Relationships and Calculus 1.3
Applying calculus skills of differentiation
Time
1. Derivative of xn
HHM 91
6D
(1 – 40)
1 period
I can differentiate algebraic functions which have positive and
negative powers of x (Qu 1 – 20)
I can differentiate algebraic functions which can be simplified
to an expression in powers of x from a surd (Qu 21 – 27)
I can differentiate algebraic functions which can be simplified
to an expression in powers of x originally as the denominator (Qu 28 – 40)
2. Derivative of axn
HHM 94
6F
(1 – 27)
1 period
I can differentiate algebraic functions which have a multiplier (Qu 1 – 18)
I can differentiate algebraic functions which have more than
one term (Qu 19 – 27)
3. Derivatives of products and quotients HHM 95
6G
(1 – 27)
1 period
I can differentiate algebraic functions containing products (Qu 1 – 16)
I can differentiate algebraic functions containing quotients (Qu 17 – 27)
4. Rate of change
HHM 92
6E
1, 3, 5, 6
period
HHM 96
6H
(6 – 14)
1 period
6I
(2,3,4)
1 period
6J
(1 – 8)
1 period
(1-9)
1 period
(2-6)
1 period
I can find the rate of change of a function
5. Applications of derivatives
I can use differentiation to solve real-life problems
6. Leibniz notation
HHM 100
I can use Leibniz Notation as an alternative to f(x)
7. Equations of tangents
HHM 101
I can determine the equation of a tangent to a curve, at a given
point by differentiation
8. Stationary points
HHM 106 6M
I can determine use the stationary points of a curve and state
their nature
9. The shape of curves
HHM 104
6L
I can determine where a function is strictly increasing/decreasing
10. Curve sketching
HHM 107
6N
(1 – 9)
3 periods
I can sketch the graph of an algebraic function by determining
stationary points and where it cuts the axes
(Extra practice
HHM 137
7I
(1-9) )
11. Closed interval
HHM 109
60
1, 2
1 period
6P
(1 – 9)
1 period
I can determine where the maximum/minimum values lie in
a closed interval
12. Graphs of derived functions
HHM 110
I can find the graph of a derived function
(The following two learning intentions are assessed in Applying calculus skills to
optimisation and area – Applications 1.4. Teach together but assess after
completing the teaching of both differentiation and integration – R&C 1.3 &
1.4.)
13. Optimisation : Maxima and minima HHM 112
6Q
(1 – 8)
1 period
14. Further applications
6R
(1 – 5)
1 period
(1 - 6)
1 period
HHM 114
I can solve optimisation problems in context using differentiation
15. Differentiation of sin x and cos x
HHM 264 14B
I have experience of differentiating sinx and cosx
16. Derivative of (a + x)n
HHM 267 14E
1, 2
1 period
17. Derivative of (ax+ b)n
HHM 269 14G
1
1 period
18. The chain rule
HHM 271 14H
(1 – 5)
1 period
I can differentiate a composite function using the chain rule
20 periods