Title: Default for Kurssimallipohja1
Course: VIERKO - Mathematics and application of mathematics 4osp

Feedback shared by this category's questions, if right: Vastauksesi on oikein.
Feedback shared by this category's questions, if partly right: Vastauksesi on osittain oikein.
Feedback shared by this category's questions, if wrong: Vastauksesi on väärin.

Q: Huoneiston pohjapiirroksessa lukee mittakaavana 1 : 50. Olohuone on 15 cm leveä ja 10 cm pitkä. Kuinka suuri on olohuoneen leveys ja pituus todellisuudessa?

Anna vastaukset metreinä ja kymmenesosien tarkkuudella. Esim. näin 6,7 m.

Leveys [...]

Pituus [...]
A: 7,5 m; 5,0 m

Q: Maastokartan mittakaava on 1:20 000. Mikä on {kilometri} km pitkän joen pituus kartalla? Anna vastaus senttimetreinä ja kymmenesosien tarkkuudella.
A: 5*{kilometri} (formula; values not in the backup's text)

Q: Pienennös (kerrotaan): Kuvan leveys piirroksessa on {pieni} cm piirrettynä. Paljonko kuvan leveys on todellisuudessa, kun pienennös on mittakaavassa 1:12?

Anna vastaus senttimetreinä ja kymmenesosien tarkkuudella.
A: 12*{pieni} (formula; values not in the backup's text)

Q: Suurennos (jaetaan): Osan pituus piirroksessa on {suuri} cm. Paljonko osan pituus on todellisuudessa, kun suurennos on tehty mittakaavassa 10 : 1?

Anna vastaus senttimetreinä ja kymmenesosien tarkkuudella.
A: {suuri}/10 (formula; values not in the backup's text)

Q: Kartan mittakaava on 1:10 000. Paljonko on matka luonnossa, jos se kartalla on {pituus} cm?

Anna vastaus metreinä ja ykkösten tarkkuudella.
A: {pituus}*100 (formula; values not in the backup's text)

Q: Kartan mittakaava on 1:20 000. Paljonko on matka luonnossa, jos se kartalla on {pituus} cm?

Anna vastaus metreinä ja ykkösten tarkkuudella.
A: {pituus}*200 (formula; values not in the backup's text)

Q: Kartan mittakaava on 1:25 000. Paljonko on matka kartalla, jos se on luonnossa {pituus} km?

Anna vastaus senttimetreinä ja kymmenesosien tarkkuudella.
A: {pituus} *4 (formula; values not in the backup's text)

Q: Laske kuvassa olevan pienennöksen oikeat mitat.

[Image: Mittakaava]

Anna vastaus metreinä ja sadasosien tarkkuudella.

Korkeus [...]

Leveys [...]
A: 1,25 m; 3,00m

Q: Lentokoneen mitat on piirretty mittakaavassa 1:700. Kuinka suuri on luonnossa lentokoneen pituus?

Anna vastaus metreinä.

[Image: mittakaava]

Pituus [...]
A: 56 m

Q: Minna tekee pikkusiskon nukkekotiin pienoismallit kuvan lipastosta käyttäen mittakaavaa 1:10.

[Image: mittakaava]

Laske nukkekodin lipaston

Pituus [...]

Leveys [...]

Korkeus [...]

Anna vastaukset senttimeterinä.
A: 10 cm; 4 cm; 12 cm

Q: Minna tekee pikkusiskon nukkekotiin pienoismallit kuvan sängystä käyttäen mittakaavaa 1:10.

[Image: mittakaava]

Laske nukkekodin sängyn

Pituus [...]

Leveys [...]

Korkeus [...]

Anna vastaukset senttimeterinä.
A: 20 cm; 7 cm; 4 cm

Q: Mikä on muurahaisen oikea pituus, kun kuva on mittakaavassa 6:1. Muurahaisen mitta kuvassa on {pituus}.

[Image: mittakaava]

Anna vastaus senttimetreinä ja sadasosien tarkkuudella ilman yksikköä.
A: {pituus}/6 (formula; values not in the backup's text)

Q: Helsingin opaskartta on tehty mittakaavassa 1:20 000. Matka eduskuntatalolta presidentin linnaan Mannerheimintieltä ja Esplanadia pitkin kartalta mitattuna {pituus} cm. Kuinka pitkä matka on todellisuudessa?

Anna vastaus kilometreinä sadasosien tarkkuudella ilman yksikköä.
A: {pituus}*0.2 (formula; values not in the backup's text)

Q: Minna tekee pikkusiskon nukkekotiin pienoismallit kuvan sängystä käyttäen mittakaavaa 1:10.

[Image: mittakaava]

Laske nukkekodin pöydän

Pituus [...]

Leveys [...]

Korkeus [...]

Anna vastaukset senttimeterinä.
A: 4 cm; 3 cm; 6 cm

Q: Laske kuvion pinta-ala ja piiri.

[Image: Pinta-ala]

Pinta-ala [...]m^2

Piiri [...]cm
A: 180; 56

Q: Laske kuvion pinta-ala ja piiri.

[Image: Pinta]

Pinta-ala [...]cm^2

Piiri [...]cm
A: 180; 56

Q: Laske kuvion pinta-ala.

[Image: Pinta]

Pinta-ala [...]cm^2
A: 108

Q: Laske sinisen kuvion pinta-ala ja piiri.

[Image: Pinta]

Pinta-ala [...]cm^2

Piiri [...]cm
A: 110; 56

Q: Laske kuvion pinta-ala.

[Image: Pinta]

Pinta-ala [...]cm^2
A: 75

Q: Laske kuvion pinta-ala ja piiri.

[Image: pinta-ala]

Pinta-ala [...]mm^2

Piiri [...]cm
A: 20; 22

Q: Laske kuvion pinta-ala ja piiri.

[Image: pinta-ala]

Pinta-ala [...]cm^2

Piiri [...]cm
A: 18; 22

Q: Laske kuvion pinta-ala.

Puolisuunnikkaan pinta-ala lasketaan kaavalla $$\frac{1}{2}\cdot(a+b)\cdot h$$, jossa a ja b ovat yhdensuuntaiset sivut (5 cm ja 7 cm). Sekä h on korkeus (6 cm)

[Image: pinta-ala]

Pinta-ala [...]cm^2
A: 36

Q: Suorakulmion pituus on {pituus} m ja leveys 18 m. Laske suorakulmion pinta-ala.

Anna vastaus ilman yksikköä.
A: {pituus}*18 (formula; values not in the backup's text)

Q: Kolmion kanta on {p} m ja korkeus 1,3 m. Laske kolmion ala.

Anna vastaus kymmenesosien tarkkuudella.
A: {p}*1.3/2 (formula; values not in the backup's text)

Q: Suunnikkaan sivujen pituudet ovat 48 cm ja 59 cm. lyhyemmät sivut ovat {p} cm:n etäisyydellä toisistaan. Laske suunnikkaan pinta-ala.
A: {p}*48 (formula; values not in the backup's text)

Q: Laske pöytälevyn pinta-ala, kun pöydän pituus on {p} m ja leveys 75 cm.

Anna vastaus kymmenesosien tarkkuudella.
A: {p}*0.75 (formula; values not in the backup's text)

Q: Laske sakkilaudan pinta-ala, kun laudan yhden tumman pikkuruudun sivun pituus on {p} cm.

Shakkilaudassa on 64 ruutua.
A: {p}*{p}*64 (formula; values not in the backup's text)

Q: Suorakulmaisen omakotitalotontin pinta-ala on 1500 m².

Kadun puoleisen tontin sivu on {p} metriä.

Kuinka pitkä on suorakulmion eli tontin toinen sivu?
A: 1500/{p} (formula; values not in the backup's text)

Q: Neliön sivun pituus on {p}. Mikä on neliön pinta-ala?
A: {p}*{p} (formula; values not in the backup's text)

Q: Suunnikkaan kannan pituus on 56 cm ja korkeus {p}.
A: 56*{p} (formula; values not in the backup's text)

Q: Ympyrän säde on {p} cm. Laske ympyrän pinta-ala.

Anna vastaus sadasosien tarkkuudella ilman yksikköä.
A: 3.141592654*{p}*{p} (formula; values not in the backup's text)

Q: Ympyrän säde on {p} cm. Laske ympyrän piiri.

