 )= sIn - 5Y es , R am ses is g uare teed fo r Strong W inds ... [A I]

[2 marks]


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Tess's Tents is planning to make a larger version of the Ramses, creatively named the Ramses II, which is ascaled version of the original. The base will be 5m by 4m

c) For the Ramses II, find:1. the new height, using similarity.

, - - - - - - - - - - - - - - - - - - - - ,similarity factorx 5-- -l.8 3x=3m .. . [AI]

[1 mark]11. the increase in volume compared to the Ramses

=4.32m3Volume, =t(4 x 5x 3)

=20m3

. .. [AI]V o l u m e ] =t(3 x 2.4x l.8)

. .. [AI]V o l u m e d i j f e r e n c e =20 - 4.32

=15.68m3 . .. [AI][3 marks]

111. How much the surface area increases

[Imark]When packed up, the Ramses rolls up into cylindrical bags of radius 15 em and length 55 em. These, in tum,will be packed into a rectangular box 3 by 2 as shown below.

As dimensions increase by a factor of 2 . ,3SA will increase by ( ~ J 259 . .. [AI ]

d) Give the dimensions of the box in emh e i g h t = 5 5 c m . . [ A I ]w id t h = 2 x 2 x 1 5

= 6 0 e m . . [ A I ]l e n g t h = 3 x 2 x 1 5

= 9 0 e m . . [ A I ]d im e n S l o n s = 5 5 x 6 0 x 9 0 e m O R . . . [ A 3 ]

[3 marks]


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2. Leila has 12.4 m of fencing with which to build a rectangular shaped garden bed. She intends tolocate the garden near a kitchen window, next to a comer of the house, as shown in the diagrambelow, with the fence projecting from one wall of the house. Fencing is not needed along the walls ofthe house.

a) If the width of the garden bed is w , and the length is (x+2.6), show that the perimeter, P, ofthe fencing is P = 2x + w + 2.6

P =X+X+ 2.6+ w=2x+ w+2.6

. . . [ M I ]

... [AI]

[2 marks]b) If there is 12.4 m of fencing show that w = 9.8 - 2x

P =12.412.4 =2x + w+ 2.6 . . . [ M I ]w=9.8-2x ... [AI]

[2 marks]c) If A m2 is the area of the garden bed, show that A =25.48+4.6x- 2X2

A=wxxA=(2.6+x)(9.8-2x) [ M I ]A =25.48 + 4.6x - 2X2 [AI]

[2 marks]


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d) What is the area if x = 0 ?

[1 marks]e) What are the dimensions of the garden bed when x = 0 ?

I W ~ 9 8 m1= 2.6m

[1 marks]f) Sketch the graph of A =18.72 + 2x - 2X 2 showing all intercepts and the turning point.

y Intercepts ... [ I A ]Shape ... [ I A ]

E~~:--~+-~-+~:--r-++~-+~~r---~-+~~T'~--r-+-~X-10 -9 -8 -7 -6 -5 2 3 4 _" ' , 6 7 8 9 [0

x

y

10

- - - - - I t 1.15,28.125 ) 1.,020 ~~-----,

(0,25.48)

(4.9, 0) I

-20

[2 marks]


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g) What is the maximum area the garden bed can be?. . . [ lA ]=28.125 m'

Accept 2 dec places as long as rounding is ok.

h) Does this graph truly represent the area of the garden? Explain.

N o . . . [ lA ]The graph shows negative x values that mean the length of the sides would be negative .

. . . [ l A ]he graph shows negative area which is not possible.

END OF EXAM 2.' . . "

. .. [ lA ]

[1 mark]

[3marks]

10MA 10 2 Sem2 Solutions

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