# Worksheet: Slopes of Tangents to Curves

Q1:

Let Suppose that the tangent to the graph of at makes an angle with the positive -axis of tangent . Find and .

• A ,
• B ,
• C ,
• D ,

Q2:

Find the points on the curve at which the tangents are parallel to the line .

• A ,
• B ,
• C ,
• D ,

Q3:

Let be the tangent to the curve at the point . Determine the gradient of and the angle it makes with the positive -axis, giving your answer to the nearest minute.

• AThe gradient of is 8, and the angle it makes with the positive -axis is .
• BThe gradient of is 4, and the angle it makes with the positive -axis is .
• CThe gradient of is 2, and the angle it makes with the positive -axis is .
• DThe gradient of is 8, and the angle it makes with the positive -axis is .
• EThe gradient of is 16, and the angle it makes with the positive -axis is .

Q4:

Find the points on the curve where the tangent has gradient 4.

• A ,
• B ,
• C ,
• D ,

Q5:

Determine the gradient of the tangent to the curve of the function when .

• A5
• B
• C
• D

Q6:

Find the points on the curve where the gradient of the tangent line is .

• A
• B
• C
• D

Q7:

Let be the tangent to the curve at the point . Determine the gradient of and the angle it makes with the positive -axis, giving your answer to the nearest minute.

• AThe gradient of is 3, and the angle it makes with the positive -axis is .
• BThe gradient of is 21, and the angle it makes with the positive -axis is .
• CThe gradient of is 7, and the angle it makes with the positive -axis is .
• DThe gradient of is 21, and the angle it makes with the positive -axis is .

Q8:

Find the points on where the tangent is parallel to the line that passes through and .

• A and
• B and
• C and
• D and

Q9:

Find the points on the curve where the tangent is parallel to the line .

• A
• B
• C
• D
• E

Q10:

Find the gradient of the tangent to at the point where .

• A
• B81
• C26
• D86

Q11:

Find the gradient of the tangent to at the point where .

• A95
• B
• C
• D

Q12:

Find the gradient of the tangent to at the point where .

• A10
• B
• C
• D

Q13:

At which points are tangents to the curve parallel to the -axis?

• A and
• B
• C
• D and

Q14:

Find the point that lies on the curve , at which the tangent to the curve is perpendicular to the straight line .

• A
• B
• C
• D

Q15:

Find the points on the curve where the tangent is perpendicular to the line .

• A ,
• B ,
• C ,
• D ,

Q16:

Find the gradient of the tangent to the curve at the point .

• A
• B
• C
• D18

Q17:

Find the gradient of the tangent to the curve at the point .

• A
• B
• C17
• D5

Q18:

Find the gradient of the tangent to the curve at the point .

• A
• B
• C11
• D20

Q19:

Find the gradient of the tangent to the curve at .

• A12
• B8
• C7
• D16

Q20:

Find the gradient of the tangent to the curve at .

• A23
• B7
• C3
• D39

Q21:

Find the gradient of the tangent to the curve at .

• A63
• B31
• C11
• D95

Q22:

Find the gradient of the tangent to the curve at .

• A12
• B3
• C
• D21

Q23:

Differentiate , and find the gradient of the tangent to its graph at .

• A , gradient of the tangent to the graph
• B , gradient of the tangent to the graph
• C , gradient of the tangent to the graph
• D , gradient of the tangent to the graph

Q24:

Differentiate , and find the gradient of the tangent to its graph at .

• A , gradient of the tangent to the graph
• B , gradient of the tangent to the graph
• C , gradient of the tangent to the graph
• D , gradient of the tangent to the graph

Q25:

Differentiate , and find the gradient of the tangent to its graph at .

• A , gradient of the tangent to the graph
• B , gradient of the tangent to the graph
• C , gradient of the tangent to the graph
• D , gradient of the tangent to the graph