IB Middle Years Programme (MYP) · Mathematics

Quadratic Expressions and Equations: Practice Questions

2 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Quadratic Expressions and Equations.

7 questions21 marksFree, no account

Question 1

1 mark

Factorize the following quadratic expression completely:
\( x^2 + 5x - 6 \)

Question 2

1 mark

Factorize the following quadratic expression completely:
\( x^2 - 12x + 36 \)

Question 3

2 marks

Factorize the following quadratic expression completely:
\( x^2 + 7x + 10 \)

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Question 4

3 marks

Solve the quadratic equation \( 3x^2 - 12 = 0 \) by using the square root method.

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Question 5

5 marks

A rectangle has a perimeter of \(20\) cm and its area is \(24\) cm\(^2\). If \(L\) and \(W\) are the length and width of the rectangle respectively, form a quadratic equation in terms of \(L\) and find the dimensions of the rectangle.

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Question 6

4 marks

Consider the quadratic expression \(x^2 + 8x + 15\).
(a) Factorize the expression completely.
(b) Hence, solve the equation \(x^2 + 8x + 15 = 0\).

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Question 7

5 marks

A rectangular garden has a length that is 3 meters more than its width. Let the width be \(x\) meters.
(a) Write an expression for the length of the garden in terms of \(x\).
(b) Given that the area of the garden is 40 m\(^2\), set up a quadratic equation in the form \(x^2 + bx + c = 0\).
(c) Solve the equation to find the dimensions of the garden. Explain why one of the solutions is rejected.

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