IB Mathematics Analysis and Approaches Number and Algebra

Question Type 1: Converting positive numbers to standard form

Question Type 2: Converting negative numbers to standard form

Question Type 1: Finding nth term given the first term and common difference

Question Type 2: Finding common difference given two terms

Question Type 3: Working with arithmetic sequences algebraically

Question Type 4: Finding sum of first n terms given first term and common difference

Question Type 5: Finding sum of first n terms and common difference given first term and last term

Question Type 6: Finding sum of first n terms given the values of other sums

Question Type 1: Finding the nth term given first term and common ratio

Question Type 2: Finding the common ratio given two terms

Question Type 3: Working with geometric sequences algebraically

Question Type 4: Finding the sum of the first n terms given first term and common ratio

Question Type 5: Finding n or the sum of first n terms when r = 1

Question Type 6: Finding common ratio or sum of first n terms given the values of other sums

Question Type 1: Finding the returns on the total value of investment after n years in the bank with simple interest

Question Type 2: Finding the returns on the total value of investment after n years in the bank with compound interest

Question Type 3: Finding initial value of investment given final value of returns after n years in the bank for different compounding values

Question Type 1: Applying exponents rules to simplify basic expressions

Question Type 2: Applying exponents rules to simplify complex expressions

Question Type 3: Rewriting expressions to apply exponents rules

Question Type 4: Finding logarithm given values for a and b

Question Type 5: Finding other values of logarithm

Question Type 1: Simple equation proofs

Question Type 2: Proving starting from the right-hand side

Question Type 3: Verifying the proof

Question Type 1: Calculating powers

Question Type 2: Rewriting equations using rational exponents

Question Type 3: Applying indices and negative exponents

Question Type 4: Using laws of logarithms

Question Type 5: Simplifying expressions to a single logarithm

Question Type 6: Using logₐ(a) = 1 and logₐ(1) = 0

Question Type 7: Using change of base formula

Question Type 8: Using logarithms to solve equations with unknown exponents

Question Type 9: Summarizing laws of exponents

Question Type 10: Summarizing laws of logarithms

Question Type 1: Finding the sum of infinite convergent geometric sequences

Question Type 1: Calculating factorials

Question Type 2: Dividing factorials

Question Type 3: Working with expressions of factorials

Question Type 4: Finding the values of combinatoric functions

Question Type 5: Solving simpler world problems involving combinatoric functions

Question Type 6: Expanding binomials using binomial theorem

Question Type 7: Finding corresponding coefficients using general binomial term

Question Type 8: Finding corresponding coefficients for fractional, multi-powered binomials

Question Type 1: Using permutations formula

Question Type 2: Accounting for the same term ordering

Question Type 3: Grouping items together

Question Type 4: Using combinations formula

Question Type 5: Applying formula multiple times for different groups of selection

Question Type 6: Applying formula to disjoint cases

Question Type 7: Writing scenarios as both permutation and combination

Question Type 8: Applying permutations and combinations separately

Question Type 9: Using binomial theorem for fractional indices

Question Type 10: Using binomial theorem for negative indices

Question Type 11: Finding coefficient of term using general binomial expansion formula

Question Type 1: Applying partial fractions on linear factors on power of 1

Question Type 2: Applying partial fractions on linear factors on higher powers

Question Type 3: Doing quadratic factors and linear factors

Question Type 1: Drawing complex numbers on the Argand diagram

Question Type 2: Multiplying by a conjugate

Question Type 3: Calculating modulus of complex numbers

Question Type 4: Calculating argument of complex numbers

Question Type 1: Converting from Cartesian to Euler and Polar

Question Type 2: Converting from Euler to polar and from polar to Cartesian

Question Type 3: Adding and subtracting complex numbers in Cartesian form

Question Type 4: Multiplying and dividing complex numbers in Cartesian form

Question Type 5: Applying multiple operations onto a complex number

Question Type 6: Performing operations on variables of complex numbers

Question type 7: Multiplying and dividing complex numbers in Euler form

Question Type 1: Finding powers of complex numbers

Question Type 2: Finding the roots of complex numbers

Question Type 3: Finding complex numbers with rational exponents

Question Type 1: Using counter examples

Question Type 2: Using contradiction without conditions

Question Type 3: Using contradiction with conditions

Question Type 4: Using induction for proving equalities

Question Type 5: Using induction for proving divisibility

Question Type 1: Finding a unique solution to a system of equations algebraically using elimination or substitution

Question Type 2: Finding a unique solution to a system of equations algebraically using matrices or Gaussian elimination

Question Type 3: Checking whether the system of linear equations has no solution, one solution or infinite number of solutions

Question Type 4: For given parameters in the linear equations, find the value of the parameter that will result in no solution, one solution or infinite number of solutions