Anna vastaus sadasosien tarkkuudella ilman yksikköä.
A: 2*3.141592654*{p} (formula; values not in the backup's text)

Q: Ympyrän halkaisija on {p} cm. Laske ympyrän pinta-ala.

Anna vastaus sadasosien tarkkuudella ilman yksikköä.
A: 3.141592654*({p}/2)*({p}/2) (formula; values not in the backup's text)

Q: Ympyrän halkaisija on {p} m. Laske ympyrän piiri.

Anna vastaus sadasosien tarkkuudella ilman yksikköä.
A: 3.141592654*{p} (formula; values not in the backup's text)

Q: Laske kuvan ympyrän pinta-ala ja piiri.

[Image: Ympyrä]

Anna vastaus kymmenesosien tarkkuudella.

Piiri = [...] cm

Pinta-ala = [...] cm^2
A: 44,9; 160,6

Q: Laske kuvan ympyrän pinta-ala ja piiri.

[Image: Ympyrä]

Anna vastaus kymmenesosien tarkkuudella.

Piiri = [...] cm

Pinta-ala = [...] cm^2
A: 22,6; 40,7

Q: Laske kuvan sinisen renkaan pinta-ala. Pienen valkoisen ympyrän säde on 4,6 cm ja koko ympyrän säde on 9,2 cm.

[Image: Rengas]

Anna vastaus kymmenesosien tarkkuudella.

Pinta-ala = [...] cm^2
A: 199,2

Q: Neliö ja puolikas ympyrä muodostavat yhdessä pinnan. Laske kuvan pinta-ala.

[Image: Ympyrä ja neliö]

Anna vastaus kymmenesosien tarkkuudella.

Pinta-ala = [...] cm^2
A: 117,9

Q: Ympyrän pinta-ala on 35,6 cm^2 . Mikä on tällöin ympyrän säde?
- Noin 3,37 cm
- Noin 11,3 cm
- Noin 5,7 cm
- Noin 35,6 cm
A: Noin 3,37 cm

Q: Ympyrän piiri on 45,8 cm. Mikä seuraavista on ympyrän halkaisija?
- Noin 14,6 cm
- Noin 22,9 cm
- Noin 3,5 cm
- Noin 7,3 cm
A: Noin 14,6 cm

Q: Kuution sivun pituus on {p} m. Mikä on kuution tilavuus?

Anna vastaus kymmenesosien tarkkuudella ilman yksikköä.
A: {p}*{p}*{p} (formula; values not in the backup's text)

Q: Suorakulmaisen särmiön sivujen pituudet ovat {p} m, 10 m ja 2 m. Mikä on kappaleen tilavuus?

Anna vastaus ykkösten tarkkuudella ilman yksikköä.
A: {p}*20 (formula; values not in the backup's text)

Q: Laske kuvan ympyrälieriön tilavuus.

[Image: tilavuus]

Anna vastaus kymmenesosien tarkkuudella.

Tilavuus V = [...]dm^3
A: 2347,6

Q: Laske kuvan kappaleen tilavuus.

[Image: suorakulmainen särmiö]

Tilavuus V = [...]cm^3
A: 70

Q: Laske kuvan kappaleen pohjan pinta-ala ja tilavuus.

[Image: kolmio pohjainen lieriö]

Anna vastaus kymmenesosien tarkkuudella.

Pohjan pinta-ala  A = [...]m^2

Tilavuus  V = [...]m^3
A: 0,9; 3,8

Q: Laske kuvan kappaleen tilavuus.

[Image: puolisuunnikas pohjana]

Tilavuus V = [...]m^3
A: 5832

Q: Laske kuvan kappaleen tilavuus.

[Image: pyramidi]

Tilavuus V = [...]m^3
A: 12

Q: Laske kuvan kappaleen tilavuus.

[Image: ympyräkartio]

Anna vastaus kymmenesosien tarkkuudella.

Tilavuus V = [...]m^3
A: 1272,3

Q: Laske kuvan kappaleen tilavuus.

[Image]

Tilavuus V = [...]cm^3
A: 35

Q: Laske pallon tilavuus.

[Image: pallo]

Anna vastaus kymmenesosien tarkkuudella.

Tilavuus V = [...]cm^3
A: 1259,8

Q: Laske kuvan kappaleen tilavuus.

[Image: suorakulmainen särmiö]

Tilavuus V = [...]cm^3
A: 16000

Q: Laske kuvan sylinterin tilavuus. Sylinterissä on siis reikä keskellä. Sisäsäde on 1 cm ja ulkosäde on 2 cm.

[Image: sylinteri]

Anna vastaus ykkösten tarkkuudella

Tilavuus V = [...]cm^3
A: 66

Q: Pallon säde on {p}. Laske pallon tilavuus sadasosien tarkkuudella.
A: 3.141592654*{p}*{p}*{p}*4/3 (formula; values not in the backup's text)

Q: Ympyräpohjaisen kartion pohjan pinta-ala on \(9\pi\) ja korkeus on {p}.

Laske kappaleen tilavuus kymmenesosien tarkkuudella.
A: 9*3.141592654*{p} (formula; values not in the backup's text)

Q: Pyramidin pohja on neliö, jonka sivun pituus on {p} cm. Pyramidin korkeus on 12 cm.

Laske pyramidin tilavuus ykkösten tarkkuudella. Anna vastaus ilman yksikköä.
A: {p}*{p}*4 (formula; values not in the backup's text)

Q: Kuution tilavuus on {p} cm^3. Mikä on kuution sivun pituus?

Anna vastaus ilman yksikköä.

Vinkki: Käytä juuria!
A: {p}^(1/3) (formula; values not in the backup's text)

Q: Lieriön pohjan pinta-ala on 40 cm^2 ja tilavuus {p}. Mikä on tällöin lieriön korkeus?

Anna vastaus ilman yksikköä.
A: {p}/40 (formula; values not in the backup's text)

Q: Ympyrälieriön pohjan säde on 4,6 cm ja korkeus {korkeus} cm. Laske ympyrälieriön tilavuus.

Anna vastaus kymmenesosien tarkkuudella ilman yksikköä.

Tilavuuden kaava: \( V=\pi \cdot r^2 \cdot h \)
A: 3.141592654*21.16*{korkeus} (formula; values not in the backup's text)

Q: Ympyrän säde on {s} cm. Laske ympyrän pinta-ala.

Anna vastaus sadasosien tarkkuudella ilman yksikköä.

Kaavat: \( A=\pi \cdot r^2 \)

\( p=2 \cdot \pi \cdot r \)
A: 3.141592654*{s}*{s} (formula; values not in the backup's text)

Q: Maastokartan mittakaava on 1:20 000. Mikä on {p} km pitkän joen pituus kartalla? Anna vastaus senttimetreinä ja kymmenesosien tarkkuudella. Esim. 12,98 cm ≈ 13,0 cm.
A: {p}*5 (formula; values not in the backup's text)

Q: Kartan mittakaava on 1:10 000. Paljonko on matka luonnossa, jos se kartalla on {p} cm?

Anna vastaus metreinä ja ykkösten tarkkuudella.
A: 100*{p} (formula; values not in the backup's text)

Q: Shakkilauta koostuu 64 neliöstä. Yhden neliön sivun pituus on {p} cm. Mikä on shakkilaudan pinta-ala?

Anna vastaus kokonaislukujen tarkkuudella ilman yksikköä.
A: {p}*{p}*64 (formula; values not in the backup's text)

Q: Pyramidin (kartio) pohjana on suorakulmainen kolmio. Kolmion kanta on 3,5 cm ja korkeus 4,6 cm. Pyramidin korkeus on {p} cm. Laske pyramidin tilavuus.

Anna vastaus kymmenesosien tarkkuudella ilman yksikköä.

Kaava: \( V=A_{pohja} \cdot h \div 3 \)
A: 8.05*{p}/3 (formula; values not in the backup's text)

Q: S-marketin asiakkailta kysyttiin ikää, mitä mieltä he ovat valikoimasta ja kuinka usein he käyvät kyseisessä kaupassa. Tutkimuksesta saatiin seuraava aineisto.

