2015 Student Test | Test and Chat

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2015 Student (Grade 11 - 12)

Questions: 30 | Answered: 0

Q1. Andrea w w as born so m m etime in th e e year 1997 and her sist e e r Charlotte sometime i n n the year 2 0 0 01. What is known for c c ertain abou t the age dif f erence of t h h e two siste r r s? It is…

3 points

ABCDE

Question 1

Q2. ሺܽ െ ܾሻ ൅ ሺܾ െ ܽ ܽ ሻ ൌ ଷ ଷ ଷ ଷ ଷ ଷ ଶ ଶ ଷ

3 points

ABCDE

Question 2

Q3. How ma n n y real solut i i ons has the equation 2 ൌ4 ?

3 points

ABCDE

Question 3

Q4. . Diana p roduces a b a a r chart whi c c h shows th e e number of four differe n n t types of trees wh ich she has c c ounted on a a biology tri p p . Heinz beli e e ves that a p ie chart would repr e e sent the ra t t io of the dif f f erent types s of trees in a a better way . What would the p p ie chart loo k like?

3 points

ABCDE

Question 4

Q5. If you ad d d all the wh o o le numbers from 2001 t t o 2031 and t t hen divide t t he sum by 3 3 1, you get;

3 points

ABCDE

Question 5

Q6. How ma n n y of the foll owing shap e e s can be drawn usin g g one contin uous line (i. e e . without lift i i ng the penc il) and with o o ut going over a line t t wice?

3 points

ABCDE

Question 6

Q7. A quadril ateral is call ed convex if all its intern n al angles ar e e less than 1 8 0°. The nu m m ber of righ t t angles in a convex qua drilateral is n n . Which of t t he followin g g lists is a co mplete listi n n g of all poss ible values o o f n ?

3 points

ABCDE

Question 7

Q8. A drinkin g glass is m a a de in the sh ape of a tru n n cated cone . . The outsid e e of the glas s s (without the upper o o r lower circl e) should b e e covered wi t t h coloured paper. How do you nee d d to cut the paper t o o completel y y cover the g g lass withou t t an overlap ? ?

3 points

ABCDE

Question 8

Q9. The dia m m eters of thr e e e semi ‐ circl es form the sides of a ri g g ht ‐ angled t r r iangle. Thei r r areas are ܺ cm², ܻ ܻ cm² and ܼ cm² as pict u u red. Which of the follo w w ing express i ons is defin i i tely correct?

3 points

ABCDE

Question 9

Q10. A squar e e bit of pap e e r is folded a long the da s s hed lines in some order and d d irection. On e of the cor n n ers of the r e e sulting sm a a ll square is cut off. T h h e piece of p p aper is the n n unfolded. H H ow many h o o les are on the inne r area of th e e piece of pa per?

3 points

ABCDE

Question 10

Q11. ඥ ሺ 201 5 5 ൅2015 ሻ ൅ ൅ ሺ 2015െ2 0 0 15 ሻ ൅ ሺ 20 1 1 5ൈ2015 ሻ ൅ ሺ 2015 ൊ 2015 ሻ ൌ

4 points

ABCDE

Question 11

Q12. The ݔ ‐ a x x is and the g g raphs of ݂ሺ ݔ ݔ ሻൌ2െݔ and ݃ሺݔሻ ൌ ൌ ݔ െ1 spli t t the co ‐ ordi i nate plane i nto

4 points

ABCDE

Question 12

Q13. Ella wan t ts to write a number int o o each circle in the diagr am on the ri ght, in such a way that each num b b er is equal t o the sum, o o f its two dir e e ct neighbo u u rs. Which n umber does Ella need to write in t t o the circle marked wit h h „?“.

4 points

ABCDE

Q14. We kno w the follo w w ing about fi v v e positive w w hole numb e e rs ܽ,ܾ,ܿ,݀ , , ݁ All the nu u mbers are d ifferent, ܾൌܿ∶݁ , ݀ ݀ ൌܽ൅ܾ a n n d ܽൌ݁െ ݀ . Which of the numbe r r s ܽ,ܾ,ܿ,݀, ݁ is the large s s t?

4 points

ABCDE

Question 14

Q15. The ge o o metric mea n n of ݊ numb ers is define d as the ݊ r r oot of the p p roduct of al l l ݊ numbers , , that is ೙ ඥ ݔ ଵ ∙ݔ ଶ ∙ ⋯ ⋯ ∙ݔ ௡ . We h h ave six num bers. The g e e ometric me a a n of three o o f them is 3, the geomet r ic mean of the other t h h ree is 12. H o o w big is th e e geometric m m ean of all s s ix numbers ? ? ଵହ ଵହ

4 points

ABCDE

Question 15

Q16. . The di a a gram show s s three conc entric circle s s and two p e e rpendicular , , common diameters o o f the three c c ircles. The t t hree grey s e e ctions are o o f equal area , the small c i ircle has radius 1 1 . What is th e product o f f the radii of the three ci r r cles? ଷ √ ଷ

