Edexcel IAL P3 June 2021 question paper and mark scheme (WMA13/01)

Try 3 P3 questions like these

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1. Functions · 5 marks

   Solve the inequality $|2x + 1| \le |x - 5|$.

   Worked answer

   1. M1 for squaring both sides to remove the modulus signs: $(2x+1)^2 \le (x-5)^2$.
   2. M1 for expanding the brackets: $4x^2 + 4x + 1 \le x^2 - 10x + 25$.
   3. M1 for rearranging to form a quadratic inequality: $3x^2 + 14x - 24 \le 0$.
   4. M1 for factorising to find the critical values: $(3x-4)(x+6) \le 0$, yielding critical values $-6$ and $\frac{4}{3}$.
   5. A1 for stating the correct closed interval $-6 \le x \le \frac{4}{3}$.

2. Numerical Methods · 7 marks

   $f(x) = x^3 - 3x - 4$.
   (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)

   Worked answer

   (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.

3. Algebraic Methods · 5 marks

   Express $\frac{x+2}{x^2 - 5x + 6} - \frac{x-1}{x^2 - 4x + 3}$ as a single fraction in its simplest form.

   Worked answer

   1. M1 for factorising $x^2-5x+6$ to $(x-2)(x-3)$.
   2. M1 for factorising $x^2-4x+3$ to $(x-1)(x-3)$.
   3. M1 for simplifying the second fraction: $\frac{x-1}{(x-1)(x-3)}$ cancels to $\frac{1}{x-3}$.
   4. M1 for creating a common denominator $(x-2)(x-3)$ and subtracting: $\frac{x+2}{(x-2)(x-3)} - \frac{x-2}{(x-2)(x-3)}$.
   5. A1 for reaching the final simplified answer $\frac{4}{(x-2)(x-3)}$.

More on these topics: Functions · Numerical Methods · Algebraic Methods

P3 topics this paper can test

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• Functions
• Numerical Methods
• Further Differentiation
• Further Integration
• Algebraic Methods
• Trigonometric Functions
• Trigonometric Addition Formulae
• Exponentials and Logarithms

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Formula booklet

Mathematical Formulae and Statistical Tables (International AS/A Level Mathematics) · Pearson Edexcel · For the 2018 IAL specification (current)