Asiakas | Ikä | Sukupuoli | Käyntikerrat viikossa
1 | 18 | mies | 2
2 | 32 | nainen | 5
3 | 18 | nainen | 1
4 | 17 | mies | 2
5 | 60 | mies | 5
6 | 21 | mies | 3
7 | 17 | nainen | 4
8 | 18 | nainen | 1
9 | 23 | nainen | 5
10 | 19 | mies | 1
11 | 16 | mies | 1
12 | 35 | nainen | 6
13 | 44 | mies | 6
14 | 29 | nainen | 4
15 | 18 | nainen | 4

Luokittele käyntikerrat viikossa alla olevaan taulukkoon ja laske suhteelliset frekvenssit ja summafrekvenssit. Pyöristä vastaukset kokonaislukuihin.

Käyntikerrat viikossa | Havaintojen lukumäärä | Suhteellinen frekvenssi % | Summafrekvenssi %
1 | [...] | [...] | [...]
2 | [...] | [...] | [...]
3 | [...] | [...] | [...]
4 | [...] | [...] | [...]
5 | [...] | [...] | [...]
6 | [...] | [...] | 100 %
Yhteensä | 15 | 100 % | ------

Mikä on sukupuolen moodi?  [...]
A: 4; 27 %; 27 %; 2; 13 %; 40 %; 1; 7 %; 47 %; 3; 20 %; 67 %; 3; 20 %; 87 %; 2; 13 %; nainen

Q: Covert units

120 000 \(m^2\) | [...] \(a\) | [...] \(ha\)
20 \(a\) | [...] \(m^2\) | [...] \(ha\)
3 400 000 \(mm^2\) | [...] \(cm^2\) | [...] \(m^2\)
5670 \(cm^2\) | [...] \(m^2\) | [...] \(a\)
3,1 \(km^2\) | [...] \(ha\) | [...] \(a\)
5,12 \(ha\) | [...] \(km^2\) | [...] \(a\)
A: 1200; 12; 2000; 0,2 / 0.2; 34000; 3,4; 0,567; 0,00567; 310; 31000; 0,00512; 512

Q: Covert units

120 \(m^3\) | [...] \(dm^3\) | [...] \(l\) (litre)
20 \(l\) | [...] \(dm^3\) | [...] \(cm^3\)
3 400 000 000\(mm^3\) | [...] \(cm^3\) | [...] \(dm^3\)
6,5 \(m^3\) | [...] \(dm^3\) | [...] \(ml\)
0,0000008 \(km^3\) | [...] \(m^3\) | [...] \(l\)
90 \(cm^3\) | [...] \(dm^3\) | [...] \(mm^3\)

Remember that 1 litre = 1 dm^3
A: 120000; 120000; 20; 20000; 3400000; 3400; 6500; 6500000; 800; 800000; 0,09; 90000

Q: Fill the tables. Remember the unit.

Scale is 1 : 1000

1 cm | 10 m
2 cm | [...]
5 cm | [...]
15 cm | [...]

Scale is 1 : 150 000

1 cm | [...] km
2 cm | [...] km
5 cm | [...] km
15 cm | [...] km

Scale is 5 : 1

5 cm | 1 cm
15 cm | [...]
150 cm | [...]
225 cm | [...]
A: 20 m / 20m; 50 m / 50m; 150 m / 150m; 1,5 / 1.5; 3; 7,5 / 7.5; 22,5 / 22.5; 3 cm / 3cm; 30 cm / 30cm; 45 cm / 45cm

Q: Fill the tables.

Scale is 1 : 1000

1 cm | 10 m
2 cm | [...]
5 cm | [...]
15 cm | [...]

Scale is 1 :1 150 000

1 cm | [...] km
2 cm | [...] km
5 cm | [...] km
15 cm | [...] km

Scale is 5 : 1

5 cm | 1 cm
15 cm | [...]
150 cm | [...]
225 cm | [...]
A: 10 m / 10m; 50 m / 50m; 150 m / 150m; 1,5 / 1.5; 3; 7,5 / 7.5; 22,5 / 22.5; 3 cm / 3cm; 30 cm / 30cm; 45 cm / 45cm

Q: Convert the unit

120 000 \(m^2\) | [...] \(a\) | [...] \(ha\)
20 \(a\) | [...] \(m^2\) | [...] \(ha\)
3 400 000 \(mm^2\) | [...] \(cm^2\) | [...] \(m^2\)
5670 \(cm^2\) | [...] \(m^2\) | [...] \(a\)
3,1 \(km^2\) | [...] \(ha\) | [...] \(a\)
5,12 \(ha\) | [...] \(km^2\) | [...] \(a\)
A: 1200; 12; 2000; 0,2 / 0.2; 34000; 3,4; 0,567; 0,00567; 310; 31000; 0,0512; 512

Q: Covert the unit

120 \(m^3\) | [...] \(dm^3\) | [...] \(l\) (litre)
20 \(l\) | [...] \(dm^3\) | [...] \(cm^3\)
3 400 000 000 \(mm^3\) | [...] \(cm^3\) | [...] \(dm^3\)
6,5 \(m^3\) | [...] \(dm^3\) | [...] \(ml\)
0,0000008 \(km^3\) | [...] \(m^3\) | [...] \(l\)
90 \(cm^3\) | [...] \(dm^3\) | [...] \(mm^3\)

Remember that 1 litre = 1 dm^3
A: 120000; 120000; 20; 20000; 3400000; 3400; 6500; 6500000; 800; 800000; 0,09; 90000

Q: Convert {area} \(m^2\) to are (a).

Give the answer without unit.
A: {area}/100 (formula; values not in the backup's text)

Q: Convert {area} \(ha\) to square meters (\(m^2\)).

Give the answer without unit.
A: {area}*10000 (formula; values not in the backup's text)

Q: Convert {vol} \(m^3\) to liter (l).

Give the answer without unit.
A: {vol}*1000 (formula; values not in the backup's text)

Q: Convert {vol} \(m^3\) to \(cm^3\).

Give the answer without unit.
A: {vol}*1000000 (formula; values not in the backup's text)

Q: Multiply and divide without the help of a calculator

a) 5 · 10 = [...]

b) 14 · 100 = [...]

c) 7,8 · 10 = [...]

d) 8,4 · 100 = [...]

e) 0,35 · 1000 = [...]

f) 700 : 10 = [...]

g) 35 : 10 = [...]

h) 35 : 100 = [...]

i) 400 : 1000 = [...]

j) 2,5 : 10 = [...]
A: 50; 1400; 78; 840; 350; 70; 3.5; 0.35; 0.4; 0.25

Q: Calculate

{a} + (+{b})
A: {a}+{b} (formula; values not in the backup's text)

Q: Calculate

{a} - (+{b})
A: {a}-{b} (formula; values not in the backup's text)

Q: Calculate

-{a} + (+{b})
A: {b}-{a} (formula; values not in the backup's text)

Q: Calculate

{a} + (-{b})
A: {a}-{b} (formula; values not in the backup's text)

Q: Calculate

{a} - (-{b})
A: {b}+{a} (formula; values not in the backup's text)

Q: Calculate

-{a} - (+{b})
A: 0-{b}-{a} (formula; values not in the backup's text)

Q: Calculate

-{a} - (-{b})
A: {b}-{a} (formula; values not in the backup's text)

Q: Calculate

-{a} + (-{b})
A: 0-{b}-{a} (formula; values not in the backup's text)

Q: Calculate

{a} · (-{b})
A: -{b}*{a} (formula; values not in the backup's text)

Q: Calculate

{a} · ({b})
A: {b}*{a} (formula; values not in the backup's text)

Q: Calculate

-{a} · ({b})
A: -{b}*{a} (formula; values not in the backup's text)

Q: Calculate

-{a} · (-{b})
A: {b}*{a} (formula; values not in the backup's text)

Q: Do the operations in this order

1. Operations in brackets ()

2. Multiplication · and division :

3. Addition + and subtraction -

a) 4 + 2 · 3 = [...]

b) 13 - 9 : 3 = [...]

c) 40 : 8 · 3 = [...]

d) 8 - (3 + 2) = [...]

e) 12 - 3 · 4 + 5 = [...]

f) 12 - 3 · (4 + 5) = [...]

g) (12 - 3) · 4 + 5 = [...]

h) 12 - (3 · 4 + 5) = [...]
A: 10; 10; 15; 3; 5; -15; 41; -5

Q: a) 50 + 3 - 2 · 5 = [...]

b) (10 - 6) · 0,5 = [...]

c) 12 : (2 · 3) = [...]

d) 2 + ((4 + 2) · 3) = [...]

e) (8 - 4) · 250 - 5 · (4 + 16)= [...]

f) 150 - (20 - (3 - 11) · 10) = [...]
A: 43; 2; 2; 20; 900; 50

Q: Calculate the area of a circle that has a radius of {r} m.

