DP Mathematics HL Questionbank

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• 18M.2.hl.TZ2.5b: Hence find the least value of \(n\) for which...
• 18M.2.hl.TZ2.5a: Express the binomial...
• 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...
• 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.TZ0.9a: Find the number of ways the twelve students may be arranged in the exam hall.
• 17N.1.hl.TZ0.10a: Show that the probability that Chloe wins the game is \(\frac{3}{8}\).
• 17N.1.hl.TZ0.4: Find the coefficient of \({x^8}\) in the expansion of \({\left( {{x^2} - \frac{2}{x}} \right)^7}\).
• 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 \({x^2}\) .
• 16M.1.hl.TZ2.6b: (i)     Show that \({n^3} - 9{n^2} + 14n = 0\). (ii)     Hence find the value of \(n\).
• 16M.1.hl.TZ2.6a: Write down the first four terms of the expansion.
• 16N.2.hl.TZ0.4: Find the constant term in the expansion of \({\left( {4{x^2} - \frac{3}{{2x}}} \right)^{12}}\).
• 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.
• 15N.1.hl.TZ0.3b: Hence find the exact value of \({(2.1)^4}\).
• 15N.1.hl.TZ0.3a: Write down and simplify the expansion of \({(2 + x)^4}\) in ascending powers of \(x\).
• 15M.2.hl.TZ1.12a: (i)     Use the binomial theorem to expand \({(\cos \theta  + {\text{i}}\sin \theta )^5}\). (ii)...