Question 1: On the coordinate grid, draw the curve y = x^2. Then, draw the tangent to the curve at the point where x = 2.

Answer: Line passing through (2,4) with slope 4

Question 2: Construct the curve y = 3x + 1 and draw a tangent at the point where x = 0. Label the tangent line.

Answer: Tangent line y = 3x + 1

Question 3: Plot the graph of y = 2x and draw the tangent to the line at x = 3.

Answer: Tangent line passing through (3,6) with slope 2

Question 4: Draw the parabola y = x^2 and construct the tangent at the point where x=1. Show your working.

Answer: Tangent line at (1,1) with slope 2

Question 5: Construct the cubic curve y = x^3. Draw the tangent to the curve at x = -1 and label it.

Answer: Tangent line with slope -3 passing through (-1,-1)

Question 6: A farmer wants to draw a tangent to the curve y = 2x^2 + 3 at the point where x = 2. Draw the tangent line.

Answer: Tangent at (2,11) with slope 8, line y = 8x - 5

Question 7: A roller coaster design involves drawing a tangent to the curve y = -x^2 + 4x at x=3. Construct this tangent.

Answer: Tangent at (3,3) with slope -2, line y = -2x + 9

Question 8: Draw the graph of y = 5x - 2 and construct the tangent at x=1.

Answer: Tangent line y = 5x - 2

Question 9: Using the curve y = x^2 + 2x, draw the tangent at the point where x=0. Show your working.

Answer: Tangent line y = 2x

Question 10: Draw the parabola y = x^2 and construct the tangent to the curve at x= -2. Explain your steps.

Answer: Tangent at (-2,4) with slope 2, line y=2x+8

Question 11: Identify and correct the mistake in the following drawing: the tangent to y = x^2 at x=1 is drawn with slope 3 but passes through (1,1).

Answer: Incorrect slope; should be slope 2, line y=2x-1