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CAT Algebra Sectional Test 2 – with Solutions

A CAT Quantitative Aptitude Algebra set mixing quadratics, logarithms, modulus inequalities, progressions and functions, with a worked solution for each problem.

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Questions
22
Duration
40 min
Marks
66

Negative marking

Attempts
100
Access
With a course
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Real test conditions

Before you launch the test

This is the computer-based test format, not a quiz page: one clock, a question palette, and no way back once a section closes. Read these first.

  • It runs in full screen. The test takes over the screen when it starts, the way the real computer-based test does.
  • Leaving it is counted. Switching away is recorded and warned about; the third time, the paper is submitted for you.
  • The clock runs for 40 minutes. Set aside that long, uninterrupted. It starts when you begin, keeps running if you close the tab, and submits the paper at zero.

About this test

CAT Algebra Sectional Test 2 Practice: Quadratics, Logs and Progressions

For CAT aspirants who have finished learning Algebra and now want mixed, exam-style practice, this Aptitude360 set is Sectional Test 2 in the CAT Quantitative Aptitude series. It covers quadratic equations, logarithms, modulus inequalities, progressions and functions in both word-problem and pure forms. Every question in this test comes with a worked solution.

Topics covered in this CAT Algebra sectional set

  • Linear equations from word problems, such as ticket pricing and integer solutions for purchases
  • Quadratic equations: forming an equation from transformed roots, common roots, integer roots of a parabola and conditions for a parabola to stay above a line
  • Modulus and rational inequalities solved by sign analysis
  • Logarithms and exponents: chained change-of-base products and exponential equations that reduce to quadratics
  • Progressions: daily savings, bouncing-ball distance, common terms of two APs and an infinite arithmetico-geometric series
  • Functions: composite functions, domain of a root over a log, inverse of a restricted quadratic and odd-power polynomial symmetry
  • Telescoping surds after rationalisation and the minimum of a two-variable quadratic expression

Key Algebra formulas to revise for CAT

  • Sum and product of roots of \( ax^{2}+bx+c=0 \): \( \alpha+\beta=-\dfrac{b}{a},\ \alpha\beta=\dfrac{c}{a} \)
  • Sum of first n terms of an AP: \( S_{n}=\dfrac{n}{2}\left[2a+(n-1)d\right] \)
  • Infinite GP sum: \( S_{\infty}=\dfrac{a}{1-r},\ |r|<1 \)
  • Log chain rule: \( \log_{a}b\times\log_{b}c=\log_{a}c \)
  • Rationalising: \( \dfrac{1}{\sqrt{a}+\sqrt{b}}=\dfrac{\sqrt{b}-\sqrt{a}}{b-a} \)

How to prepare Algebra for CAT more effectively

  • Substitute a new variable, such as a power of three, when exponential terms differ only in the exponent.
  • Plot critical points on a number line before testing signs in a rational or modulus inequality.
  • Write out the first few terms of a log product or surd sum to spot the cancellation pattern.
  • Check the domain of logs and square roots before counting integer solutions.

Who this CAT Algebra practice set is for

It suits CAT and OMET aspirants in the practice stage who know the basic Algebra concepts and want to build speed and accuracy across mixed question types.

FAQs about CAT Algebra Sectional Test 2 – with Solutions

What topics come under Algebra in CAT Quant?
Algebra in CAT Quant usually covers linear and quadratic equations, inequalities, modulus, logarithms, progressions, functions, and surds and indices. Many questions combine two of these ideas in one problem.
How do you find the number of integer solutions of a modulus inequality?
First remove the modulus. If the modulus of x is less than a, x lies between minus a and a, and if it is greater than a, x lies outside that range. Solve for the variable and count the integers in the resulting solution set, including end points only when equality is allowed.
When is the sum of an infinite geometric progression finite?
The sum of an infinite GP is finite only when the absolute value of the common ratio is less than one. The sum then equals the first term divided by one minus the common ratio.
How do you solve exponential equations that look like quadratics?
Replace the repeated power, such as three raised to x, with a single variable so the equation becomes a quadratic. Solve the quadratic, keep only values greater than zero for the power, and convert back to find x.

Test structure

How the paper is split, and how long each part runs. A section you have finished cannot be returned to.

SectionQuestionsTime
CAT Algebra Sectional Test - 22240 min

Marking & rules

Total marks
66 across 22 questions.
Negative marking
A wrong answer costs marks. Leaving a question unanswered costs nothing.
Attempts
100 in total. An attempt is spent the moment you begin one.

What you get when you submit

The analysis is ready the moment you submit the paper.

Score and accuracy

Marks, percentage, right, wrong and skipped, and the time you took.

Section by section

The same figures for each section, so a weak one cannot hide in an average.

The full answer key

Every question with your answer, the right one, the working, and the video where there is one.

Where you stand

Your score against the spread of everyone else who has sat this test.

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