Edexcel IAL P1 Graphs and Transformations Questions
Sketching cubics, quartics and reciprocals; transformations of graphs (translations, stretches, reflections); function notation.
- P1 · Pure Mathematics 1
- Non-calculator
- 30 practice questions
What the questions test
The 30 P1 graphs and transformations practice questions cover:
Worked example 1
A cubic curve crosses the x-axis at $x = -2$, $x = 1$, and $x = 4$. It crosses the y-axis at the point $(0, 16)$. Find the equation of the curve in the form $y = ax^3 + bx^2 + cx + d$.
Mark scheme
- M1 for writing the equation in the factored form $y = k(x+2)(x-1)(x-4)$.
- M1 for substituting $(0, 16)$ to find $k$: $16 = k(2)(-1)(-4) \implies 16 = 8k$.
- A1 for finding $k = 2$.
- A1 for expanding to get $y = 2(x^3 - 3x^2 - 6x + 8) = 2x^3 - 6x^2 - 12x + 16$.
Worked example 2
Find the x-coordinates of all the points of intersection between the curves $y = x(x+3)$ and $y = x^3(x+3)$.
Mark scheme
- M1 for equating the functions: $x^3(x+3) = x(x+3)$.
- M1 for bringing all terms to one side and factorising: $x(x+3)(x^2 - 1) = 0$.
- M1 for further factorising $x^2-1$ to $(x-1)(x+1)$.
- A1 for listing all four correct x-coordinates: $x = 0, -3, 1, -1$.
FAQ
What graphs and transformations is in Edexcel IAL P1?
Sketching cubics, quartics and reciprocals; transformations of graphs (translations, stretches, reflections); function notation.
Is P1 a calculator paper?
No. P1 is non-calculator, so every graphs and transformations question has to be done by hand, with exact values where the question asks for them.
How are P1 graphs and transformations 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.