Name: ...................................................
10A
Date: ...................................................
INSTRUCTIONS
• You should use a calculator where appropriate.
• You must show ALL necessary WORKING/SOLUTION clearly.
T3 CA 3
TOTAL MARKS:
40
1. 𝑦 = 3𝑥 2 − 12𝑥 + 7
a. Find the value of
𝑑𝑦
𝑑𝑥
when 𝑥 = 5.
……………………………… [ ___ /3]
b. Find the coordinates of the point on the graph of 𝑦 = 3𝑥 2 − 12𝑥 + 7 where the gradient is 0.
( .................... , .................... )
[ ___ /2]
2. A curve has equation 𝑦 = 𝑥 3 − 𝑎𝑥 + 𝑏.
The stationary points of the curve have coordinates (2, 𝑘) and (−2, 10 − 𝑘).
Work out the value of a, the value of b, and the value of k.
a = .............................. , b = .............................. , k = .............................. [ ___ /6]
3. The curve with the equation 𝑦 = 3𝑥 2 − 12𝑥 + 7 is plotted and a tangent with gradient −8 is drawn on
the curve.
a. Find the coordinates of the point where the tangent meets the curve.
( .................... , .................... )
[ ___ /4]
b. What is the equation of the tangent?
……………………………… [ ___ /3]
4. The equation of a curve is 𝑦 = 4𝑥 3 − 3𝑥. Determine:
a. the coordinates of the turning point.
( .................... , .................... ) and ( .................... , .................... ) [ ___ /5]
b. the equation of the tangent to the curve at the point where x = 1.
……………………………… [ ___ /5]
c. maxima and minima for this function. Give reasons for your answers.
[ ___ /3]
5. The equation of a curve is 𝑦 = 5 − 3𝑥 − 2𝑥 4 . Find 𝑓′′(𝑥) .
……………………………… [ ___ /3]
6. The tangent to the curve 𝑦 = 5𝑥 − 2𝑥 2 at the point (2, 2) meets the 𝑦 − 𝑎𝑥𝑖𝑠 at point P. Find the
coordinates of P.
( .................... , .................... )
[ ___ /6]