4 points

ABCDE

Question 16

Q17. In the p ast 20 years the populat ion of Arnb e e rg has incre ased by 40 % % . In the sam e time span the population of Berghaus en has incre ased by 60 % % . In total th e e population of the two v v illages has i ncreased by

4 points

ABCDE

Question 17

Q18. Bibi roll s a die whic h h has the nu m m bers 1, 2, 3 3 , 4, 5, 6 on i i ts faces. At t t he same ti m m e Tina rolls a die which has the nu m m bers 2, 2, 2 , 5, 5, 5 on i t t s faces. Tin a a wins if she rolls a num b b er higher th an Bibi. Wh a a t is the probability that Tina wi n n s? ଵ ଻ ଻ ହ ଵ ଵଵ

4 points

ABCDE

Question 18

Q19. There a r r e 2015 mar b b les in a pip e e . They are n umbered 1 t t o 2015. Ma r r bles whose digits add u p p to the same num b b er, have th e e same colo u r and marbl e e s whose di g g its have a d i fferent sum m , have a diff e e rent colour. Ho w w many diffe rent colours do the mar b b les in the p i i pe have?

4 points

ABCDE

Q20. On a st a a ndard die t h h e sum of th e numbers o o n opposite f f aces is alwa ys 7. Two identical st a a ndard dice a a re shown i n n the figure. How many d d ots could t h h ere be on t h h e non ‐ visible right ‐ hand f ace (marke d d with “?”)?

4 points

ABCDE

Question 20

Q21. Die Aus s s agen

5 points

AECBD

Question 21

Q22. The cur v v e in the dia gram is defi n n ed by the e quation ଶ ଶ ଶ ଶ ሺ ݔ ݔ ൅ ݕ െ 2ݔሻ² ൌ 2 ሺ ሺ ݔ ൅ ݕ ሻ Which of t h h e lines a,b,c , , d is the y – a a xis?

5 points

ABCDE

Question 22

Q23. The foll o o wing table is the multi p p lication tabl l e of the nu m m bers 1 to 1 0 0 . • 1 2 3 ... 10 What is the sum of all 1 00 products in the com p p lete table? 1 1 2 3 ... 10

5 points

ABCDE

Question 23

Q24. . How m m any regular n ‐ sided sha p p es are ther e e , whose an g g les (in degr e es) are

5 points

ABCDE

Question 24

Q25. How m a a ny three ‐ di g g it whole nu mbers can b b e written as the sum of e e xactly nine different p o o wers of

5 points

ABCDE

Question 25

Q26. How ma n n y different t t riangles ܣ ܤ ܥ whose sid e lengths ar e e whole nu m m bers are th e e re, if ∠ ܣ ܤ ܥ ܥ ൌ 90° and ܣܤ ൌ 20 ? ( ( Hint: Two t r r iangles are c c alled differ e e nt if they a r r e not congr u u ent.)

5 points

ABCDE

Q27. In the r e e ctangle ܣ ܤ ܥ ܥ ܦ pictured , , ܯ ଵ is the m m idpoint of ܦ ܦ ܥ , ܯ ଶ the midpoint o f f ܣܯ ଵ , ܯ ଷ t h h e midpoint o o f ܤܯ ଶ and ܯ ସ the mid p p oint of ܥܯ ଷ . Dete r r mine the ra t t io of the ar e e a of the qu a a drilateral ܯ ܯ ଵ ܯ ଶ ܯ ଷ ܯ ସ to the area of the recta n n gle ܣܤܥܦ . ଻ ଷ ଻ ଽ ଽ ଵ

5 points

ABCDE

Question 27

Q28. . On a b oard there a a re blue and red rectang l l es. Exactly 7 7 of the rect a a ngles are s q q uares. Ther e e are 3 more red r e e ctangles th a a n blue squa res. There a r re also two m m ore red sq u u ares than b lue rectangl e e s. How many blue r r ectangles a r r e there on t t he board?

5 points

ABCDE

Question 28

Q29. The 96 m m embers of a counting c c lub are stan ding in a cir c c le counting . . They start w w ith 1, 2, 3, e e tc., each person in t h h e circle sayi ng the next number in t u u rn. If a me m m ber of the c c lub says an e even numb e e r, he steps out of the c c ircle. The re maining me m m bers conti n n ue, startin g g the second round with 9 9 7. They co n n tinue in thi s s way until o n n ly one me m m ber of the c lub is left. W W hich numb e e r did this p e e rson say in r r ound one?

5 points

ABCDE

Question 29

Q30. Indepen dently from each other B B ill and Bob s substitute t h h e letters in t t he word KA A NGAROO w i th numbers, s o o that the r e e sulting num bers are mu l ltiples of 11. They both s s ubstitute di f f ferent lette rs with different di g g its and sa m m e letters wi t t h the same d digits (K  0) . . Bill obtains the biggest possible nu m m ber and Bob the sm allest possi b b le. In both c a a ses one let t t er is substit uted with t h e same digi t t . Which digi t is that?

5 points

ABCDE

2015 Student Test | Test and Chat