IGCSE Additional Math 14.5. Find gradients, tangents and normals Topic Practice

CAIE IGCSE Additional Math 14.5. Find gradients, tangents and normals question practice helps you revise this syllabus point with the course map in view. Use this page to focus on one topic, check the style of questions available, and connect each attempt back to the knowledge area it is testing.

EduNinja keeps Additional Math practice aligned to CAIE, so you can move from topic review into exam-style question bank work without losing the syllabus structure. Start with a small set, mark the weak steps, then return to nearby topic links when a definition, graph, calculation, or explanation needs repair.

14.5.1—Find gradients, tangents and normals

[Maximum number: 4]

A curve has equation $y=\frac{2+\sin 3 x}{x+1}$ .

Find the equation of the normal to the curve at the point where x=0.

[Maximum number: 6]

In this question a and b are constants.
The normal to the curve $\mathrm{y}=\frac{\mathrm{a}}{\mathrm{x}}+3 \mathrm{x}-2$ at the point where x=1 has equation $\mathrm{y}=-\frac{1}{4} \mathrm{x}+\mathrm{b}$ . Find the values of a and b.

(a)

Find the equation of the normal to the curve $y=x^{3}-7 x^{2}+12 x-5$ at the point (1,1).

[ 5 ]

(b)

Find the x -coordinates of the two points where the normal cuts the curve again. Give your answers in the form $x=a \pm \sqrt{b}$ where a and b are integers.

[ 5 ]

In this question p and q are constants.

The normal to the curve $y=\frac{p}{x^{2}}+5 x-2$ , at the point where x=1, has equation y=-x+q.
Find the values of p and q.

[Maximum number: 7]

A curve has equation $y=2 x \cos x$ . The normal to the curve at ( $\pi,-2 \pi$ ) meets the x-axis and y-axis at points P and Q. Find the exact area of triangle POQ.

A curve has equation $y=\ln (5-3 x)$ where $x<\frac{5}{3}$ . The normal to the curve at the point where x=-5, cuts the x-axis, at the point P.

Find the equation of the normal and the x-coordinate of P.

(a)

Sketch the graph of the curve $\mathrm{y}=\ln (4 \mathrm{x}-3)$ on the axes, stating the intercept with the x -axis. [2]

[ 2 ]

(b)

Find the equation of the tangent to the curve $y=\ln (4 x-3)$ at the point where x=2.

[ 5 ]

[Maximum number: 6]

A curve has equation $y=5 \mathrm{e}^{2 x-1}+\mathrm{e}$ . The tangent to the curve at the point where x=1 cuts the x-axis at the point P.

Find the equation of the tangent in the form y=m x+c, where m and c are exact values, and hence find the x-coordinate of P.

[Maximum number: 3]

The equation of a curve is $y=x \sin x$ .

Find the equation of the tangent to the curve at $x=\frac{\pi}{2}$ in the form y=m x+c.

[Maximum number: 6]

The diagram shows the curve $y=5 \mathrm{e}^{2 x}-3$ . The curve meets the y -axis at the point A . The tangent to the curve at A meets the x -axis at the point B . Find the length of AB .

0 selected

Question 3(b)

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