IB · Mathematics: Analysis & Approaches SL & HL · Functions

Modulus, odd/even & inequalities: IB Mathematics: Analysis & Approaches questions with answers

Free Modulus, odd/even & inequalities questions for IB Mathematics: Analysis & Approaches (SL & HL), HL only, part of Functions. Each question has the answer and the marking points an examiner would look for.

Generate a full Modulus, Odd/even & Inequalities worksheet →All Functions questions

Modulus, odd/even & inequalities practice questions

Question 1Structured · 6 marksA* challenge

Solve the inequality xx − 4 ≤ −2.

[6]
Show answers and mark scheme
PartAnswer and marking pointsMarks
83 ≤ x < 4
do not multiply by (x − 4) without knowing its sign: bring everything to one side M1
3x − 8x − 4 ≤ 0 A1
critical values x = 83, x = 4 A1A1
sign diagram or graph (M1)
83 ≤ x < 4 A1
6
Question 2Structured · 6 marksA* challenge

Solve the inequality xx − 4 ≤ −1.

[6]
Show answers and mark scheme
PartAnswer and marking pointsMarks
2 ≤ x < 4
do not multiply by (x − 4) without knowing its sign: bring everything to one side M1
2x − 4x − 4 ≤ 0 A1
critical values x = 2, x = 4 A1A1
sign diagram or graph (M1)
2 ≤ x < 4 A1
6
Question 3Structured · 5 marks

Solve the inequality |3x − 2| > |x + 6|.

[5]
Show answers and mark scheme
PartAnswer and marking pointsMarks
x < −1 or x > 4
squaring both sides, or considering cases M1
(3x − 2)2 − (x + 6)2 > 0 (A1)
critical values x = −1, x = 4 A1A1
x < −1 or x > 4 A1
5
Question 4Structured · 6 marksA* challenge

Solve the inequality x − 1x + 1 ≤ 3.

[6]
Show answers and mark scheme
PartAnswer and marking pointsMarks
x ≤ −2 or x > −1
do not multiply by (x + 1) without knowing its sign: bring everything to one side M1
−2x − 4x + 1 ≤ 0 A1
critical values x = −2, x = −1 A1A1
sign diagram or graph (M1)
x ≤ −2 or x > −1 A1
6
Question 5Structured · 5 marks

Solve the inequality |3x + 5| > |x − 4|.

[5]
Show answers and mark scheme
PartAnswer and marking pointsMarks
x < −92 or x > −14
squaring both sides, or considering cases M1
(3x + 5)2 − (x − 4)2 > 0 (A1)
critical values x = −92, x = −14 A1A1
x < −92 or x > −14 A1
5
Question 6Structured · 6 marksA* challenge

Solve the inequality x − 4x + 3 ≤ −1.

[6]
Show answers and mark scheme
PartAnswer and marking pointsMarks
−3 < x ≤ 12
do not multiply by (x + 3) without knowing its sign: bring everything to one side M1
2x − 1x + 3 ≤ 0 A1
critical values x = 12, x = −3 A1A1
sign diagram or graph (M1)
−3 < x ≤ 12 A1
6

More Functions questions

Functions, composites & inversesQuadratics & the discriminantRational functionsExponential & log functionsTransformations of graphsPolynomials & roots

Want a mentor, not just a paper?

Riyaz Shaikh has mentored IGCSE, IB and A Level students for 15+ years, one-on-one, online and in Mumbai. The hardest questions on this site are the ones he uses to find a student's weak points.

Meet Riyaz →

Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in