Inequality Proofs (Leaving Cert Mathematics): Quizzes

📚Quizzes
Revision NotesModel AnswersQuizzesFlashcardsExam Questions
Inequality Proofs
Sign up to keep practising.Create a free account to play more quizzes and track your progress.

Practise the questions

9 questions from this quiz

Show

What is the key technique for proving inequalities according to the note?

Use a squared term

Why are squared terms useful in inequality proofs?

A squared is always ≥0\ge 0

What is the first step when proving a2+b2≥2aba^2+b^2 \ge 2ab?

Bring all terms to one side

What does a2+b2−2aba^2+b^2-2ab factorise to?

(a−b)2(a-b)^2

What does showing (a−b)2≥0(a-b)^2 \ge 0 prove?

a2+b2≥2aba^2+b^2 \ge 2ab

What is x2−x+1x^2-x+1 in completed square form?

(x−12)2+34(x-\frac{1}{2})^2+\frac{3}{4}

Why does (x−12)2+34>0(x-\frac{1}{2})^2+\frac{3}{4}>0 prove x2+1>xx^2+1>x?

Squared term + positive = positive

When proving x2+1>xx^2+1>x, what is the first rearrangement?

x2−x+1>0x^2-x+1>0

Which expression is guaranteed to be positive for all real nn?

(n+3)2+5(n+3)^2+5

Explore Leaving Cert Mathematics Revision Notes by Topics

Inequalities

Modulus

Inequality Proofs & Discriminants

Explore Leaving Cert Mathematics Model Answers by Topics

Inequalities

Modulus

Inequality Proofs & Discriminants

Explore Leaving Cert Mathematics Flashcards by Topics

Inequalities

Modulus

Inequality Proofs & Discriminants

Explore Leaving Cert Mathematics Exam Questions by Topics

Inequalities

Modulus

Inequality Proofs & Discriminants

Join 100,000+ Leaving Cert students studying Quizzes with us.

Select your subjects, and get access to A+ resources today.