Edexcel IAL P1 Algebra Questions
Indices, surds, quadratics (discriminant, completing the square), simultaneous equations, inequalities.
- P1 · Pure Mathematics 1
- Non-calculator
- 119 practice questions
What the questions test
The 119 P1 algebra practice questions cover:
Worked example 1
Let $f(x) = 5 - 4x - 2x^2$.
(a) Express $f(x)$ in the form $A - B(x+C)^2$, where $A$, $B$, and $C$ are integers.
(b) State the maximum value of $f(x)$ and the value of $x$ at which it occurs.
(c) Solve $f(x) = 0$, giving your answers in exact form.
Mark scheme
(a) M1 Factors out $-2$ from the $x$ terms: $5 - 2(x^2 + 2x)$.
- M1 Completes the square inside the bracket: $5 - 2((x+1)^2 - 1)$.
- A1 Expands and simplifies to obtain $7 - 2(x+1)^2$.
(b) B1 States the maximum value is $7$.
- B1 States this occurs at $x = -1$.
(c) M1 Sets $7 - 2(x+1)^2 = 0$ and rearranges to $(x+1)^2 = \frac{7}{2}$.
- A1 Solves for $x$ by square rooting, yielding $x = -1 \pm \sqrt{\frac{7}{2}}$ (or equivalent exact surd).
Worked example 2
Solve the simultaneous equations $x - y = 2$ and $x^2 - xy + y^2 = 7$.
Mark scheme
M1 Rearranges the linear equation to make $y$ the subject: $y = x - 2$.
- M1 Substitutes this expression into the quadratic equation: $x^2 - x(x - 2) + (x - 2)^2 = 7$.
- M1 Expands the brackets correctly: $x^2 - x^2 + 2x + (x^2 - 4x + 4) = 7$.
- A1 Simplifies to a 3-term quadratic equation: $x^2 - 2x - 3 = 0$.
- M1 Factorises the quadratic: $(x - 3)(x + 1) = 0$.
- A1 Finds the $x$-values: $x = 3$ and $x = -1$.
- A1 Substitutes back into the linear equation to find the corresponding $y$-values, giving the final solution pairs $x = 3, y = 1$ and $x = -1, y = -3$.
FAQ
What algebra is in Edexcel IAL P1?
Indices, surds, quadratics (discriminant, completing the square), simultaneous equations, inequalities.
Is P1 a calculator paper?
No. P1 is non-calculator, so every algebra question has to be done by hand, with exact values where the question asks for them.
How are P1 algebra 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.