BrainteenAges 16–17MathsWorksheet

Tangents and normals (AS-style)

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Work out each answer exactly unless the question asks you to round. Show your working.

1.Find the equation of the tangent to the curve y = −x³ − 2x at the point where x = −1. Give your answer in the form y = mx + c.

2.Find the equation of the tangent to the curve y = x³ − 4x² + 1 at the point where x = −1. Give your answer in the form y = mx + c.

3.Find the equation of the tangent to the curve y = −2x³ − 8√x at the point where x = 1. Give your answer in the form y = mx + c.

4.Find the equation of the tangent to the curve y = −3x² + 4 + 2/x² at the point where x = −1. Give your answer in the form y = mx + c.

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Work out each answer exactly unless the question asks you to round. Show your working.

Licence: Crayonbird original

About this activity

Quick, accurate calculation and recall of number facts, building the fluency harder maths depends on.

Made for ages 16–17. That’s Grade 11–12 in the US, Year 12–13 in England, SS 2–3 in Nigeria and Class 11–12 in India.

Print it at home or school – it fits a standard A4 or US Letter page.
Print the answer key too, so marking takes seconds.
Play it on screen: answers are marked instantly and children earn stars.
Write on it on a tablet or touchscreen with a finger or stylus – no printer needed.

Pair an easier sheet with a harder one in the same session so practice always ends on a success.
Time one try, then beat it a few days later – children love racing their own best rather than others.
Treat mistakes as information: note what went wrong next to each incorrect answer.

Time needed: About 15–25 minutes
You’ll need: A printer (or a tablet to work on screen), a pencil and an eraser
Difficulty: On level (AS-style) – pitched at ages 16–17
Answer key: Yes – print it with the sheet or on its own

United States

England (UK)

Nigeria

India