DP Mathematics HL Questionbank

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Directly related questions

• 18M.3dm.hl.TZ0.5a: Write down the auxiliary equation and use it to find an expression for ${f_n}$ in terms of $n$.
• 16M.3dm.hl.TZ0.4c: Find a simplified expression for ${u_n} + {v_n}$ given that, (i)     $n$ is even. (ii)    ...
• 16M.3dm.hl.TZ0.4b: Use strong induction to prove that the solution to the recurrence relation...
• 16M.3dm.hl.TZ0.4a: Solve the recurrence relation ${v_n} + 4{v_{n - 1}} + 4{v_{n - 2}} = 0$ where...
• 16N.3dm.hl.TZ0.3f: Find the smallest value of $n$ for which ${u_n} > 100\,000$.
• 16N.3dm.hl.TZ0.3e: Find the value of ${u_{20}}$.
• 16N.3dm.hl.TZ0.3d: (i)     Given that $A = \frac{1}{{\sqrt 5 }}\left( {\frac{{1 + \sqrt 5 }}{2}} \right)$, use the...
• 16N.3dm.hl.TZ0.3c: (i)     Write down the auxiliary equation for this recurrence relation. (ii)     Hence find the...
• 16N.3dm.hl.TZ0.3b: Show that ${u_{n + 2}} = {u_{n + 1}} + {u_n}$.
• 16N.3dm.hl.TZ0.3a: Find the values of ${u_1},{\text{ }}{u_2},{\text{ }}{u_3}$.
• 17N.3dm.hl.TZ0.2a: Find an expression for ${u_n}$ in terms of $n$.
• 17M.3dm.hl.TZ0.4b: Solve the recurrence relation ${u_{n + 2}} - 2{u_{n + 1}} + 5{u_n} = 0$ given that...
• 17M.3dm.hl.TZ0.4a: Verify that the recurrence relation is satisfied by \[{u_n} = A{\alpha ^n} + B{\beta...
• 15N.3dm.hl.TZ0.2c: A second recurrence relation, where ${v_1} = {u_1}$ and ${v_2} = {u_2}$, is given by...
• 15N.3dm.hl.TZ0.2b: Find an expression for ${u_n}$ in terms of $n$.
• 15N.3dm.hl.TZ0.2a: Use the recurrence relation to find ${u_2}$.
• SPNone.3dm.hl.TZ0.5a: The sequence $\{ {u_n}\}$ , $n \in {\mathbb{Z}^ + }$ , satisfies the recurrence relation...
• 14M.3dm.hl.TZ0.4: (a)     (i)     Write down the general solution of the recurrence relation...
• 15M.3dm.hl.TZ0.3a: The sequence $\{ {u_n}\} ,{\text{ }}n \in \mathbb{N}$, satisfies the recurrence relation...
• 15M.3dm.hl.TZ0.3b: The sequence $\{ {v_n}\} ,{\text{ }}n \in \mathbb{N}$, satisfies the recurrence relation...
• 15M.3dm.hl.TZ0.3c: The sequence $\{ {v_n}\} ,{\text{ }}n \in \mathbb{N}$, satisfies the recurrence relation...
• 14N.3dm.hl.TZ0.5a: State the value of ${u_1}$.
• 14N.3dm.hl.TZ0.5d: After they have played many games, Pat comes to watch. Use your answer from part (c) to estimate...
• 14N.3dm.hl.TZ0.5b: Show that ${u_n}$ satisfies the recurrence...
• 14N.3dm.hl.TZ0.5c: Solve this recurrence relation to find the probability that Andy wins the ${n^{{\text{th}}}}$...