Unit 5: Calculus

Topic 5.3: Differentiating Powers Questions

Practice 20 exam-style questions for IB Math AA SL Topic 5.3. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.

1Find3 marks

2026

A curve has equation

y = 2 x^{2} - 8 x + 3

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2Find2 marks

2026

Find the gradient of the curve

y = x^{3} - 5 x + 1

at the point where

x = 1

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3Find2 marks

2026

Differentiate

f (x) = 3 x^{4} - 7 x^{2} + 2 x - 5

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4Write down1 mark

2023

A curve passes through the point

(0, 1)

and satisfies

\frac{d y}{d x} = x^{2} - 2 y + 5

. Write down the gradient of the curve at

(0, 1)

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5Find1 mark

2024

A town's population, in thousands,

t

years after 2000 is modelled by

P (t) = 250 (1.012)^{t}

. Find

P^{'} (40)

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6Find3 marks

2026

A curve has equation

y = x^{3} - 4 x

. Find dy/dx, and hence the gradient when

x = 2

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7Find2 marks

2026

The curve

y = x^{2} + 2 x

has gradient 10 at one point. Find the x-coordinate of that point.

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8Write down1 mark

2026

Write down the gradient of the curve at

x = 2

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9Write down1 mark

2026

Write down the derivative of

x^{5}

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10Show that1 mark

2026

Show that

f^{'} (x) = 12 x^{2}

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11Find3 marks

2026

A curve has equation y = 2x² − 8x + 3.

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12Find1 mark

2026

Differentiate y = 4x⁵ + 9.

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13Find2 marks

2026

Find the gradient of the curve y = x³ − 5x + 1 at the point where x = 1.

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14Find2 marks

2026

Differentiate f(x) = 3x⁴ − 7x² + 2x − 5.

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15Find1 mark

2024

A population, in thousands, is modelled by

Q (t) = \frac{800}{1 + 3 e ^{- 0.05 t}}

, where

t

is in years. Find

Q^{'} (20)

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16Find2 marks

2026

The curve y = x² + 2x has gradient 10 at one point. Find the x-coordinate of that point.

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17Find1 mark

2026

Differentiate

y = 4 x^{5} + 9

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18Write down1 mark

2021

Let

f (x) = 2 x^{5} + a x^{2} - 9

, where

a

is a constant. Write down

f^{'} (x)

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19Write down2 marks

2026

Let

h (x) = x^{6} - p x^{3} + q

, where

p

and

q

are constants. Write down

h^{'} (x)

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20Write down2 marks

2026

Let

f (x) = 3 x^{5} + a x^{3} - b x + c

, where

a

b

and

c

are constants. Write down

f^{'} (x)

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