CAIE A-Level Mathematics A2 3.6.1 Root Location Questions
Practise bracketing and locating roots using sign changes, graphs and numerical reasoning.
- Syllabus
- 2028–2030
- Course
- Mathematics 9709
- Level
- A2
Exam points
- use sign changes to bracket a root in a stated interval
- sketch graphs to establish the number and location of roots
- justify root-location conclusions from calculated values
CAIE A-Level Mathematics A2 3.6.1 Root Location Questions question 1
[Maximum number: 2]
The constant a is such that ∫0axe21x dx=6.
Verify by calculation that a lies between 2.2 and 2.4.
Calculate the value of a relevant expression or values of a relevant pair of expressions at 2.2 and 2.4. Values to at least 2 sf.
Need all relevant values but only one (pair) needs to be correct to score M1. Complete set of values for their expression. If not comparing with 0, then the comparison must be clear.
Example 12.2<2.33 and 2.4>2.30
Example 2 f(a)=a-2-e^-1/2 a OEf(2.2)=-0.132f(2.4)=0.0988
Example 3 f(a)=2 a e^1/2 a-4 e^1/2 a+4f(2.2)=5.20f(2.4)=6.65
Example 4 f(a)=2 a e^1/2 a-4 e^1/2 a-2f(2.2)=-0.80f(2.4)=0.65
Complete the argument correctly with correct calculated values. Accept truncated
values. Allow work on a smaller interval.
Example 1 A clear explanation is needed.
Example 2 f(2.2)=-0.132 <0f(2.4)=0.0988 >0 OE
Example 3 f(2.2)=5.20 <6f(2.4)=6.65 >6
Example 4 f(2.2)=-0.80 <0f(2.4)=0.65 >0
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