This 9th class maths chapter 4 online test covers Chapter 4 of the Class 9 Mathematics course, Factorization. It has 25 multiple-choice questions, shown one at a time, and it marks itself the moment you finish. There is no timer and no sign-up. When you press finish you get your score, and every question is shown again with your answer, the correct option and a short explanation of why that option is right. An Urdu medium version of the same test is given further down this page.
What Chapter 4 Covers
The 25 questions are spread across the whole unit rather than one exercise, so the test is a fair check of whether you are ready for a class test or the annual paper:
- Factorising by taking out a common factor, such as 12x + 36.
- Perfect squares and the difference of squares, including 4x2 − 12x + 9 and finding square roots of expressions.
- Sum and difference of cubes — a3 + b3, a3 − b3, 8x3 + 27 and x3 − 27.
- Cubes of binomials — recognising x3 + 3x2 + 3x + 1 and 8x3 + 60x2 + 150x + 125.
- HCF and LCM of algebraic expressions, and the rule that their product equals the product of the two expressions.
- Factorising trinomials such as 3y2 − 11y + 6, and the pairing trick for (x + 1)(x + 2)(x + 3)(x + 4) + 1.
- Degree of a polynomial — linear, quadratic and cubic — and applications such as a profit function R(x) = −x2 + 6x − 8.
Revise These Before You Start
Most marks in this unit are lost on the same few points. Read through these once before attempting the test:
- HCF × LCM = the product of the two expressions. This single identity answers several questions in the set.
- a3 + b3 = (a + b)(a2 − ab + b2) and a3 − b3 = (a − b)(a2 + ab + b2). The sign inside the bracket is the opposite of the sign outside for the middle term.
- The HCF takes the lowest power of each common factor; the LCM takes the highest.
- A quadratic has degree 2 and a cubic has degree 3 — the degree is the highest power, not the number of terms.
- x3 + 3x2 + 3x + 1 is (x + 1)3. Learn the binomial cube pattern and these become instant.
- For (x + 1)(x + 2)(x + 3)(x + 4) + 1, pair the outer and inner brackets first so both pairs give the same quadratic.
How the Test Works
- 25 questions, one at a time, with Next and Previous buttons.
- No timer, so you can work a calculation out on paper before answering.
- Automatic marking the moment you finish.
- Answer review with the correct option and an explanation for every question.
- Retake as many times as you like, and your score is not stored anywhere.
Start the Chapter 4 Online Test
Always look for a common factor first — several questions become much easier once the obvious factor is outside the bracket. Keep a pen and rough paper beside you: the numerical questions are quick, but they are much easier to get right written down than in your head. Aim for 20 out of 25 or better before you move on to the next unit.
Chapter 4 Online Test — Urdu Medium
Urdu medium students can attempt the same Chapter 4 test with every question, option and explanation written in Urdu. It behaves exactly like the English test above: 25 questions one at a time, no timer, and a full answer review at the end.
Mistakes Students Make in This Unit
When you look through your answer review, check whether any of your wrong answers came from these:
- Mixing up the signs inside the bracket for the sum and difference of cubes.
- Taking the highest power for the HCF and the lowest for the LCM, which is the wrong way round.
- Calling an expression cubic because it has three terms rather than because its degree is 3.
- Multiplying all four brackets out in the pairing question instead of pairing them.
- Forgetting the ± when taking a square root of an expression.
What to Do After the Test
A score on its own teaches you very little. Go through the answer review properly and write down the number of every question you got wrong, along with the topic it came from. If two or three of them come from the same section of the unit, that section is what you revise next — not the whole chapter again. Then retake the test a day or two later rather than immediately, because answering correctly from memory is not the same as understanding it. Once you are consistently scoring above 20, move on and come back to this test in your final week of revision.
Frequently Asked Questions
What is the relationship between HCF and LCM?
The product of the HCF and the LCM of two expressions equals the product of the expressions themselves. If you know three of those four quantities you can always find the fourth.
How do I factorise (x + 1)(x + 2)(x + 3)(x + 4) + 1?
Pair the first with the last and the middle two: (x + 1)(x + 4) = x2 + 5x + 4 and (x + 2)(x + 3) = x2 + 5x + 6. Put y = x2 + 5x + 4, and the expression becomes y(y + 2) + 1 = (y + 1)2, a perfect square.
How do I tell a quadratic from a cubic?
By the highest power of the variable, called the degree. Degree 2 is quadratic, degree 3 is cubic. The number of terms makes no difference.
Is this test free?
Yes. There is no sign-up, no limit on retakes and nothing is locked. Your score is not saved or shared.
Related Class 9 Maths Resources
Carry on with the Chapter 4 test paper for written practice, the Chapter 3 online test (Sets and Functions), the Chapter 5 online test (Linear Equations and Inequalities). For full-length practice, download the 25 Class 9 Maths guess papers, each a complete 75-mark bilingual paper. You can also browse all Class 9 Maths test papers and every Class 9 Maths online test, or open the Class 9 Mathematics section for everything in one place.
Studying the other subjects too? There are self-marking chapter tests for Class 9 Physics and Class 9 Biology, and you can browse the whole Class 9 section by subject.