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Find equations of tangents and normals

12th grade (Year 13 in England) · 16 questions · Common Core: HSG.GPE.B.5 · England: A-level Pure Mathematics

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  1. Question 1

    Find the equation of the tangent to y = x² − 5x + 2 at x = −1. Type the right-hand side of y = … .

    Answer

  2. Question 2

    Find the equation of the normal to y = x² − x + 3 at x = 2. Type the right-hand side of y = … (fractions are fine).

    Answer

  3. Question 3

    Find the equation of the tangent to y = 2x² − 5x − 1 at x = −1. Type the right-hand side of y = … .

    Answer

  4. Question 4

    Find the equation of the normal to y = x² − 4x − 3 at x = 3. Type the right-hand side of y = … (fractions are fine).

    Answer

  5. Question 5

    Find the equation of the tangent to y = 3x² − 4x − 2 at x = −3. Type the right-hand side of y = … .

    Answer

  6. Question 6

    Find the equation of the normal to y = x² + 2x − 1 at x = −3. Type the right-hand side of y = … (fractions are fine).

    Answer

  7. Question 7

    Find the equation of the tangent to y = x² − 4x − 3 at x = −2. Type the right-hand side of y = … .

    Answer

  8. Question 8

    Find the equation of the normal to y = x² − x − 2 at x = 2. Type the right-hand side of y = … (fractions are fine).

    Answer

  9. Question 9

    Find the equation of the tangent to y = −x² − 5x − 2 at x = −1. Type the right-hand side of y = … .

    Answer

  10. Question 10

    Find the equation of the normal to y = x² + 3x + 6 at x = 3. Type the right-hand side of y = … (fractions are fine).

    Answer

  11. Question 11

    Find the equation of the tangent to y = 2x² − 2x + 3 at x = −3. Type the right-hand side of y = … .

    Answer

  12. Question 12

    Find the equation of the normal to y = x² − 4x + 6 at x = 0. Type the right-hand side of y = … (fractions are fine).

    Answer

  13. Question 13

    Find the equation of the tangent to y = x² + 3x + 5 at x = 3. Type the right-hand side of y = … .

    Answer

  14. Question 14

    Find the equation of the normal to y = x² + 3x + 4 at x = 0. Type the right-hand side of y = … (fractions are fine).

    Answer

  15. Question 15

    Find the equation of the tangent to y = x² − x at x = 0. Type the right-hand side of y = … .

    Answer

  16. Question 16

    Find the equation of the normal to y = x² − 3x + 5 at x = 2. Type the right-hand side of y = … (fractions are fine).

    Answer

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Answer key: Find equations of tangents and normals

  1. 1. -7x+1

  2. 2. -(1/3)x+17/3

  3. 3. -9x-3

  4. 4. -(1/2)x-9/2

  5. 5. -22x-29

  6. 6. (1/4)x+11/4

  7. 7. -8x-7

  8. 8. -(1/3)x+2/3

  9. 9. -3x-1

  10. 10. -(1/9)x+73/3

  11. 11. -14x-15

  12. 12. (1/4)x+6

  13. 13. 9x-4

  14. 14. -(1/3)x+4

  15. 15. -x

  16. 16. -x+5