Give the answer with 2 decimals.
A: {r}**2*3.141592654 (formula; values not in the backup's text)

Q: Calculate the area of a circle that has a diameter of {r} cm.

Give the answer with 2 decimals and without unit.
A: ({r}/2)**2*3.141592654 (formula; values not in the backup's text)

Q: The round metal wire has a cross-sectional diameter of {r} mm. Calculate the cross-sectional area of the wire.

Give the answer with 2 decimals.
A: ({r}/2)**2*3.141592654 (formula; values not in the backup's text)

Q: Calculate the perimeter of a circle. The radius of the circle is {r} m.

Give the answer with 2 decimals.
A: 2*3.141592654*{r} (formula; values not in the backup's text)

Q: Calculate the perimeter of a circle. The diameter of the circle is {d} m.

Give the answer with 2 decimals and without unit.
A: {d}*3.141592654 (formula; values not in the backup's text)

Q: Solve x

[Image: Right angled triangle with adjacent sides 8 and 15.]
A: 17

Q: Solve x

[Image: Right angled triangle with adjacent side 5 and 12.]
A: 13

Q: Solve x

[Image: Right angled triangle with adjacent side 7 and hyptenuse 12.]
A: 24

Q: Solve x

[Image: Right angled triangle with adjacent side 8 and hypotenuse 10.]
A: 6

Q: Solve x

[Image: Right angled triangle with adjacent side 8,5 cm and 19,4 cm.]

Give the answer in tenths and with unit.
A: 17.4 / 17.4
Partly right: 17 (50%)

Q: Solve x

[Image: Adjacent sides x and hypotenuse 4,6 cm.]

Give the answer in tenths and give the unit.
A: 3.3 / 3.3
Partly right: 3.2 (90%); 3.2 (90%)

Q: Solve x

[Image: Adjacent sides 3,4 cm and 9,1 cm.]

Give the answer in tenths and give the unit.
A: 9.7 / 9.7

Q: A triangular lot has sides measuring 25 meters, 36 meters, and 39 meters. Is it a right triangle?
A: No / No it's not / It's not / It is not / No, it is not

Q: A ladder is leaning against a wall. If the ladder is 10 meters long and the distance from the foot of the ladder to the wall is {p} meters, how far up the wall does the ladder reach?

Give the answer in tenths and with unit.
A: (100-{p}**2)**(1/2) (formula; values not in the backup's text)

Q: Find the length of the diagonal of a rectangle whose sides measure {p} cm and 8,2 cm.

Give the answer in tenths and with unit.
A: ({p}**2+8.2**2)**(1/2) (formula; values not in the backup's text)

Q: A right triangle has one leg measuring {p} cm and the hypotenuse measuring 13,9 cm. Find the length of the other leg.

Give the answer in tenths and with unit.
A: (13.9**2-{p}**2)**(1/2) (formula; values not in the backup's text)

Q: Calculate
a) 10 : (-2) = [...]
b) -6 : (-2) = [...]
c) -15 : 5 = [...]
d) 8 : 2 = [...]
e) -18 : (-9) = [...]
f) 28 : (-7) = [...]
A: -5; 3; -3; 4; 2; -4

Q: Calculate

a) 3^2 = [...]

b) 8^2 = [...]

c) 12^2 = [...]

d) (-2)^2 = [...]

e) (-6)^2 = [...]

f) 3^3 = [...]

g) 5^3 = [...]

h) (-2)^3 = [...]
A: 9; 64; 144; 4; 36; 27; 125; -8

Q: Calculate

a) \(\sqrt {9}\) = [...]

b) \(\sqrt {36}\) = [...]

c) \(\sqrt {64}\) = [...]

d) \(\sqrt {144}\) = [...]

e) \(\sqrt {10000}\) = [...]

f) \(\sqrt {1}\) = [...]
A: 3; 6; 8; 12; 100; 1

Q: \[a)\frac{1}{3}\cdot\frac{1}{4}=\]
[...]

[...]
\[b)\frac{2}{3}\cdot\frac{6}{7}=\]
[...]

[...]
\[c)\frac{3}{4}\cdot\frac{2}{3}=\]
[...]

[...]
\[d)\frac{1}{4}\cdot\frac{2}{5}=\]
[...]

[...]
\[e) 3\cdot\frac{1}{6}=\]
[...]

[...]
\[f)\frac{2}{7}\cdot 2=\]
[...]

[...]
A: 1; 12; 4; 7; 1; 2; 1; 10; 1; 2; 4; 7
Partly right: gap 3 12 (50%); gap 4 21 (50%); gap 5 6 (50%); gap 6 12 (50%); gap 7 2 (50%); gap 8 20 (50%); gap 9 3 (50%); gap 10 6 (50%)

Q: \[a)\frac{1}{4}+\frac{2}{4}=\]
[...]

[...]
\[b)\frac{1}{8}+\frac{3}{8}=\]
[...]

[...]
\[c)\frac{1}{3}+\frac{2}{6}=\]
[...]

[...]
\[d)\frac{1}{4}+\frac{3}{8}=\]
[...]

[...]
\[e)\frac{2}{7}+\frac{1}{3}=\]
[...]

[...]
\[f)\frac{1}{6}+\frac{2}{5}=\]
[...]

[...]
A: 3; 4; 1; 2; 2; 3; 5; 8; 13; 21; 17; 30
Partly right: gap 3 4 (50%); gap 4 8 (50%); gap 5 4 (50%); gap 6 6 (50%)

Q: \[a)\frac{2}{3}-\frac{1}{3}=\]
[...]

[...]
\[b)\frac{6}{7}-\frac{2}{7}=\]
[...]

[...]
\[c)\frac{2}{3}-\frac{1}{6}=\]
[...]

[...]
\[d)\frac{5}{8}-\frac{1}{2}=\]
[...]

[...]
\[e)\frac{4}{5}-\frac{4}{7}=\]
[...]

[...]
\[f)\frac{1}{2}-\frac{1}{5}=\]
[...]

[...]
A: 1; 3; 4; 7; 1; 2; 1; 8; 8; 35; 3; 10
Partly right: gap 5 3 (50%); gap 6 6 (50%)

Q: \[a)\frac{1}{2}:\frac{3}{2}=\]
[...]

[...]
\[b)\frac{2}{5}:\frac{3}{4}=\]
[...]

[...]
\[c)\frac{1}{2}:\frac{1}{6}=\] | [...]
\[d) 2:\frac{1}{2}=\] | [...]
\[e)\frac{4}{5}:2=\]
[...]

[...]
\[f)\frac{3}{4}:5=\]
[...]

[...]
A: 1; 3; 8; 15; 3; 4; 2; 5; 3; 20
Partly right: gap 1 2 (50%); gap 2 6 (50%)

Q: Convert decimal numbers to fractions

a) 0,7 =
[...]

[...]
b) 0,33 =
[...]

[...]
c) 1,57 =
[...]

[...]
d) 0,249 =
[...]

[...]
e) 0,9 =
[...]

[...]
f) 0,27 =

_________
[...]

[...]
A: 7; 10; 33; 100; 157; 100; 249; 1000; 9; 10; 27; 100

Q: Convert fractions to decimal numbers, use , (comma) as the decimal separator.

\[a)\frac{1}{10}=\] | [...]
\[b)\frac{6}{10}\] | [...]
\[c)\frac{1}{2}\] | [...]
\[d)\frac{1}{4}\] | [...]
\[e)\frac{3}{4}\] | [...]
\[f)\frac{1}{8}\] | [...]
A: 0,1; 0,6; 0,5; 0,25; 0,75; 0,125

Q: Convert mixed numbers to fractions

\[a)1\frac{1}{4}\]
[...]

[...]
\[b)2\frac{1}{8}=\]
[...]

[...]
\[c)1\frac{2}{3}\]
[...]

[...]
\[d)2\frac{3}{4}\]
[...]

[...]
\[e)1\frac{2}{7}\]
[...]

[...]
\[f)3\frac{5}{6}\]
[...]

