ASK ARCHIE MATHEMATICS

Transcription

1 ASK ARCHIE MATHEMATICS GRADE 8 ANSWER SHEET Paper Ref: AAM8b TIME: TOTAL MARKS: Hurs 100 Frmulas: A πr A l b 1 A b h Write ur name in this blck C πr P l + b P S + S 1 + S 3 Write ur teachers name in this blck m + c Questin Result ut f Questin TOTAL Result ut f

2 Questin 1 Yu have been shrtlisted t becme the net James Bnd and have been asked t answer the fllwing questins as part f the interview prcess. 8 (a) Simplif: ( 5)(0) + 3 (1) (b) Calculate: 0 (1) (c) Write 48 as a prduct f its (d) What is the mean f the numbers belw? prime factrs (1) 4; 9; and 14 () (e) What are the factrs f 8? (1) Questin Undefined 1; ; 4; In part tw f the interview u need t simplif the epressins belw int their simplest frm, write ur answers and shw ur wrkings in the spaces prvided. [6] (a) (1) 13 (b) 3( + 4) + 5( 3) (3) (c) 4( 3 3 ) (3) 4 9 6

3 (d) () (e) 3 ( + 4) (3) [1] Questin 3 In part three f the interview u need t decipher the cde and answer the questins that fllw: Letter Value (V) Letter a b c d e Cded Value (C) (a) The letter f has a Letter Value f 6, what is the Cded Value fr the letter f? (1) f 8 (b) What is the frmula that has been used t determine the cded value? (Use the letter V t represent the Letter Value and the letter C t represent the Cded Value ) () C 3 V +10 (c) What wrd is represented b the cde 49; 73; 46; 46; 5; 70? (3) MULLET [6] 3

4 Questin 4 As the wrld s mst famus secret agent u need t be able t slve equatins. Determine the value f in the equatins belw; shw all ur wrkings (a) () 0 (b) 4( 5) + 3( 4) 4 3 () (c) Write ur final answers t the questins abve in the spaces prvided belw: (3) (a) (b) (c) Bnd; James Bnd! (d) Lk at the statement belw: ( + 10) +15 If the statement abve is true fr all values, then what shuld appear in the dtted b? () [9] 4

5 Questin 5 James Bnd gets assigned a missin where he has t travel frm Lndn t Clumbia ( kilmeters), then frm Clumbia t Grahamstwn and then he needs t return back t Lndn with the stlen cmputer chip. The distance frm Lndn t Clumbia is 580 kilmetres shrter than the distance frm Grahamstwn t Lndn and the distance frm Clumbia t Grahamstwn is 441 kilmetres further than Lndn t Clumbia. Lndn Clumbia Grahamstwn If the ttal distance f the trip is 3067 kilmetres, then what is the distance frm Grahamstwn t Lndn? (Shw all ur wrkings) L C L G C G Grahamstwn t Lndn km [5] 5

6 Questin 6 James Bnd receives a tp secret SMS with three pieces f infrmatin. The SMS is shwn in the picture belw and this is the infrmatin u need t use t answer the questins. (a) On the Cartesian plane belw plt and label pint A (1) (b) (c) On the Cartesian plane belw u need t draw the straight line using the equatin that was SMS d t u. A(- 3; - 5) + 1 B( p; 5) (3) James Bnd has been tld that his car is in a secret cave with the c-rdinates B(p; 5) and is tld that this lies n the straight line he has drawn. Find the value f p and hence James Bnd s car. () Wrkings (1;3) (0;1) ( 1; 1) A( 3; 5) [6] 6

7 Questin 7 James Bnd is in his car watching a terrrist s helicpter hver abve the ne twer f the Lndn bridge. The diagram belw shws the distances required t answer the ke questins that fllw. H 170 metres 100 metres T S 80 metres B (a) What is the height f the twer n the left? (Find the distance frm B t T) (3) BT ( Pthag ) BT 60 m (b) Hw high is the helicpter abve the left hand twer? (Find the value f ) (4) HB 170 HB 150m 80 ( Pthag ) HT r metres (c) What distance wuld a trped have t travel frm the helicpter t hit the tp f the twer n the right; if the distance TS is als equal t? (Find the length f HS) (3) HS HS 17,8 metres ( Pthag ) [10] 7

