Graphs 8

4 marks · Normal

The curve is drawn for .

Curve \( y = x^2 + 2 \) with point at \( x=1 \).

(a)

Draw a tangent to the curve at , and estimate its gradient.

[3 marks]

(b)

Write down the equation of the tangent to the curve at , using the gradient found in part (a).

[1 mark]

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

(a) 2

(b) y = 2x + 1

Common mistakes: Using wrong point for tangent; Not using y = mx + c

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Draws or describes a reasonable tangent at (or method to find gradient).

M2 (a) · 1 mark · Uses rise/run (e.g., using two points on the tangent) to estimate gradient.

A1 (a) · 1 mark · Correct estimate for gradient (accept answers in range 1.7 to 2.3).

A2 (b) · 1 mark · Correct equation of the tangent line at , follow-through their value from (a), must pass through (1,3). (follow-through)

Worked solution

a) Draw a tangent at ; approximate the gradient by looking at two clear points on the tangent.

b) The tangent passes through (1,3). Equation: so .