[...]
A: 5; 4; 17; 8; 5; 3; 11; 4; 9; 7; 23; 6

Q: The temperature was {a}°C in the morning. By the evening, it dropped by {b}°C. What is the temperature in the evening?
A: {a}-{b} (formula; values not in the backup's text)

Q: Alex had €{a} in his bank account. He withdrew €{b}. What is his new balance in euros?
A: {a}-{b} (formula; values not in the backup's text)

Q: In a game, a player scored -{a}0 points in the first round and {b}0 points in the second round. What is the total score?
A: (0-{a}+{b})*10 (formula; values not in the backup's text)

Q: Matti buys a pair of shoes for 50 € and 3 shirts for {a} € each. He uses a {b}0 € discount coupon. How much does he spend in total?
A: 3*{a}+50-(10*{b}) (formula; values not in the backup's text)

Q: You order 3 large pizzas for {a} € each and 2 small pizzas for {b} € each. How much do you pay in total?
A: 3*{a}+2*{b} (formula; values not in the backup's text)

Q: Salmon needs to be cooked for 20 minutes plus 10 minutes per kilogram. How many minutes should you cook a {a} kg salmon for?
A: 20 + 10*{a} (formula; values not in the backup's text)

Q: A fuel tank is {a}/5 full. If the tank holds {b} liters when full, how many liters of fuel is there in the tank?
A: {a}/5*{b} (formula; values not in the backup's text)

Q: Saara has read 3/4 of her book. If the book has {a}0 pages, how many pages has she read?
A: 10*3/4*{a} (formula; values not in the backup's text)

Q: A recipe for 20 pancakes calls for 2/3 cup of sugar. If you want to make half of the recipe, how much sugar do you need?

[...] cup
A: 0,33 / 1/3

Q: Scale of a map is 1 : 20 000.

What is the distance in nature if the distance in map is {p} cm?

Give the answer in meters and with a unit.
A: {p}*200 (formula; values not in the backup's text)

Q: Scale of a map is 1 : 20 000.

What is the distance in map if the distance in nature is {t} m?

Give the answer in centimeters and with a unit.
A: {t}/200 (formula; values not in the backup's text)

Q: Calculate the volume.

The shape of a sport center is a half sphere. Calculate the volume when the diameter is {t} m.

Give the answer as a whole number without unit.
A: 4/3*3.141592654*({t}/2)**3 (formula; values not in the backup's text)

Q: Calculate the area.

The base of a triangle is  70 m and the height is {t} m. Calculate the area of the triangle.

Give the answer as a whole number and without a unit.
A: {t}*35 (formula; values not in the backup's text)

Q: Calculate the area.

[Image: are]

h = {h} mm

Give the answer in tenths and without a unit.
A: 14.6*{h} (formula; values not in the backup's text)

Q: Covert the units

230 000 \(m^2\) | [...] \(a\) | [...] \(ha\)
21,3 \(a\) | [...] \(m^2\) | [...] \(ha\)
9 400 000 \(mm^2\) | [...] \(cm^2\) | [...] \(m^2\)
A: 2300; 23; 2130; 0,213 / 0.213; 94000; 9,4

Q: Covert the units

2,55 \(m^3\) | [...] \(dm^3\) | [...] \(l\) (litre)
8 \(l\) | [...] \(dm^3\) | [...] \(cm^3\)
9 900 000 000 \(mm^3\) | [...] \(cm^3\) | [...] \(m^3\)
A: 2550; 2550; 8; 8000; 9900000; 9.9 / 9.9

Q: Calculate the area and the perimeter of a circle.

The diameter of the circle is 24 cm.

Give the answer in tenths.

Area = [...] \(cm^2\)

Perimeter = [...] \(cm\)
A: 452,4 / 452.4; 75,4 / 75.4
Partly right: gap 1 452 (50%); gap 1 452,3 (50%); gap 2 75 (50%)

Q: Calculate the volumes of the following objects.

[Image: volume]

V=[...] \(cm^3\)

[Image: volume2]

Round the answer to whole number.

V=[...] \(dm^3\)

[Image: volume 3]

V=[...] \(cm^3\)
A: 560; 2309; 560

Formulas

Circle

$$ A = \pi r^2$$

$$p=2\pi r$$

Triangle

$$ A = ah\div 2 $$

Volume

Rectangular prism $$ V=a\cdot b\cdot c$$

Circular cylinder $$ V= \pi r^2 h$$

Cone $$ V= A\cdot h \div 3$$

Circular cone $$ V= \pi r^2 h \div 3$$

Sphere $$ V=\frac{4}{3} \pi r^3$$

 Pythagora theorem $$a^2+b^2=c^2$$

Q: Solve x

 when h={h}.

[Image: pytha]

Give the answer in tenths.
A: (10.24+{h}**2)**(1/2) (formula; values not in the backup's text)

Q: Solve x
when the h = {h}

[Image: pythagoras]

Give the answer with one decimal.
A: (625-{h}**2)**(1/2) (formula; values not in the backup's text)

Q: Formula for the area of a square is A = a^2 where a is the side length of the square. If the side length of a square is {a} m, how many square meters is the area of the square? Don't write the unit in the answer.
A: {a}*{a} (formula; values not in the backup's text)

Q: Formula for the volume of a cube is A = a^3 where a is the side length of the cube. If the side length of a cube is {a} m, how many cubic meters is the volume of the cube? Don't write the unit in the answer.
A: {a}*{a}*{a} (formula; values not in the backup's text)

Q: The area of a square is 64 m^2. What is the length of one side of the square?

[...] m
A: 8

Q: Calculate

-{a} - (-{b})
A: 0-{a}+{b} (formula; values not in the backup's text)

Q: Change to decimal number:

a) 20 % = [...]

b) 35 % = [...]

c) 57 % = [...]

d) 94,7 % = [...]

e) 221 % = [...]

f) 0,07 % = [...]
A: 0.2; 0.35; 0.57; 0.947; 2.21; 0.0007

Q: Change to percent

a) 0,4 =  [...] %

c) 1,2 =  [...] %

c) 0,56 =  [...] %

b) 13 = [...] %

c) 0,571 = [...] %

d) 0,0052 = [...] %
A: 40; 120; 56; 1300; 57.1; 0.52

Q: What is

a) 20 % of 80? [...]

b) 4 % of 150? [...]

c) 5 % of 900?  [...]

d) 30 % of 80?  [...]

e) 200 % of 30?  [...]

f) 25,5 % of 460?  [...]
A: 16; 6; 45; 24; 60; 117.3

Q: How many percent is

a) 2 of 50? [...] %

b) 15 of 75? [...] %

c) 400 of 1600? [...] %

d) 3 of 75? [...] %

e) 200 of 50 000? [...] %

f) 60 of 25? [...] %
A: 4; 20; 25; 4; 0.4; 240

Q: How many percentage did the price of gasoline change when it

a) first increased by 10 % and then decreased by 10 %? [...] %

b) first increased by 15 % and then decreased by 8 %? [...] %

c) first decreased by 20 % and then increased by 30 %? [...] %
A: 1; 5.8; 4

Q: What is the base value in the following cases?
a) The product's price decreased by 8 %, after which the price was 1200 €. [...]
b) The value-added tax is 26 % of the product's selling price. [...]
c) In 2019, a certain hand sanitizer had a market share of 20 % of the European hand sanitizer market. [...]
d) The bookshelf cost 400 € with a 60 % discount. [...]
A: the original price; the selling price; European hand sanitizer market; the original price
Gap 1 offers: the original price; the selling price; European hand sanitizer market
Gap 2 offers: the original price; the selling price; European hand sanitizer market
Gap 3 offers: the original price; the selling price; European hand sanitizer market
Gap 4 offers: the original price; the selling price; European hand sanitizer market

Q: A new iPhone 12 costs 1278 € and a used iPhone 11 costs 749 €.

a) By what percentage is the iPhone 12 more expensive than the iPhone 11?

[...] %

b) By what percentage is the iPhone 11 cheaper than the iPhone 12?

[...] %
A: 70.6; 41.4

Q: The Norwegian salmon has two prices marked: 14,50 € and 8,00 €, with the higher amount crossed out.

a) By how many euros has the price been reduced? [...] €

b) By what percentage has the price of the Norwegian salmon decreased?

[...] %

c) By what percentage was the original price higher than the discounted price?

[...] %
A: 6.5; 44.8; 81.25

Q: Timo worked at the same place for two summers.

In the first summer, he earned 1520 euros, and in the second summer, he earned 1610 euros.

By what percentage did Timo's salary increase?

[...] %
A: 5.9

Q: In 2003, Niko was 176 cm tall, and the following year he was already 184 cm tall.

