IB Math Studies
Mrs. Drehmer
2.1 Organization of Numbers
5 , and -5. Complete the table below, showing
, these numbers belong to.
1.
Consider the numbers 5, 0.5,
which of the number sets,
2.
Given Z the set of integers, Q the set of rational numbers, and R the set of
real numbers:
a)
Write down an element that belongs to R ∩ Z.
b)
Write down an element that belongs to Q ∩ Z’.
c)
Write down an element that belongs to Q’.
d)
Use a Venn diagram to represent the sets Z, Q and R.
IB Math Studies
Mrs. Drehmer
Indices/Exponents
\
IB Math Studies
Mrs. Drehmer
Prime Numbers/Factors/Multiples
IB Math Studies
Mrs. Drehmer
2.2 Numbers in Calculations
http://www.sciencegeek.net/Chemistry/taters/Unit0SigFigCounting.htm
1.
2.
How many significant figures does each number have?
To what place value has the number been rounded?
a)
43.5
b)
5673.7
c)
1200
d)
4.001
e)
0.00452
f)
0.00340
g)
784000
h)
0.450
i)
4503450
Round the following values to the requested number of significant figures or
place value:
a)
2.526 [2 sf]
e)
0.4523 [2 sf]
b)
2.526 [hundredths]
f)
3.684 [tenths]
c)
24650 [1 sf]
g)
5.6720 [hundredths]
d)
45627 [3 sf]
h)
0.04537 [3 sf]
IB Math Studies
Mrs. Drehmer
2.2 Numbers in Calculations
When we round our answers, we are changing an exact answer into an approximate
error. This introduces error into our calculation. IB expects you to find how much
error there is.
To find percent error, find the difference between the exact answer and the
approximate answer, and then divide by the exact answer. Multiply by 100 to
change to percent.
𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝑒𝑟𝑟𝑜𝑟 =
3.
4.
𝑣𝐴 − 𝑣𝐸
× 100
𝑣𝐸
Given the equation p  r 2  2qr ,
a)
Calculate the exact value of p then q = 3.6 and r = 24.
b)
Write your answer correct to two significant figures.
c)
Find the percentage error between a) and b).
For each figure below:
a)
b)
c)
Use your formula booklet to find the exact area.
Round your answer to the nearest tenth.
Calculate the percentage error between your two answers.
IB Math Studies
Mrs. Drehmer
2.3 Standard Form
1.
A box contains 1.81 x 1024 atoms. One third of them are carbon, the other
two thirds are oxygen. How many carbon atoms are in the box? How many
oxygen atoms?
2.
a)
Given x = 2.6 × 104 and y = 5.0 × 10−8, calculate the value of w = x × y.
Give your answer in the form 𝑎 × 10𝑘 where 1 ≤ 𝑎 < 10 and 𝑘 ∈ ℤ.
b)
Which two of the following statements about the nature of x, y, and w
are incorrect.
3.
4.
The total weight of 256 identical pencils is 4.24 kg.
Calculate the weight of one pencil, in kg.
a)
Give your answer exactly.
b)
Give your answer correct to three significant figures.
c)
Write your answer to part b) in the form a  10 k where 1  a  10 and
k  .
Let x  6.4  107 and y  1.6  108 .
Find
a)
x
y
b)
y  2x
giving your answers in the form a  10 k where 1  a  10 and k   .
IB Math Studies
Mrs. Drehmer
2.4 International Units of Measure
1.
A field is 91.4 m long and 68.5 m wide.
a)
Calculate the area of the field in m2.
b)
Calculate the area of the field in cm2.
c)
Express your answer to b) in the form
𝑎 × 10𝑘 , where 1 ≤ 𝑎 < 10 𝑎𝑛𝑑 𝑘 ∈ ℤ.
2.
3.
The speed of sound in air is given as 300 m s-1.
a)
How many metres does sound travel in air in one hour?
b)
Express your answer to part a) correct to two significant figures.
a)
Convert 0.001673 litres to millilitres (ml). Give your answer to the nearest ml.
The SI unit for energy is Joules. An object with mass m travelling at speed v has energy
given by
b)
1
mv 2 (Joules).
2
Calculate the energy of a comet of mass 351223 kg travelling at speed 176.334
m/sec. Give your answer correct to six significant figures.
In the SI system of units, distance is measured in metres (m), mass in kilograms (kg), and
time in seconds (s). The momentum of an object is given by the mass of the object
multiplied by its speed.
c)
Write down the correct combination of SI units (using m, kg, s) for momentum.