8 Questin 8 James Bnd s favurite drink is the Martini and it is made up f gin and vermuth nl. This is made up f gin and vermuth in a rati f 5,5 parts gin t 1,5 parts vermuth. Highest pint Highest pint A glass can hld a maimum f 100ml Olive (a) (b) (c) The barman purs the gin and the vermuth int the glass befre adding the live. If there is 70 ml f liquid in the glass then hw much space is left in the glass? (1) 30 ml When the barman drps the live int the glass the space left abve the liquid in the glass decreases t 8ml. What is the vlume f the live if 1ml 1cm 3? () 30ml 8ml cm When the martini is first pured it cntains 70 ml f liquid in ttal. Hw man milliliters f gin make up this martini? () ml (d) If James Bnd takes a 0ml sip f his martini and this particular sip has a rati f 9 parts gin t 1 part vermuth; then what will the rati f gin t vermuth in his glass becme? (Write rati in its simplest frm) (3) 9 10 New rati 0 18ml gin :15 37 :13 hence ml vermuth [8] 8

9 Questin 9 James Bnd walks int the casin t pla sme rulette. On a rulette wheel the numbers frm 0 36 appear arund the utside f the wheel. 18 f these numbers are painted red, 18 f the numbers are painted black and the number zer is painted green. A small metal ball is thrwn int the wheel when it is spinning and this lands n ne f the numbers. (a) What is the prbabilit f the ball landing n a number painted red? () (b) 18 numbers are painted red 18 numbers are painted black Zer is painted green Fill in the dtted bes n the tree diagram belw, this will help u with questin (c). The bes at the bttm shw sme f the pssible utcmes and the prbabilit f these ccurring. (3) R G B RR R G B R G B R G B 34 RG c c c c 18 RB (c) If u spin the wheel twice; find the prbabilit that the ball lands n red at least nce? () GR BR [7] 9

10 Questin 10 James Bnd is n his M6 super scter at the starting pint and is driving thrugh the streets f Lndn n his wa t drp ff the cmputer chip at the destinatin. Destinatin 70 d 50 b n Starting pint (a) Find the value f angles b; and n (Give a reasn fr each statement.) (4) b n ( Vert pp) ( C int erir // lines) ( Angles n str line) (b) Find the value f angle d, (Give reasns where required) (3) d 1 50 ( alt angles // lines) d 70 ( alt angles // lines) d 10 [7] 10

11 Questin 11 Belw is a picture f the James Bnd scter; The M6. Varius angles have been given, use ur knwledge f gemetr t answer the questins that fllw. D C E A 40 F 0 B (a) What is the value f? (3) ( Et angle f Δ) 60 (b) What is the value f? () 80 ( Angles in a Δ) (c) The titanium bar CF can be flded at C and etended s that pint F mves t pint B. When this happens then AC will be equal in length t CB. Hw man degrees will increase b when this happens? (3) CBA ˆ 40 increases b 40 ACB ˆ 100 ( Iss Δ) [8] 11

12 Questin 1 James Bnd takes his lad friend n a date t the Lndn Glden Ee. James Bnd discvers a bmb planted under the seat in their pd. It has a ke pad t fill in a cde t diffuse it. Attached t the bmb is a nte that gives a few clues t the cde and then sas; Enj ur evening James. Yu have ten minutes left t decipher the message and fill in the blcks belw which will represent the cde needed t diffuse the bmb. Clue 1: The median is 7 Clue : The mde is 9 Clue 3: The range is 7 Clue 4: The mean is 6 Write the numbers in the blcks belw. Smallest Biggest [5] 1

13 Questin 13 James Bnd diffuses the bmb and cntinues his wnderful date n Lndn s Glden Ee; a huge wheel that s highest pint is 135 metres abve the grund. Use this infrmatin and the diagram belw t help answer the questins that fllw. A 60 m 7 B (a) If the highest pint f the Lndn Glden Ee is 135 metres, then hw far abve the grund is the lwest pint f the wheel? (1) 15 metres (b) Calculate the circumference f the Lndn Glden Ee () π (60) 376,99 metres (c) If it takes 3 minutes t travel frm pint A t pint B (clckwise), then what speed is the Dis tan ce Lndn Glden Ee rtating at? Speed (Answer in km/hur) (3) time 376,99 s s 75,4 m 3min metres 5,13m / min 1.51km / hur [6] 13

14 Questin 14 James Bnd s favurite car is the Astn Martin DB9 and the lg that appears n the frnt is shwn belw. It is made up f a heagn inside a rectangle with the dimensins shwn belw. All 6 sides f the heagn are equal in length. 4 cm A B 4 7 cm C D What is the area f the shaded regin in the lg? (Find the area f A + B + C + D) Area f rec tan cm gle Area f heagn cm 7 6 Area f shaded regin cm cm cm [5] 14