Edexcel IAL P3 Numerical Methods Questions
Locating roots of f(x) = 0 by a change of sign; approximate solutions using iteration xₙ₊₁ = g(xₙ), including cobweb/staircase diagrams. (Newton–Raphson is Further Pure 1, not P3.)
- P3 · Pure Mathematics 3
- Calculator allowed
- 39 practice questions
What the questions test
The 39 P3 numerical methods practice questions cover:
Worked example 1
$f(x) = x^3 - 3x - 4$.
(a) Show that $f(x) = 0$ has a root in $(2, 3)$. (2)
(b) Rewrite the equation in the form $x = \sqrt[3]{3x + 4}$ and use this iteration with $x_0 = 2$ to find $x_1, x_2, x_3, x_4$ each to 4 d.p. State the value of the root to 3 d.p. (5)
Mark scheme
(a) $f(2) = 8 - 6 - 4 = -2 < 0$; $f(3) = 27 - 9 - 4 = 14 > 0$ M1 A1.
(b) $x_1 = \sqrt[3]{10} = 2.1544$; $x_2 = \sqrt[3]{10.4633} = 2.1872$; $x_3 = \sqrt[3]{10.5616} = 2.1940$; $x_4 = \sqrt[3]{10.5821} = 2.1955$ M1 A1 A1 A1. Root $\approx 2.196$ A1.
Worked example 2
The equation $\cos x = x$ has a unique root $\alpha$ in $[0, 1]$. Using the iteration $x_{n+1} = \cos x_n$ with $x_0 = 0.5$, find $x_1$, $x_2$, $x_3$, and $x_4$ each to $4$ d.p. (Angle in radians.)
Mark scheme
$x_1 = \cos 0.5 = 0.8776$ M1 A1. $x_2 = \cos 0.8776 = 0.6390$ A1. $x_3 = \cos 0.6390 = 0.8027$ A1. $x_4 = \cos 0.8027 = 0.6948$ A1 A1.
FAQ
What numerical methods is in Edexcel IAL P3?
Locating roots of f(x) = 0 by a change of sign; approximate solutions using iteration xₙ₊₁ = g(xₙ), including cobweb/staircase diagrams. (Newton–Raphson is Further Pure 1, not P3.)
Is P3 a calculator paper?
Yes, a calculator is allowed in P3, but method marks are only given for working you write down.
How are P3 numerical methods questions marked?
With M marks for a correct method, A marks for accurate answers that depend on the M mark before them, and B marks for independent results, as in the worked examples on this page.