Edexcel A-Level Mathematics Paper 1: Pure Mathematics Sample 2023

Questions in this quiz

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1. Question 1

   Expand and simplify $(2x - 3)^2 - (x + 1)(x - 2)$.

2. Question 2

   The polynomial $p(x) = x^3 - 4x^2 - 11x + 30$ has a root at $x = 2$. Which expression is a factor of $p(x)$?

3. Question 3

   Solve $2x^2 - 7x + 3 = 0$ using the quadratic formula. Which is a correct solution?

4. Question 4

   What is the remainder when $x^3 + 2x^2 - 5x + 4$ is divided by $(x - 1)$?

5. Question 5

   Given $f(x) = 3x - 2$ and $g(x) = x^2 + 1$, find $g(f(2))$.

6. Question 6

   True or False: The function $f(x) = \frac{1}{x}$ is an odd function.

7. Question 7

   The curve $y = x^2 - 4x + 3$ crosses the $x$-axis at which points?

8. Question 8

   Which of the following describes the range of $f(x) = \sqrt{x}$ where $x \geq 0$?

9. Question 9

   Find the gradient of the curve $y = x^3$ at the point where $x = 2$ using differentiation from first principles.

10. Question 10

    Differentiate $f(x) = 5x^4 - 2x^2 + 7$ with respect to $x$.

11. Question 11

    True or False: The derivative of $y = e^x$ is $y' = e^x$.

12. Question 12

    If $\int (6x^2 - 3) \, dx = ax^3 + bx + c$, what are the values of $a$ and $b$?

13. Question 13

    A curve has the derivative $\frac{dy}{dx} = 4x - 2$. If the curve passes through $(1, 3)$, what is the equation of the curve?