During the same period, his weight increased from 73 kg to 79 kg.

a) By what percentage did Niko's height change over the year? [...] %

b) By what percentage did Niko's weight change over the year? [...] %

c) Which grew more in percentage terms, Niko's weight or height? [...]

d) How many percentage points was the difference in the relative change between Niko's weight and height? [...]
A: 4.5; 8.2; weight; 3.7
Gap 3 offers: weight; height

Q: A party's support drops from 19 percent to 12 percent.

a) By how many percentage points does the support drop? [...]

b) By what percentage does the support drop? [...] %
A: 7; 37

Q: The original price of the food is 12,60 €. Due to the last sale day, the shopkeeper reduces the price by 30 %.

a) How much is the discount in euros? [...] €

b) How much does the customer have to pay for the item after the discount?[...] €
A: 3.78; 8.82

Q: a) Calculate the interest rate when the interest on a loan of 32 000 € is 1664 € in six months.

Assume that the interest rate remains the same for the entire year.

[...] %

b) Mr. Digi takes out a loan of € 1400 from the bank to buy himself a new LG OLED TV.

How much does Mr. Digi repay the bank in total when he pays back the loan and interest at the same time, 7 months after taking out the loan? The annual interest rate on the loan is 8,3 %.

Hint: Think about how many percent the interest is per month and multiply this by seven. After this, you can easily calculate the interest portion of the loan.

[...] €
A: 10.4; 1467.78

Q: A poor math teacher had luck in the Eurojackpot and won a little pocket money, namely 90 million euros.

After some small celebrations and charitable donations, he had 40 million euros left.

He invested this amount in a stable growth account with an interest rate of 2,8 percent.

How much did the lottery win produce in interest income

a) annually?  [...] €

b) monthly?  [...] €

c) daily?  [...] €

d) hourly?  [...] €
A: 1120000; 93333; 3069; 127.85

Q: a) The initial amount of the bill was 345,00 €. You pay the bill 112 days late, and the annual late payment interest rate is 8,6%. How much do you have to pay in interest?  [...] €

b) You invest 2000,00 € in fund shares with an expected return of 14 % per year.

If the increase is steady, what is the expected value of your investment in 3 months? [...] €
A: 9.1; 2070

Q: Value-added tax is 25,5 % and is calculated from the pre-tax price.

a) What is the value-added tax when the pre-tax price is 86 €?   [...]€

b) What is the pre-tax price when the price with tax is 44,64 €? [...]  €

c) What is the price with tax when the pre-tax price is 21 €?  [...] €

d) What is the price with tax when the value-added tax is 33,60 €?  [...] €
A: 21.93; 35.57; 26.36; 165.36

Q: Value-added tax is 25,5 % and is calculated from the pre-tax price.

a) What is the value-added tax when the price including tax is 118 €?  [...]

b) What is the pre-tax price when the price including tax is 67,50 €?  [...]

c) What is the price including tax when the pre-tax price is 43,30 €?  [...]

d) What is the pre-tax price when the value-added tax is 1050,60 €?  [...]
A: 23.98; 53.78; 54.34; 4120

Q: [Image: Diagram that shows the body temperature of a camel change]

Here you can see a graph which tells you how the body temperature of a camel changes over 24 hours. The vertical axis is the body temperature and the horizontal axis tells you at what time it has been measured.

Question: At what time is the body temperature of the camel at is highest?
- In the morning
- Before 12 o’clock
- In the afternoon
- In the evening
- At night
A: In the afternoon

Q: [Image: Diagram that shows the body temperature of a camel change]

Here you can see a graph which tells you how the body temperature of a camel changes over 24 hours. The vertical axis is the body temperature and the horizontal axis tells you at what time it has been measured.

Question: At what time is the body temperature of the camel at its lowest?
- 6:00
- 10:00
- 14:00
- 18:00
- 22:00
- 2:00
A: 2:00

Q: [Image: Diagram that shows the body temperature of a camel change]

Here you can see a graph which tells you how the body temperature of a camel changes over 24 hours. The vertical axis is the body temperature and the horizontal axis tells you at what time it has been measured.

Question: What is the body temperature of the camel at 20:00?
- I am not an expert – how can I tell!
- 35 degrees
- 36 degrees
- 37 degrees
- 38 degrees
- It burns!
A: 37 degrees

Q: [Image: Diagram for average sleep requirement]

The average need for sleep per night considering a person’s age. The vertical axis tells you how many hours of sleep and the horizontal axis gives a person’s age.

Question: How much sleep does a 20 years old person need?
- 10 hours
- 9 hours
- 8 hours
- 7 hours
- 6 hours
- 5 hours
- Young people do not need to sleep
A: 7 hours

Q: [Image: Diagram for average sleep requirement]

Question: At what age can people manage with 6 hours sleep at night?
- Everyone can manage
- After your 35th birthday
- At about 50 years old
- Over 60 years old people
A: At about 50 years old

Q: [Image: Diagram for average sleep requirement]

Question:  How many hours does a 90-year-old person need to sleep?
- 24 h...at that age they sleep all the time
- 4,5 h
- 5 h
- 5,5 h
- 6,5 h
A: 5,5 h

Q: [Image: Diagram for the number of British citizens living in Finland]

In this graph you can see how the number of British citizens has grown in Finland from 1996 to 2003. The vertical axis presents the number of people and the horizontal axis tells the year.

Question: In what year was the population of the British at its lowest? Give the year as your answer.
A: 1996

Q: [Image: Diagram for the number of British citizens living in Finland]

In this graph you can see how the number of British citizens has grown in Finland from 1996 to 2003. The vertical axis presents the number of people and the horizontal axis tells the year.

Question: What was the growth of the number of British citizens from 1996 to 2003 in Finland?
- 850
- 900
- 950
- 1000
- Something else
A: 850

Q: [Image: Diagram for the number of British citizens living in Finland]

Question: When were there 2 200 British citizens living in Finland? Give the answer in numbers, for example 2019.
A: 2000

Q: [Image: A time-distance graph]

In this picture you can see Mikko’s riding kilometers versus the time [h] he has used.

Question: What is Mikko’s velocity?
- About 5 km/h
- About 10 km/h
- About 12 km/h
- About 15 km/h
A: About 12 km/h

Q: [Image: A time-distance graph]

In this picture you can see Mikko’s riding kilometers versus the time ( h ) he has used.

QUESTION: How many kilometers has Mikko cycled when he has used 10 hours? He does not change his velocity during that time.
A: About 120 km

Q: [Image: A time-distance graph]

In this picture you can see Mikko’s riding kilometers versus the time [h] he has used.

QUESTION: Does Mikko have constant speed or does his speed alternate?
- Mikko rides his bike with constant speed
- Mikko rides his bike with alternating speed
- I can’t get a hold of this one. I don’t know.
A: Mikko rides his bike with constant speed

Q: [Image: A time-distance graph]

In this picture you can see Mikko’s riding kilometers versus the time [h] he has used.

QUESTION: How many kilometers has Mikko cycled when he has used 10 hours? He does not change his velocity during that time.
- About 50 km
- About 80 km
- About 100 km
- About 120 km
A: About 120 km

Q: [Image: Bar diagram of TV shows]

In this bar chart you can see the number of TV viewers on the vertical axis and the TV show on the horizontal axis.

By using this bar chart you have to decide which one of the following statements is true.
- Columbo is three times as popular as Ritari Ässä.
- The Muppet Show is watched twice as much as Ritari Ässä.
- Uutiset (The News) is watched nearly twice as much as Ritari Ässä.
- Nobody has ever been keen to watch these shows.
A: Uutiset (The News) is watched nearly twice as much as Ritari Ässä.

Q: [Image: A graph of support for parties]

Support for parties. What argument or which arguments are true according to the above graph?
- The support for party A is double compared to the support for party B.
- The support for party C is double compared to the support for party B.
- Other parties (=Muut) are supported by hardly anyone.
- The support for party A is double compared to the support for party C.
A: The support for party A is double compared to the support for party B.

Q: When Pekka finished his basic education his marks on 12 subjects were:

8, 8, 7, 9, 6, 7, 6, 8, 7, 7, 6, 9

What is the mean of Pekka’s grades?  Use one decimal (round up or down if necessary)

[...]
A: 7.3

Q: Tero Pitkämäki threw the javelin and his 6 best throws are

91,53 m

91,33 m

91,23 m

91,11m

90,54 m

90,33 m

Calculate the mean and give the answer by using two decimals (round up/down if necessary).

