CAIE A-Level Mathematics 2.1.1 Modulus equations
Practise solving modulus equations and inequalities, sketching |ax+b| graphs, and selecting valid intervals from critical values.
- Syllabus
- 2028–2030
- Course
- Mathematics 9709
- Level
- AS
Exam points
- sketch y=|ax+b| with the correct vertex, symmetry and straight-line branches
- solve |linear| equations by comparing same-sign and opposite-sign linear cases
- reject extraneous critical values when a modulus inequality gives only one interval
2.1.1—Modulus equations question 1
[Maximum number: 7]
Question (a)
(a)
Sketch, on the same diagram, the graphs of y=|3 x-5| and y=2 x+7.
[ 2 ]
Draw V-shaped graph with vertex on positive x-axis
B1
Draw (more or less) correct graph of y=2 x+7 with smaller gradient
B1
And crossing y-axis above y-intercept of modulus graph.
Question (b)
(b)
Solve the equation |3 x-5|=2 x+7.
[ 3 ]
Solve 3 x-5=2 x+7 to obtain x=12
B1
Attempt solution of linear equation where signs of 3 x and 2 x are
different
M1
3 x-5=-2 x-7 OE.
Obtain x=−52
A1
Alternative solution for question 4(b)
State or imply non-modulus equation (3x−5)2=(2x+7)2
B1
Must be working with (3x−5)2=(2x+7)2.
Attempt solution of 3-term quadratic equation
M1
Obtain −52 and 12
A1
Question (c)
(c)
Hence solve the equation 3y+1−5=2×3y+7, giving your answer correct to 3 significant figures.
[ 2 ]
Apply logarithms and use power law for 3y=k where k>0 or
correct equivalent
M1
Using their positive answer from part (b)
or greater accuracy; and no other values.
Obtain 2.26
A1
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