Question Bank

Choose skills and questions to build your own practice session.

72 questions available3 available skillsMore Higher Maths content is coming later

72 matching questions

Basic differentiation

Practice · 8 questions

  1. Differentiate a power

    Differentiate f(x)=x5f(x)=x^5.
    Question 11 markAlgebraicNot attempted
    Open question

  2. Differentiate a sum of powers

    Differentiate y=3x4−2x2+7y=3x^4-2x^2+7.
    Question 22 marksAlgebraicNot attempted
    Open question

  3. Evaluate a derivative

    For f(x)=x3+2xf(x)=x^3+2x, find f′(2)f'(2).
    Question 32 marksNumericalNot attempted
    Open question

  4. Find gradient at a point

    The curve has equation y=2x3−x2y=2x^3-x^2. Find the gradient of the curve when x=1x=1.
    Question 43 marksNumericalNot attempted
    Open question

  5. Tangent gradient

    Find the gradient of the tangent to y=x4−3xy=x^4-3x at x=2x=2.
    Question 53 marksNumericalNot attempted
    Open question

  6. Stationary point condition

    For y=x2−6x+4y=x^2-6x+4, find the xx-coordinate of the stationary point.
    Question 63 marksNumericalNot attempted
    Open question

  7. Exam-style tangent problem

    The curve y=x3−4x+1y=x^3-4x+1 has a tangent at the point where x=2x=2. Find the gradient of this tangent.
    Question 73 marksNumericalNot attempted
    Open question

  8. Exam-style stationary point

    A curve has equation y=x3−12x+5y=x^3-12x+5. Find the positive xx-coordinate of a stationary point.
    Question 84 marksNumericalNot attempted
    Open question

Chain rule

Practice · 34 questions

  1. Identifying the inside function

    For the function y=(4x+3)6y=(4x+3)^6, which expression is the inside function?
    Question 11 markMultiple-choiceNot attempted
    Open question

  2. Identifying the inside function in a quadratic composite

    For the function y=(2x2−5)4y=(2x^2-5)^4, which expression should be treated as the inside function when using the chain rule?
    Question 21 markMultiple-choiceNot attempted
    Open question

  3. Basic chain rule with (ax+b)n(ax+b)^n

    Differentiate y=(3x+2)5y=(3x+2)^5 with respect to xx.
    Question 32 marksAlgebraicNot attempted
    Open question

  4. Basic chain rule with (ax−b)n(ax-b)^n

    Differentiate y=(5x−4)3y=(5x-4)^3 with respect to xx.
    Question 42 marksAlgebraicNot attempted
    Open question

  5. Chain rule with a constant multiplier

    Differentiate y=2(4x+1)6y=2(4x+1)^6 with respect to xx.
    Question 52 marksAlgebraicNot attempted
    Open question

  6. Chain rule with quadratic inside functions

    Differentiate y=(x2+4)5y=(x^2+4)^5 with respect to xx.
    Question 62 marksAlgebraicNot attempted
    Open question

  7. Chain rule with quadratic inside functions

    Differentiate y=(3x2−2)4y=(3x^2-2)^4 with respect to xx.
    Question 72 marksAlgebraicNot attempted
    Open question

  8. Chain rule with fractional powers

    Differentiate y=(2x+7)1/2y=(2x+7)^{1/2} with respect to xx.
    Question 82 marksAlgebraicNot attempted
    Open question

  9. Chain rule with negative powers

    Differentiate y=(x2+1)−3y=(x^2+1)^{-3} with respect to xx.
    Question 92 marksAlgebraicNot attempted
    Open question

  10. Recognising when the chain rule is useful

    Which of the following functions are most naturally differentiated using the chain rule?
    Question 101 markMultiple-choiceNot attempted
    Open question

  11. Gradient at a point using chain rule

    For y=(2x+3)4y=(2x+3)^4, calculate the gradient of the curve at the point where x=1x=1.
    Question 113 marksNumericalNot attempted
    Open question

  12. Chain rule with a two-term inside derivative

    Differentiate y=(x2+4x)5y=(x^2+4x)^5 with respect to xx.
    Question 123 marksAlgebraicNot attempted
    Open question

  13. Gradient at a point with a constant multiplier

    For y=3(2x2−1)3y=3(2x^2-1)^3, calculate the value of dydx\frac{dy}{dx} when x=2x=2.
    Question 133 marksNumericalNot attempted
    Open question

  14. Chain rule with negative powers and positive-power final form

    Differentiate y=(3x−2)−4y=(3x-2)^{-4} with respect to xx, giving your answer with positive powers.
    Question 143 marksAlgebraicNot attempted
    Open question

  15. Gradient at a point with square-root chain rule

    For y=5x+4y=\sqrt{5x+4}, calculate dydx\frac{dy}{dx} when x=1x=1.
    Question 153 marksNumericalNot attempted
    Open question

  16. Rewrite square root then apply chain rule

    Differentiate y=7x−3y=\sqrt{7x-3} with respect to xx.
    Question 163 marksAlgebraicNot attempted
    Open question
Future Higher Maths coverage

This is a preview of what's coming. You'll be able to search and practise it once it's ready.

Lines, Circles and Sequences9 planned paths

Straight Lines · Circles · Sequences

Vectors6 planned paths

Vector Connections · Vector Operations

Calculus14 planned paths

Differentiation · Integration · Applying Calculus

Algebra and Trigonometry17 planned paths

Polynomials · Logarithms and Exponentials · Trigonometric Skills · Functions and Graphs · Intersections

Orthic — Learn with Precision