[...] m
A: 91.01

Q: In this frequency table you can see the students’ grades and how many of them got the same grade. Calculate the mean. Use one decimal when answering.

Grade | Number of students
1 | 2
2 | 5
3 | 7
4 | 12
5 | 4
Total | 30

[...]
A: 3.4

Q: 8 workers were asked about their monthly earnings. Here you have the list of their answers:

  1450 €

  2100 €

  1680 €

  1850 €

  1920 €

  3100 €

  2340 €

  1800 €

Calculate the mean. Give the answer on the accuracy of one €. Write numbers only when answering.

[...]
A: 2030

Q: Calculate the mean of the following lengths:

52 cm, 50 cm, 49 cm, 53 cm, 47 cm, 48 cm, 51 cm

[...] cm
A: 50

Q: Here you have a list of wages in euros. Can you find out the median?

1450

2100

1680

1850

1920

3100

2340

1800

2400

[...]
A: 1920

Q: What is the median when the values are

1450

2100

1680

1850

1920

3100

2340

1800

[...]
A: 1885

Q: A distance between two places was measured and here are the results. What is the median?

52 cm, 50 cm, 49 cm, 53 cm, 47 cm, 48 cm, 51 cm

[...]
A: 50

Q: Jarmo’s grades are from the top to the bottom:

5, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9

Calculate (if possible) the median.

[...]
A: 7

Q: A group of students has pets as listed:

a cat, a cat, a dog, a dog, a dog, a dog, a dog, a dog, a guinea pig, a rabbit, a horse, a horse, a budgie, a turtle.

Find the median (if possible).
- a cat
- a dog
- a horse
- You don't have a median!
A: You don't have a median!

Q: A group of students has pets as listed:

a cat, a cat, a dog, a dog, a dog, a dog, a dog, a dog, a guinea pig, a rabbit, a horse, a horse, a budgie, a turtle.

Find the mode (if possible).
- a cat
- a dog
- a horse
- You don't have a mode!
A: a dog

Q: What is the mode in the given data?

2 €, 2 €, 2 €, 5 €, 15 €, 15€, 20 €

[...] €
A: 2

Q: What is the median in the given data?

2 €, 2 €, 2 €, 5 €, 15 €, 15€, 20 €

[...] €
A: 5

Q: What is the mode in this data?

Opinion | Frequency
bad | 6
quite bad | 8
good | 14
excellent | 9
- good
- bad
- quite bad
- excellent
A: good

Q: What is the mode in this data?

Pocket money | Number of persons
0-4 € | 5
5-9 € | 22
10-14 € | 7
15 €or more | 3
- 0-4 €
- 5-9 €
- 10-14 €
- 15 € or more
- Something else
A: 5-9 €

Q: Here we have a bar chart of students’ grades. On the vertical axis is the number of students and on the horizontal axis are the grades from 1 to 5.

Calculate the average and use one decimal when you add your answer.

[Image: Diagram for grade distributions, grade 1 has 4, grade 2 has 10, grade 3 has 12, grade 4 has 6 and grade 5 has 2 occurren]
The average is [...]
A: 2.8

Q: Here we have a bar chart of students’ grades. On the vertical axis is the number of students and on the horizontal axis are the grades from 1 to 5.

Calculate the mode.

[Image: Diagram for tudent's grades, grade 1 has 4, grade 2 has 10, grade 3 has 12, grade 4 has 6 and grade 5 has 2 occurrences]
The mode is [...]
A: 3

Q: Here we have a bar chart of students’ grades. On the vertical axis is the number of students and on horizontal axis are the grades from 1 to 5.

Calculate the median and use one decimal when you add your answer.

[Image: Diagram for tudent's grades, grade 1 has 4, grade 2 has 10, grade 3 has 12, grade 4 has 6 and grade 5 has 2 occurrences]
The median is [...]
A: 3

Q: 10 cereal packs were weighted. The weights were:

386 g, 370 g, 402 g, 422 g, 397 g, 392 g, 388 g, 400 g, 405 g, 390 g

What is the range of measured weights?
- 370g - 422 g
- 395,2 g
- 394,5
- 392 g - 397 g
A: 370g - 422 g

Q: Reduce the following expressions. Use x^2 as x squared. Order the terms of polynomials from highest degree to lowest.

a)    x + x + x = [...]

b)    x + 2x + 3x = [...]

c)    2x + 4x + 2 + 3 = [...]

d)    x^2 + x^2 + 3x^2 = [...]

e)    x^2 + 2x^2 +4x - x + 9 - 3 = [...]

f)     x + x + 2x + 2 + 3 = [...]

g)    9x^2 + 13 + 3x -2x^2 + 3x - x + 7 = [...]
A: 3x; 6x; 6x+5 / 6x + 5; 5x^2; 3x^2+3x+6 / 3x^2 + 3x + 6; 4x+5 / 4x + 5; 7x^2+5x+20 / 7x^2 + 5x + 20

Q: Reduce the following expressions

a)    (x + 4) + (x + 3) = [...]

b)    9x + 2 - (5x - 3) = [...]

c)     – (2x – 1) – ( –8x + 6) = [...]

d)    2 (4x + 6) = [...]

e)    10 (x^2 + 2x) = [...]

f)     x (5 - 4x) = [...]

g)    (x + 1) (x + 1) = [...]

h)    (5 + 4x) (2x + 4) = [...]
A: 2x+7 / 2x + 7; 4x+5 / 4x + 5; 6x+7 / 6x + 7; 8x+12 / 8x + 12; 10x^2+20x / 10x^2 + 20x; -4x^2+5x / -4x^2 + 5x; x^2+2x+1 / x^2 + 2x + 1; 8x^2+26x+20 / 8x^2 + 26x + 20

Q: Solve the following proportions by using cross multiplication

a) \(\frac{6}{4}=\frac{90}{x}\)  , x = [...]

b) \(\frac{72}{24}=\frac{x}{4}\)  , x = [...]

c) \(\frac{3}{5}=\frac{12}{x}\)  , x = [...]

d) \(\frac{2x}{8}=\frac{5}{2}\)  , x = [...]
A: 60; 12; 20; 10

Q: In a bakery, a recipe for 20 cookies requires 15 dl of flour. If the bakery wants to bake 60 cookies, how much flour will they need?

[...] dl
A: 45

Q: Complete the table below when the quantity and price are directly proportional.

Quantity (kg) | Price (€)
[...] | 4,50
1 | [...]
2 | 18,00
[...] | 45,00
10 | [...]
A: 0.5; 9; 5; 90

Q: Pekka runs 4 km in 20 minutes. Determine the values for the blank spots in the table.

Time (min) | Distance (km)
20 | 4
40 | [...]
10 | [...]
7 | [...]
A: 8; 2; 1.4

Q: It costs 6,50 € to buy 2,5 kg of apples. How much would 8 kg of apples cost?

[...] €
A: 20.8

Q: A hiker took 3 hours for a 10 km trip. Use proportion to calculate how long the trip would take for:

a) A 25 km trip

[...] hours

b) A 40 km trip

[...] hours
A: 7.5; 12

Q: The pick and mix candies cost 0,79€ per 100g. Use proportion to calculate how much candy you could get for 3€?

[...] kg
A: 0.38

Q: A machine uses 8 kWh of electricity to run for 4 hours. How much electricity will the machine use if it runs for 10 hours?

[...] kWh
A: 20

Q: A clothing factory requires 2 meters of fabric to produce 3 shirts. How much fabric is needed to produce 18 shirts?

[...] m
A: 12

Q: A welder uses 3 meters of welding rod to weld 6 metal plates. How much welding rod will be needed to weld 15 metal plates?

[...] m
A: 7.5

Q: A vehicle consumes 8 liters of fuel to travel 100 kilometers. How much fuel will it consume to travel 350 kilometers?

[...] liters
A: 28

Q: A factory produces 50 items in 5 hours. How many items will the factory produce in 12 hours?

[...] items
A: 120

Q: A water tank is filling at a rate of 10 liters per minute. How much water will the tank have after 6 hours?

[...] liters
A: 3600

Q: A farm requires 40 kilograms of fertilizer to treat 50 hectares of land. How many kilograms of fertilizer will be needed to treat 120 hectares of land?

