DP Mathematics HL Questionbank

• Syllabus

1.3

Sub sections and their related questions

Counting principles, including permutations and combinations.

• 12M.2.hl.TZ2.4a: In how many ways can they be seated in a single line so that the boys and girls are in two...
• 12M.2.hl.TZ2.4b: Two boys and three girls are selected to go the theatre. In how many ways can this selection be...
• 13M.1.hl.TZ1.13b: (i)     Explain why the total number of possible outcomes for the results of the 6 games is...
• 13M.2.hl.TZ1.8a: Find the number of ways this can be done if the three girls must sit together.
• 13M.2.hl.TZ1.8b: Find the number of ways this can be done if the three girls must all sit apart.
• 10M.2.hl.TZ1.7: Three Mathematics books, five English books, four Science books and a dictionary are to be placed...
• 13M.2.hl.TZ2.11b: A number of distinct points are marked on the circumference of a circle, forming a polygon....
• 11N.3ca.hl.TZ0.2a: Show that \(n! \geqslant {2^{n - 1}}\), for \(n \geqslant 1\).
• 09M.2.hl.TZ2.8: Six people are to sit at a circular table. Two of the people are not to sit immediately beside...
• 14M.2.hl.TZ1.3: Find the number of ways in which seven different toys can be given to three children, if the...
• 14N.1.hl.TZ0.10a: Find the number of selections Grace could make if the largest integer drawn among the four cards...
• 14N.1.hl.TZ0.10b: Find the number of selections Grace could make if at least two of the four integers drawn are even.
• 15M.2.hl.TZ2.2a: Determine how many possible groups can be chosen.
• 15M.2.hl.TZ2.2b: Determine how many groups can be formed consisting of two males and two females.
• 15M.2.hl.TZ2.2c: Determine how many groups can be formed consisting of at least one female.
• 16M.1.hl.TZ2.6a: Write down the first four terms of the expansion.
• 16M.1.hl.TZ2.6b: (i)     Show that \({n^3} - 9{n^2} + 14n = 0\). (ii)     Hence find the value of \(n\).
• 16N.2.hl.TZ0.4: Find the constant term in the expansion of \({\left( {4{x^2} - \frac{3}{{2x}}} \right)^{12}}\).
• 17N.1.hl.TZ0.4: Find the coefficient of \({x^8}\) in the expansion of \({\left( {{x^2} - \frac{2}{x}} \right)^7}\).
• 17N.1.hl.TZ0.10a: Show that the probability that Chloe wins the game is \(\frac{3}{8}\).
• 17N.2.hl.TZ0.9a: Find the number of ways the twelve students may be arranged in the exam hall.
• 17N.2.hl.TZ0.9b: Find the number of ways the students may be arranged if Helen and Nicky must sit so that one is...
• 17N.2.hl.TZ0.9c: Find the number of ways the students may be arranged if Helen and Nicky must not sit next to each...
• 18M.2.hl.TZ2.5a: Express the binomial...
• 18M.2.hl.TZ2.5b: Hence find the least value of \(n\) for which...

The binomial theorem: expansion of \({\left( {a + b} \right)^n}\), \(n \in N\) .

• 12M.2.hl.TZ1.9: Find the constant term in the expansion of...
• 12M.1.hl.TZ2.4a: Expand and simplify \({\left( {x - \frac{2}{x}} \right)^4}\).
• 12M.1.hl.TZ2.4b: Hence determine the constant term in the expansion...
• 12N.1.hl.TZ0.2: Expand and simplify \({\left( {\frac{x}{y} - \frac{y}{x}} \right)^4}\).
• 08M.2.hl.TZ1.1: Determine the first three terms in the expansion of \({(1 - 2x)^5}{(1 + x)^7}\) in ascending...
• 10N.1.hl.TZ0.3: Expand and simplify \({\left( {{x^2} - \frac{2}{x}} \right)^4}\).
• 13M.1.hl.TZ2.3: Expand \({(2 - 3x)^5}\) in ascending powers of x, simplifying coefficients.
• 11M.2.hl.TZ1.5b: Hence, or otherwise, find the coefficient of \(x\) in the expansion of...
• 09N.2.hl.TZ0.4: (a)     Find the value of \(n\) . (b)     Hence, find the coefficient of \({x^2}\) .
• 14M.2.hl.TZ1.8a: Find the term in \({x^5}\) in the expansion of \((3x + A){(2x + B)^6}\).
• 14M.2.hl.TZ2.5: Find the coefficient of \({x^{ - 2}}\) in the expansion of...
• 13N.1.hl.TZ0.12g: (i)     Write down an expression for the constant term in the expansion of...
• 13N.1.hl.TZ0.12b: Expand \({\left( {z + {z^{ - 1}}} \right)^4}\).
• 15M.1.hl.TZ1.4a: Expand \({(x + h)^3}\).
• 15M.1.hl.TZ2.2: Expand \({(3 - x)^4}\) in ascending powers of \(x\) and simplify your answer.
• 15M.2.hl.TZ1.12a: (i)     Use the binomial theorem to expand \({(\cos \theta  + {\text{i}}\sin \theta )^5}\). (ii)...
• 15N.1.hl.TZ0.3a: Write down and simplify the expansion of \({(2 + x)^4}\) in ascending powers of \(x\).
• 15N.1.hl.TZ0.3b: Hence find the exact value of \({(2.1)^4}\).
• 16M.1.hl.TZ2.6a: Write down the first four terms of the expansion.
• 16M.1.hl.TZ2.6b: (i)     Show that \({n^3} - 9{n^2} + 14n = 0\). (ii)     Hence find the value of \(n\).
• 16N.2.hl.TZ0.4: Find the constant term in the expansion of \({\left( {4{x^2} - \frac{3}{{2x}}} \right)^{12}}\).
• 17N.1.hl.TZ0.4: Find the coefficient of \({x^8}\) in the expansion of \({\left( {{x^2} - \frac{2}{x}} \right)^7}\).
• 17N.1.hl.TZ0.10a: Show that the probability that Chloe wins the game is \(\frac{3}{8}\).
• 17N.2.hl.TZ0.9a: Find the number of ways the twelve students may be arranged in the exam hall.
• 17N.2.hl.TZ0.9b: Find the number of ways the students may be arranged if Helen and Nicky must sit so that one is...
• 17N.2.hl.TZ0.9c: Find the number of ways the students may be arranged if Helen and Nicky must not sit next to each...
• 18M.2.hl.TZ2.5a: Express the binomial...
• 18M.2.hl.TZ2.5b: Hence find the least value of \(n\) for which...