13 real exam questions with step-by-step video solutions · Try each question yourself first, then open the video solution to check your working. Stuck? Ask Axi below – it knows this page’s questions.
New · Axi
Stuck on a tangent or normal question?
Axi, our AI tutor, answers questions on any tangent or normal problem on this page – no copying, no pasting, no sign-up.
What are you stuck on? Ask about any tangent or normal question on this page and I will talk you through it.
Axi answers from this page’s question, tutorial and worked solution. Live Axi reads and marks your own working in the app.
1EDEXCEL C1 June 2014 Q10
Question image is broken on examsolutions.net (dead upload, reported). The video solution below walks through the question.
View video solution (2 parts)
Part (a):
Part (b):
2CIE P1 November 2013 Q10
The diagram shows the curve y = (3 - 2x)^3 and the tangent to the curve at the point (1/2, 8). (i) Find the equation of this tangent, giving your answer in the form y = mx + c. [5] (ii) Find the area of the shaded region. [6]
View video solution (2 parts)
Part (a):
Part (b):
3EDEXCEL C1 June 2013 Q11
Figure 2 shows a sketch of the curve H with equation y = 3/x + 4, x not equal to 0. (a) Give the coordinates of the point where H crosses the x-axis. (1) (b) Give the equations of the asymptotes to H. (2) (c) Find an equation for the normal to H at the point P(-3, 3). (5) This normal crosses the x-axis at A and the y-axis at B. (d) Find the length of the line segment AB. Give your answer as a surd. (3)
View video solution (3 parts)
Part (a):
Part (b):
Part (c):
4EDEXCEL C1 January 2013 Q11
Question image is broken on examsolutions.net (dead upload, reported). The video solution below walks through the question.
View video solution (2 parts)
Part (a):
Part (b):
5OCR C1 June 2012 Q6
Question image is broken on examsolutions.net (dead upload, reported). The video solution below walks through the question.
View video solution (1 part)
Part (a):
6EDEXCEL C1 June 2011 Q10
The curve C has equation y = (x + 1)(x + 3)^2. (a) Sketch C, showing the coordinates of the points at which C meets the axes. (4) (b) Show that dy/dx = 3x^2 + 14x + 15. (3) The point A, with x-coordinate -5, lies on C. (c) Find the equation of the tangent to C at A, giving your answer in the form y = mx + c, where m and c are constants. (4) Another point B also lies on C. The tangents to C at A and B are parallel. (d) Find the x-coordinate of B. (3)
View video solution (4 parts)
Part (a):
Part (b):
Part (c):
Part (d):
7EDEXCEL C1 January 2011 Q11
The curve C has equation y = (1/2)x^3 - 9x^(3/2) + 8/x + 30, x > 0. (a) Find dy/dx. (4) (b) Show that the point P(4, -8) lies on C. (2) (c) Find an equation of the normal to C at the point P, giving your answer in the form ax + by + c = 0, where a, b and c are integers. (6)
View video solution (1 part)
Part (a):
8EDEXCEL C1 June 2010 Q11
Question image is broken on examsolutions.net (dead upload, reported). The video solution below walks through the question.
View video solution (2 parts)
Part (a):
Part (b):
9EDEXCEL C1 January 2010 Q6
The curve C has equation y = ((x + 3)(x - 8))/x, x > 0. (a) Find dy/dx in its simplest form. (4) (b) Find an equation of the tangent to C at the point where x = 2. (4)
View video solution (2 parts)
Part (a):
Part (b):
10EDEXCEL C1 June 2009 Q11
The curve C has equation y = x^3 - 2x^2 - x + 9, x > 0. The point P has coordinates (2, 7). (a) Show that P lies on C. (1) (b) Find the equation of the tangent to C at P, giving your answer in the form y = mx + c, where m and c are constants. (5) The point Q also lies on C. Given that the tangent to C at Q is perpendicular to the tangent to C at P, (c) show that the x-coordinate of Q is (1/3)(2 + sqrt(6)). (5)
View video solution (3 parts)
Part (a):
Part (b):
Part (c):
11EDEXCEL C1 January 2009 Q11
The curve C has equation y = 9 - 4x - 8/x, x > 0. The point P on C has x-coordinate equal to 2. (a) Show that the equation of the tangent to C at the point P is y = 1 - 2x. (6) (b) Find an equation of the normal to C at the point P. (3) The tangent at P meets the x-axis at A and the normal at P meets the x-axis at B. (c) Find the area of triangle APB. (4)
View video solution (3 parts)
Part (a):
Part (b):
Part (c):
12EDEXCEL C1 January 2008 Q9
The curve C has equation y = f(x), x > 0, and f'(x) = 4x - 6sqrt(x) + 8/x^2. Given that the point P(4, 1) lies on C, (a) find f(x) and simplify your answer. (6) (b) Find an equation of the normal to C at the point P(4, 1). (4)
View video solution (2 parts)
Part (a):
Part (b):
13EDEXCEL C1 January 2008 Q10
The curve C has equation y = (x + 3)(x - 1)^2. (a) Sketch C showing clearly the coordinates of the points where the curve meets the coordinate axes. (4) (b) Show that the equation of C can be written in the form y = x^3 + x^2 - 5x + k, where k is a positive integer, and state the value of k. (2) There are two points on C where the gradient of the tangent to C is equal to 3. (c) Find the x-coordinates of these two points. (6)