[...] kg
A: 96

Q: Kari and Tiina made a joint investment, where Kari paid 30 € and Tiina paid 40 €. Kari's share of the profit was 81 €. What was Tiina's share of the profit?

[...] €
A: 108

Q: The boss pays a total of 800€. Use proportion to determine how the money should be divided, given that Timo worked for 11,5 hours and Pekka worked for 6,5 hours.

Timo gets [...]
Pekka gets [...]
A: 511; 288

Q: Fill in the table with travel times and average speeds when the distance is constant.

Time ( h ) | Average speed (km/h)
10 | [...]
5 | 40
[...] | 50
2,5 | [...]
[...] | 100
A: 20; 4; 80; 2

Q: A trip to summer cottage is 180 km. The table shows average speeds at which the trip was taken, along with the corresponding travel times. Determine the values for the blank spots in the table.

Average speed (km/h) | Travel time ( h )
45 | 4
90 | [...]
[...] | 6
80 | [...]
A: 2; 30; 2.25

Q: Five students took 20 hours to finish the surface treatment of the apartment walls. How many students would have completed the same task in 12 hours? Answer in whole numbers.

[...] students
A: 9

Q: Maija rides her bike to school at a speed of 15 km/h, and it takes her 7 minutes. At what speed does Mikko walk if it takes him 18 minutes to cover the same distance?

[...] km/h
A: 5.8

Q: Two pumps can pump 50,000 dm³ of water in about four hours. How long would it take to pump the same amount of water if three more pumps were used?

[...] hours
A: 1.6

Q: When driving at 80 km/h, the trip takes 6 hours. How much time would the trip take if the speed was 60 km/h?

[...] hours
A: 8

Q: A worker can finish a task in 8 hours. How long will it take if 4 workers are assigned the same task, assuming they all work at the same rate?

[...] hours
A: 2

Q: A contractor appoints 36 workers to build a wall. They could finish the task in 12 days. But due to some unavoidable reasons, only 16 workers turned up. How many days will 16 workers take to finish the same task?

[...] days
A: 27

Q: A ship with 18 men onboard has enough food for 70 days. The ship rescues 10 men from a stranded vessel. How long will the food last now?

[...] days
A: 45

Q: The construction company submitted the following bid for a grandstand project: 150 000 euros if the work is completed in 100 days. If the company completes the work in a different amount of time, the price is determined so that "time and price are inversely proportional." How much would the company charge if they completed the grandstand in:

a) 80 days

[...] €

b) 120 days

[...] €
A: 187500; 125000

Q: Solve the equations

a) 6x = 30

x = [...]

b) 3x = 21

x = [...]

c) -3x = 21

x = [...]

d) −x = 7
x = [...]
A: 5; 7; -7; -7

Q: Solve the equations

a) \(\frac{x}{3}=15\)

x = [...]

b) \(5=\frac{x}{6}\)

x = [...]

c) \(\frac{20}{x}=5\)

x = [...]

d) \(2=\frac{50}{x}\)

x = [...]
A: 45; 30; 4; 25

Q: Solve the equations

a)    2x + 1 = 5

x = [...]

b)    9x - 1 = 80

x = [...]

c)     6x + 1 = 37

x = [...]

d)    10x - 5 = 85

x = [...]
A: 2; 9; 6; 8

Q: Solve the equations

a)    4x = 2x + 6

x = [...]

b)    6x = -3x - 27

x = [...]

c)     -4x = -6x + 8

x = [...]

d)    x = 3x + 14

x = [...]
A: 3; -3; 4; -7

Q: Solve the equations

a)    2 (x+3) = 14

x = [...]

b)    9x - 2 = 7 (2x – 1)

x = [...]

c)     11+8 (2x-5) = 16+x

x = [...]
A: 4; 1; 3

Q: Solve the equations

a) \(\frac{3(x-1)}{4}=2x\)

x = [...]

b) \(\frac{2x}{5}+\frac{3x}{2}+2=40\)

x = [...]

c) \(\frac{x}{4}-1=\frac{x-6}{3}\)

x = [...]
A: -0.6; 20; 12

Q: Solve the equations

a) \(\frac{7x-(2-3x)}{5}=-9\)

x = [...]

b) \(\frac{x}{4}-\frac{2x-3}{3}=x-16\)

x = [...]
A: -4.3; 12

Q: Solve the equations

a) \(\frac{x}{2}+\frac{x}{5}+\frac{x}{4}+120=x\)

x = [...]

b) \(\frac{3}{4}-\frac{1}{8x}=0\)

x = [...]
A: 2400; 0.167

Q: Ville owns twice as much forest as Pekka. How much does each person own if together they own 81 hectares of forest?

Ville owns [...] hectares
Pekka owns = [...] hectares
A: 54; 27

Q: Jussi's salary is 350 € greater than Pekka's salary. Together, they earn 5450 €. What are their salaries?

Jussi earns [...] €
Pekka earns [...] €
A: 2900; 2550

Q: Tiina and Kaisa baked doughnuts. Tiina baked 23 more doughnuts than Kaisa. How many doughnuts did each bake if they baked a total of 145 doughnuts?

Tiina baked [...] doughnuts

Kaisa baked [...] doughnuts
A: 84; 61

Q: The base fare for a taxi is 9,50 €, and the cost per kilometer is 1,85 €. How far can you travel for 30 €?

You can travel [...] km
A: 11.08

Q: The price of a device is 360 €. The device can also be rented for 25 € per day. Solve the equation to find out how long the device must be rented for for it to be cheaper to buy it.

[...] days
A: 15

Q: Arttu, Bea, and Carlos are making money. Bea earns €50 more than Arttu, and Carlos earns 2,5 times as much as Arttu. How much does Arttu earn if, together, Arttu, Bea, and Carlos earn 1175 €?

Arttu earns [...] €
A: 250

Q: Laura ate half of the candies on the table, Joel ate a third of them, and Lenni got the remaining five candies. How many candies were there in total?

[...] candies
A: 30

Q: Asher ran a certain distance 2 minutes faster and Brian 3 minutes faster than Caleb. Calculate the time taken by Asher if the total time for all three was 40 minutes.

Asher's time was [...] minutes.
A: 13

Q: The cost of painting a house as a fixed-price contract is 1500 €, which also includes the cost of the paint. If the work is done by the hour, the hourly wage is 24 €, and the paint costs 640 €. How long can the painting job take for it to be more cost-effective to have it done at an hourly rate?

[...] hours
A: 35

Q: Solve the equation

a) \({x}^{2}=36\)

x = [...] or x = [...]

b) \({x}^{2}=81\)

x = [...] or x = [...]

c) \({x}^{2}=169\)

x = [...] or x = [...]
A: 6; -6; 9; -9; 13; -13

Q: Solve the equation

a) \(2{x}^{2}-32=0\)

x = [...] or x = [...]

b) \(11{x}^{2}-99=0\)

x = [...] or x = [...]

c) \({x}^{2}-144=0\)

x = [...] or x = [...]
A: 4; -4; 3; -3; 12; -12

Q: The area of a square-shaped sauna is 9 square meters. Calculate the length of one side of the sauna.

[...] m
A: 3

Q: The area of a square-shaped table is 1,44 m^2. Calculate the length of one side of the table.

[...] m
A: 1.2

Q: Electrical Power P can be calculated using the current I and the resistance R using the formula: P = R ⋅ I^2.

a) Calculate the power when the resistance R = 100 Ω and the current I = 2,0 A.

P = [...] W

b) Calculate the current I, when the power P = 2300 W and resistance R = 2000 Ω.

I = [...] A
A: 400; 1.07

Q: 3.    Kinetic energy is calculated using mass and velocity, and its magnitude is:

\(E=\frac{1}{2}m{v}^{2}\)

a) What is the kinetic energy of a car with a mass of 1400 kg and a velocity of 90 km/h?

E = [...] J

b) A full trailer combination has a mass of 30 tons and a kinetic energy of 7,5 MJ. What is the velocity of the combination?

v = [...] m/s
A: 437500; 22.4

Q: Calculate the base value, if
a) 50 % of a number is 40  [...]
b) 20 % of a number is 500  [...]
c) 15 % of a number is 30  [...]
d) 25 % is 13  [...]
e) 125 % is 100  [...]
f) 3 % is 60  [...]
A: 80; 2500; 200; 52; 80; 2000

Reduce the answers if possible in all exercises.