Mathematics Pure Math 2,3 9709: NUMERICAL METHODS Topical Past Paper Questions
Cambridge AS & A Level Mathematics Pure Math 2,3 (9709) past-paper questions on NUMERICAL METHODS, free. This topic is frequently examined across 23 exam sessions. Sign in for the full topic-segregated question bank and AI worksheets.
Sample questions
(a) By sketching a suitable pair of graphs, show that the equation $ \sec\left(\frac{1}{3}x\right)=3e^{-x} $ has exactly one root in the interval $ 0 [2] [2] (d) Use this iterative formula, with initial value $ x_{1}=1 $, to calculate $ \alpha $ correct to 3 decimal places. Give…
The constant $a$ is such that $\int_{0}^{a} x e^{\frac{1}{2}x} \, dx = 6$. (a) Show that $a = 2 + e^{-\frac{1}{2}a}$. [5] (b) Verify by calculation that $a$ lies between 2.2 and 2.4. [2] (c) Use an iterative formula based on the equation in part (a) to determine $a$ correct to 2…
Let $ f(x)=2x^{3}-5x^{2}+4 $. (a) Show that if a sequence of values given by the iterative formula $$ x_{n+1}=\sqrt{\frac{4}{5-2x_{n}}} $$ converges, then it converges to a root of the equation $ f(x) = 0 $. [2] (b) The equation has a root close to 1.2. Use the iterative formula…
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