Trends from 2017 and 2018 alevel:
- Solving in terms of a and b.
- Solve inequality involving modulus in exact form.
- Secondary school syllabus like remainder theorem appear in N2017. R-formula appear in specimen paper.
- Using integration techniques to evaluate arc length given the formula.
- Applications of 1st order Differential equation: Motion with resistance proportional to velocity came out in N2017.
- Applications of 2nd order Differential equation: Electric circuits came out in N2018.
- Applications of integration such as arc length, surface area of revolution and centroid. Applications of integation
- Applications of 1st order DE such as motion, population growth, orthogonal trajectories, mixture problems, Torricelli’s Law, Newton’s Law of cooling. 1st order DE applications
- Applications of 2nd order DE such as vibrating springs and electric circuits Applications of 2nd order DE
- Odd/even functions, floor/ceiling functions
Example 1: Volume of revolution in 2017 alevel P2 4b
Let a=2 so we can visualise the shape of the graph
Example 2: Solution curve for Differential equation. 2014 alevel P1
This is solution for part iv.
It can be sketched without expressing the solution in the form x=f(t)
DHS J1 2018 Aug Test
Suppose we want to sketch the curve C and the line y=-2x+2 on the same graph
Note how the line y-2x+2 is entered.
Adjust the Tmax to 1% more so the graph displays correctly.
2011 alevel P1 Q11
Usually the sequence of transformation can be found by the replacement method. However, it can be tough to find the replacement for complicated functions. For such cases, we can use the general linear transformation c f(bx+a)+d to find the sequence.
cf(bx+a)+d = Translate by a units in the negative X direction, then scale by a factor of 1/b parallel to the X-axis, then scale by a factor of c parallel to the Y-axis, then translate by d units in the positive Y direction.
Example 1: 2015 P1 8ii
Example 2: 2015 P1 2ii
Graphical approach will yield x> 1.732. Notice Cambridge answer is not rounded to x>1.74 to satisfy the non-rounded inequality but rounded to 3 s.f.
Considering example 1 and example 2, we conclude that in real life applications questions, when rounding off your answer to 3 s.f, round off such that the rounded off answer still satisfies the non-rounded off inequality.
Vector distance questions are common in alevel and carries 5 or 6 marks. Knowing the vector distance formulas can help to solve such questions easily and quickly.
Useful in questions like this
Alevel 2014 P2
SRJC 2018 J2 MYE
Suppose we want to sketch the graph from -3 to 8.
- Enter by pressing “Math, Piecewise”.
2. Adjust the window setting to the required domain.
3. Trace the end point at -3 since it is not 1 complete cycle.