Math Tests - mathematics practice questions

Convert units of time (seconds and minutes)

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Units of time

1 min (minute) = 60 s (seconds)
1 h (hour) = 60 min

hmins×60×60÷60÷60

1.5 h = $1{1/2}$h = 1 h 30 min
1 h = 60 × 60 s= 3600 s


Convert units of time (seconds, minutes and hours)

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Units of time

1 min (minute) = 60 s (seconds)
1 h (hour) = 60 min

hmins×60×60÷60÷60

1.5 h = $1{1/2}$h = 1 h 30 min
1 h = 60 × 60 s= 3600 s


Convert units of time (months)

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Units of time

1 min (minute) = 60 s (seconds)
1 h (hour) = 60 min

hmins×60×60÷60÷60

1.5 h = $1{1/2}$h = 1 h 30 min
1 h = 60 × 60 s= 3600 s

day = 24 h
week = 7 days (Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday)

month = from 28 to 31 days
MonthNumber of days
January31
February28 or 29
March31
April30
May31
June30
July31
August31
September30
October31
November30
December31

year = 12 months = 365 days = 52 weeks 1 day
leap year = 12 months = 366 days = 52 weeks 2 days

A leap year is a year in which an extra day is added to the calendar in order to synchronize it with the seasons. In leap years, February 29th is added as leap day, which doesn't exist in a normal year (February has normally 28 days). A leap year occurs every 4 years - the year has to be evenly divided by 4 (2004, 2008, 2012), but not by 100 (1800, 1900, 2100). However, if it is divisible by 400, it's again a leap year (2000).



Convert metric units of length (cm, dm, m)

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Metric units of length


m... meter
dm... decimeter
cm... centimeter

1 m = 100 cm = 10 dm
1 dm = 10 cm
mdmcm×10×10÷10÷101 m1 m10 dm100 cm50 cm5 dm10 cm1 dm5 cm


Convert metric units of length (easy)

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Metric units of length


1 cm (centimeter) = 10 mm (milimeter)
1 dm (decimeter) = 10 cm
1 m (meter) = 100 cm = 10 dm
1 km (kilometer)= 1000 m
kmmdmcmmm×10×10×10×1000÷1000÷10÷10÷10


Convert metric units of length (medium)

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Metric units of length


1 cm (centimeter) = 10 mm (milimeter)
1 dm (decimeter) = 10 cm
1 m (meter) = 100 cm = 10 dm
1 km (kilometer)= 1000 m
kmmdmcmmm×10×10×10×1000÷1000÷10÷10÷10


Convert metric units of length (difficult)

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Metric units of length


1 cm (centimeter) = 10 mm (milimeter)
1 dm (decimeter) = 10 cm
1 m (meter) = 100 cm = 10 dm
1 km (kilometer)= 1000 m
kmmdmcmmm×10×10×10×1000÷1000÷10÷10÷10


Convert and compare US units of length (inches, feet, yards)

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Customary units of length

1 inch (in) ≅ 2.54 centimeters (cm)
1 foot (ft or ′) = 12 in ≅ 30.48 cm
1 yard (yd) = 3 ft = 36 in ≅ 0.91 meter (m)
1 mile (mi)= 1760 yd ≅ 1.6 kilometer (km)



Convert metric units of area

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Metric units of area

1 cm2 = 10 mm × 10 mm = 100 mm2
1 dm2 = 10 cm × 10 cm = 100 cm2

1 m1 dm1 dm²1 m²

1 m2 = 10 dm × 10 dm = 100 dm2 = = 10000 cm2
1 km2 = 1000 m × 1000 m = 1000000 m2

kmmdmcmmm×10×10×10×1000km²dm²cm²mm²×100×100×100×1000000


Convert and compare units of mass (kg and g)

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Metric units of mass

1 g (gram) = 1000 mg (milligram)
1 kg (kilogram)= 1000 g
1 t (ton) = 1000 kg

tkggmg×1000×1000×1000÷1000÷1000÷1000

1 dkg (dekagram) =10 g
1 kg (kilogram)= 1000 g = 100 dkg



Convert and compare US units of mass (ounces and pounds)

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Customary units of mass

1 pound (lb) = 16 ounces (oz) ≅ 0.45 kilogram (kg)
1 oz ≅ 28 grams (g)
1.5 lb = 16 + 8 = 24 oz
$1/2$ lb = 8 oz



Convert and compare units of volume (l and hl)

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l (L)... liter
hl (hL)... hectoliter

1 hl =100 l
hlldlclml×10×10×10×100÷100÷10÷10÷10


Convert and compare units of volume (l and ml)

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l (L)... liter
ml (mL)... mililiter

1 l =1000 ml
hlldlclml×10×10×10×100÷100÷10÷10÷10


Metric units of measurement as decimals (easy)

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Convert metric units of speed/velocity

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Velocity unit conversion

Velocity is measured as distance traveled per certain unit of time, e.g. if car drives 40 km/h, that means that a car drives 40 km every hour (40 km in one hour, 80 in two hours, 120 in three hours. etc.). The American equivalent is mph (miles per hour). Since this is a combination of units (distance divided by time), when recalculating to different units of velocity we need to pay attention to both units (time and distance), and determine how to change them.

If we are moving 2 m/s, it means that every second we travel 2 meters. How many meters will we travel in one hour? One hour has 3600 seconds.

$$2;m/s=$$
$$=2×3600=7200;m/s$$

In one hour we will travel 7200 m. And how many kilometers will we move in 1 hour? We know that 1 km is equal to 1000 m.

$$ 7200;m/s=7.2;km/s $$

If a car is moving 90 km/h, how many meters per second will it drive? In this case we have to multiply 90 by 1000 to calculate the meters (90 km=90000 m). At the same time we have to divide the value by 3600 since one hour has 3600 seconds:

$$90;km/h={90000;m}/{3600;s}=25;m/s$$

So the car is driving 25 m/s. But what is his speed in km/min? As we know, 1 hour has 60 minutes. It means that in one minute it will drive:

$$90;km/h=$$
$$={90;km}/{60;min}=1.5;km/min$$


   
   

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