Edexcel IAL P1 Maths Revision: Pure Mathematics 1
Everything for Edexcel International A Level P1 (Pure Mathematics 1) in one place: what each topic covers, an exam-style question with its mark scheme for each topic, and 348 practice questions with instant marking.
- 1h 30min written paper (75 marks), calculator not permitted
- 6 topics
- 348 questions
P1 topics
P1 Algebra
Indices, surds, quadratics (discriminant, completing the square), simultaneous equations, inequalities.
Example question
Express $\frac{5 + \sqrt{7}}{3 - \sqrt{7}}$ in the form $a + b\sqrt{7}$, where $a$ and $b$ are integers.
Show the mark scheme
M1 Multiplies both numerator and denominator by $3 + \sqrt{7}$.
- M1 Expands the numerator: $(5)(3) + 5\sqrt{7} + 3\sqrt{7} + (\sqrt{7})^2 = 15 + 8\sqrt{7} + 7$.
- A1 Correctly simplifies the numerator to $22 + 8\sqrt{7}$.
- M1 Expands and simplifies the denominator: $3^2 - (\sqrt{7})^2 = 9 - 7 = 2$.
- A1 Divides the numerator by 2 to obtain the final answer $11 + 4\sqrt{7}$.
P1 Coordinate Geometry
Straight lines, gradient, midpoint, perpendicular/parallel, equation of a line, distance formula.
Example question
The equation of a line \(L_1\) is \(3x + 4y - 12 = 0\).
Find the gradient of \(L_1\).
Find the coordinates of the \(x\)-intercept and the \(y\)-intercept of \(L_1\).
Show the mark scheme
Rearrange \(3x + 4y - 12 = 0\) into \(y = mx + c\):
\(4y = -3x + 12 \implies y = -\frac{3}{4}x + 3\). M1
Gradient \(m = -\frac{3}{4}\). A1\(y\)-intercept is \(c = 3\), so \((0, 3)\). A1
\(x\)-intercept occurs when \(y = 0 \implies 3x - 12 = 0 \implies x = 4\). So \((4, 0)\). A1
P1 Trigonometry
Sine and cosine rules; area of a triangle = ½ab sin C; radian measure, arc length and sector area; graphs of sin, cos and tan and their symmetries; exact values.
Example question
A sector of a circle has a radius of \(9 \text{ cm}\) and an area of \(45 \text{ cm}^2\).
- Calculate the size of the central angle, \(\theta\), in radians.
- Hence, calculate the perimeter of the sector.
Show the mark scheme
- Area \(= \frac{1}{2}r^2\theta \implies 45 = \frac{1}{2}(9^2)\theta\) M1
\(45 = 40.5\theta \implies \theta = \frac{45}{40.5} = \frac{10}{9}\) radians (or \(1.11\) rad). A1 - Arc length \(= r\theta = 9 \times \frac{10}{9} = 10 \text{ cm}\). M1
Perimeter \(= r + r + \text{arc length} = 9 + 9 + 10\) M1
Perimeter \(= 28 \text{ cm}\). A1
P1 Differentiation
Gradient of a tangent as a limit; differentiating xⁿ and sums of such terms; gradients, tangents and normals; the second derivative.
Example question
Find the equation of the tangent to the curve $y = x^2 - 6x + 8$ at the point $(4, 0)$. Give your answer in the form $y = mx + c$.
Show the mark scheme
- M1 for differentiating to find $\frac{dy}{dx} = 2x - 6$.
- M1 for substituting $x=4$ to find the gradient $m = 2(4) - 6 = 2$.
- M1 for using the line equation formula with point $(4, 0)$ and $m=2$: $y - 0 = 2(x - 4)$.
- A1 for simplifying to $y = 2x - 8$.
P1 Integration
Indefinite integration of xⁿ (n ≠ −1) and sums of such terms; finding the constant of integration from a point on the curve.
Example question
Given that $\frac{dy}{dx} = 3x^2 + 4x$ and that $y = 10$ when $x = 2$, find an expression for $y$ in terms of $x$.
Show the mark scheme
- M1 for integrating $\frac{dy}{dx}$ to find $y = x^3 + 2x^2 + c$.
- M1 for substituting $x = 2$ and $y = 10$ into their integrated expression: $10 = (2)^3 + 2(2)^2 + c$.
- M1 for solving to find $c$: $10 = 8 + 8 + c \implies c = -6$.
- A1 for the final equation $y = x^3 + 2x^2 - 6$.
P1 Graphs and Transformations
Sketching cubics, quartics and reciprocals; transformations of graphs (translations, stretches, reflections); function notation.
Example question
Find the exact coordinates of the points of intersection of the curves $y = \frac{12}{x}$ and $y = x - 4$.
Show the mark scheme
- M1 for equating the functions: $\frac{12}{x} = x - 4$.
- M1 for multiplying by $x$ and rearranging into a quadratic: $x^2 - 4x - 12 = 0$.
- M1 for solving the quadratic: $(x-6)(x+2) = 0 \implies x=6$ or $x=-2$.
- A1 for substituting back to find the full coordinates: $(6, 2)$ and $(-2, -6)$.
FAQ
What is on the Edexcel IAL P1 exam?
P1 Pure Mathematics 1 is assessed by a 1h 30min written paper (75 marks), calculator not permitted. It covers Algebra, Coordinate Geometry, Trigonometry, Differentiation, Integration, Graphs and Transformations.
Can I use a calculator in P1?
No. P1 is the only non-calculator IAL maths paper, so practise exact arithmetic, surds and fractions by hand.
How many P1 practice questions are there?
348 exam-style P1 questions across 6 topics, each with an Edexcel-style mark scheme (M, A and B marks).