2.10.1 Partial fractions Quiz: Pearson Edexcel Maths, Unit 2

The 20 questions

1. What is the typical method to decompose 3 / ((x + 1)(x + 2)) into partial fractions?

   • Ax + B / (x + 1)
   • A / (x + 1)^2
   • A / (x + 1) + B / (x + 2)
   • A(x + 1) + B(x + 2)

2. How do you set up the partial fractions for a repeated linear factor denominator (x + 1)^2(x + 2)?

   • A / (x + 1) + B / (x + 2)^2
   • A / (x + 1) + B / (x + 1)^2 + C / (x + 2)
   • A / (x + 1)^2 + B / (x + 2)
   • Ax + B / (x + 1)^2 + C / (x + 2)

3. When splitting an improper algebraic fraction, what must be done first?

   • Cross multiplication
   • Differentiation
   • Polynomial long division
   • Completing the square

4. To find constant A in 5 / ((x - 1)(x + 3)) = A / (x - 1) + B / (x + 3), what substitution is used?

   • x = -3
   • x = 1
   • x = 0
   • x = 3

5. What type of numerator is placed over a linear factor in partial fractions?

   • Linear
   • Zero
   • Constant
   • Quadratic

6. What is the gradient of a straight line perpendicular to y = 2x + 3?

   • 2
   • 1/2
   • -1/2
   • -2

7. Which form represents the general equation of a straight line using a point and gradient?

   • ax + by + c = 0
   • x^2 + y^2 = r^2
   • y - y1 = m(x - x1)
   • y = mx + c

8. What is the gradient condition for two distinct straight lines to be parallel?

   • m1 = m2
   • m1 * m2 = -1
   • m1 + m2 = 0
   • m1 = -m2

9. What represents the general Cartesian equation of a circle centred at the origin?

   • y = mx + c
   • (x - a)^2 + (y - b)^2 = r
   • x^2 + y^2 = r^2
   • ax + by = r^2

10. What are the coordinates of the centre of the circle (x - 3)^2 + (y + 4)^2 = 25?

    • (3, 4)
    • (-3, 4)
    • (-3, -4)
    • (3, -4)

11. What is the radius of the circle given by x^2 + y^2 - 6x + 8y = 0?

    • 5
    • sqrt(5)
    • 10
    • 25

12. Which trigonometric function is commonly used to model periodic phenomena like tides?

    • Linear
    • Reciprocal
    • Exponential
    • Sine

13. Which function type is standard for modelling unconstrained population growth or radioactive decay?

    • Exponential
    • Reciprocal
    • Quadratic
    • Linear

14. What functional relationship models inverse proportion, such as pressure and volume?

    • Quadratic
    • Reciprocal
    • Exponential
    • Linear

15. How many terms maximum can a denominator have in this A-level partial fractions specification?

    • 3 terms
    • 2 terms
    • 4 terms
    • 1 term

16. What is the coefficient of x when expanding the denominator (2x + 1)(x - 3)?

    • -6
    • 2
    • -5
    • -3

17. What form does the numerator take when the denominator has an irreducible quadratic factor like x^2 + 1?

    • A
    • A / x
    • Ax^2 + Bx + C
    • Ax + B

18. What value of y-intercept does the line y - 5 = 2(x - 3) possess?

    • -1
    • 2
    • 5
    • 3

19. What is the radius length if a circle equation is given as (x + 2)^2 + (y - 1)^2 = 49?

    • 7
    • 14
    • 24.5
    • 49

20. Which algebraic technique follows partial fraction decomposition when integrating a rational function?

    • Factorisation
    • Differentiation
    • Integration
    • Long division

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