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: 4]
Question (a)
(a)
By sketching a suitable pair of graphs, show that the equation
sec2x=−ex
has only one root in the interval 0<x<21π.
[ 2 ]
Sketch a relevant graph, e.g. y= 2 x
May be sketching 2 x and -e^-x
For y= 2 x correct shape, asymptote in correct position. Cuts at (0,1)
For -e^x correct shape, cuts at (0,1)
For y= 2 x correct shape, correct max/min, cuts axis at /4
For -e^-x correct shape, cuts at (0,-1)
Complete scale not needed, but should have enough
to imply the key points for both graphs.
Sketch a second relevant graph, e.g. y=-e^x and justify the given statement
Needs to mark intersection with a dot, a cross, or say roots at points of intersection, OE.
Question (b)
(b)
Show by calculation that this root lies between 0.9 and 1 .
[ 2 ]
Calculate the values of a relevant expression or pair of expressions at
x=0.9 and x=1
E.g. aligned & -4.401<-2.460
& -2.403>-2.718aligned or aligned & -1.94<0
& 0.315>0aligned
(or gathered0.179>0
-0.048<0gathered for the reciprocal graphs).
Complete the argument correctly with correct calculated values
All question bank results loaded