Skills Checklist | IB Math AISL

Skill Checklist

Track your progress across all skills in your objective. Mark your confidence level and identify areas to focus on.

16 Skills Available

Track your progress:

Don't know

Working on it

Confident

📖 = included in formula booklet • 🚫 = not in formula booklet

Track your progress:

Don't know

Working on it

Confident

📖 = included in formula booklet • 🚫 = not in formula booklet

Arithmetic Sequences

2 skills

Identifying arithmetic sequences

SL Core 1.2

A sequence is arithmetic if the difference between consecutive terms is constant, ie un+1−un=d, the common difference, for all n. For example,

1,6,11,16…

is arithmetic, but

2,5,9,11

is not since 9−5=4=5−2=3.

General term

SL Core 1.2

The nth term in an arithmetic sequence is given by

un=u1+(n−1)d📖

where u1 is the first term and d is the common difference.

Geometric Sequences

2 skills

Identifying Geometric Sequences

SL Core 1.3

A sequence is geometric if the ratio between consecutive terms is always constant, i.e.

unun+1=ris constant for all n∈N(r=1)🚫

We call r the common ratio.

For instance, the sequence

8,2,21,81…

is geometric with r=41, but

3,6,9,12…

is not since 69=23=2=36.

General Term of a Geometric Sequence

SL Core 1.3

The nth term of a geometric sequence is given by

un=u1rn−1📖

where u1 is the first term and r is the common ratio.

Arithmetic Series

2 skills

A series is the sum of a sequence

SL Core 1.2

The sum of terms in a sequence is called a series.

Calculating arithmetic series

SL Core 1.2

The sum of the first n terms in an arithmetic sequence is given by

Sn=2n(2u1+(n−1)d)📖

or equivalently

Sn=2n(u1+un)📖

Σ summation notation

4 skills

Understanding summation notation

SL Core 1.2

As a shortcut for writing out long sums, we can use the symbol ∑ with the following "settings":

n=(start value)∑end value of n(term depending on n)

Here n is called the index, but other letters can also be used in place of n.

Sum of a constant

SL Core 1.2

k=1∑nc=c+c+⋯+c=n⋅c🚫

Sums with scalar multiples

SL Core 1.2

k=1∑ncak=ck=1∑nak🚫

Splitting a sum in Σ form

SL Core 1.2

For any series of the form k=1∑nak and any integer m between 1 and n, we can split the series at the index m:

k=1∑nak=k=1∑mak+k=m+1∑nak

Geometric Series

1 skill

Finite Geometric Series

SL Core 1.3

The sum of the first n terms in a geometric sequence is given by:

Sn=r−1u1(rn−1)=1−ru1(1−rn)📖

Compounding (Appreciation & Depreciation)

5 skills

Depreciation

SL Core 1.4

FV=PV×(1−100r)n

where FV is the future value, PV is the present value, n is the number of years, and r% is the annual depreciation rate of the item.

Compound Interest Formula

SL Core 1.4

FV=PV×(1+100kr)kn

where FV is the future value, PV is the present value, n is the number of years, k is the number of compounding periods per year, and r% is the nominal annual rate of interest.

Using TVM Solver (Calculator) - Compound Interest

SL Core 1.4

You should understand the meaning of each variable and know how to use your calculator's Finance/TVM Solver:

Field (on calculator)	Meaning
N	Total number of payment periods (i.e. number of years × periods per year).
I%	Nominal annual interest rate (expressed as a percent, NOT a decimal).
PV	Present value, or starting amount. At the start of the problem, if money leaves your pocket, PV must be negative. If money enters your pocket, PV must be positive.
PMT	Payment amount per period (for regular payments).
FV	Future value, or ending amount. At the end of the problem, if money enters your pocket, FV must be positive. If money leaves your pocket, FV must be negative.
P/Y	Payments per year. 12 for monthly payments, 4 for quarterly, 2 for semi-annual, and 1 for annual.
C/Y	Compounding periods per year. Same time periods as P/Y are possible.
PMT: End / Begin	Payment timing mode. End means payments occur at the end of each period (most common). Begin means payments occur at the start of each period (like rent paid in advance).

To solve for an unknown, move your calculator's cursor to the unfilled slot and press alpha → enter.

Be very careful if P/Y is different from C/Y. The letter N will always be the number of payment periods, or in other words the number of years times P/Y.

Positive & Negative Cash Flows (TVM)

SL Core 1.4

Whenever you use the Finance App (TVM Solver) on your calculator, it's critical that you enter and interpret the signs correctly:

When you receive money from a bank or savings account, that value is positive, because you're gaining money.

When you send money to a bank, that value is negative, because you're losing money.

Inflation & Real Value

SL Core 1.4

The real interest rate (needed when a question involves inflation) is given by r%=c%−i%, where c% represents the given interest rate (the nominal rate) and i% represents the inflation rate.

Note: You can calculate the real interest rate r% and enter it directly into the TVM solver (when required) as the nominal annual interest rate (I% on your calculator), since the TVM solver does not account for inflation effects in its standard calculations.