Lesson 4.4
4.4 The equation of a tangent and normal at any point on a curve Quiz: AQA Further Maths, Unit 4
20 questions
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Lesson 4.4, The equation of a tangent and normal at any point on a curve: 20 multiple choice questions for the AQA GCSE Further Maths (8365), Unit 4: Calculus, written with Revision Ninja.
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The 20 questions
-
What is the angle between the tangent and the normal to a curve at a point?
- 180 degrees
- 0 degrees
- 45 degrees
- 90 degrees
-
If a tangent has gradient 2, what is the gradient of the normal?
- -2
- 1/2
- -1/2
- 2
-
The curve y = x^2 at x = 2 has tangent gradient 4. What is the normal gradient?
- -1/4
- 4
- -4
- 1/4
-
What is the equation of the tangent to y = x^2 at (2, 4)?
- y = 4x + 4
- y = 4x - 4
- y = x - 2
- y = 2x
-
What is the equation of the normal to y = x^2 at (2, 4)?
- y = x/4 + 3.5
- y = -4x + 12
- y = -x/4 + 4
- y = -x/4 + 4.5
-
What is the equation of the tangent to y = x^3 at (1, 1)?
- y = x
- y = 3x + 2
- y = 3x - 2
- y = 3x - 1
-
For y = 2x^2 - 3x, what is the gradient at x = 1?
- 1
- -1
- 4
- 2
-
The point (1, -1) lies on y = 2x^2 - 3x. What is the equation of the tangent there?
- y = 2x - 3
- y = x + 2
- y = x - 2
- y = -x
-
The normal to y = x^2 at (1, 1) crosses the y-axis at which y-value?
- 2.5
- 1
- -1.5
- 1.5
-
For y = 1/x at x = 2, what is the gradient of the tangent?
- 1/2
- -1/4
- -1/2
- 1/4
-
What is the equation of the tangent to y = x^3 - x at x = 0?
- y = -x
- y = x
- y = 0
- y = -x + 1
-
The normal to y = x^2 at x = -3 passes through the y-axis at which point?
- (0, 9)
- (0, 10)
- (0, 6)
- (0, 9.5)
-
At which point on y = x^2 is the tangent parallel to the x-axis?
- (0, 0)
- (2, 4)
- (-1, 1)
- (1, 1)
-
The tangent to y = x^2 + 1 at x = 3 meets the x-axis at which point?
- x = 8/3
- x = 4/3
- x = 3
- x = -4/3
-
What is the gradient of the normal to y = 4 - x^2 at (1, 3)?
- 2
- -1/2
- 1/2
- -2
-
What gradient does a line perpendicular to the tangent to y = 2x^2 at x = 2 have?
- -8
- 8
- -1/8
- 1/8
-
Which is the equation of the tangent to y = x^2 at (a, a^2)?
- y = 2ax - a^2
- y = 2x - a^2
- y = 2ax + a^2
- y = ax - a^2
-
The tangent to y = x^3 - 2x at x = 2 meets the y-axis at which point?
- (0, -20)
- (0, -4)
- (0, 16)
- (0, -16)
-
For which x does the tangent to y = x^2 - 6x have gradient 0?
- 0
- 3
- 6
- -3
-
The tangent to y = 2x^2 + 1 at x = 2 has what y-intercept?
- -7
- -9
- 7
- 9
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