CAT Algebra Sectional Test 6 – with Solutions

CAT Algebra Practice Test 6: Modulus Graphs, Log Series and Polynomials

CAT Algebra Sectional Test 6 helps a student check whether algebra methods hold up on unfamiliar CAT-style problems. This Aptitude360 set covers simultaneous equations, quadratic roots, integer-coefficient polynomials, modulus regions, logarithm series, factorial sums and functions. Full written solutions show a method for every problem.

Areas covered in Algebra Sectional Test 6

• Conditions for a unique solution of simultaneous linear equations
• Quadratics whose roots are consecutive even integers and divisibility rules for integer polynomials
• Minimising total distance along a road and areas or lattice points of modulus regions
• Sums of reciprocal logarithms and floor values of logarithms
• Series with repeated digits, factorial-weighted terms and last digits of a surd's power
• Fractional part, linear composition and recursively defined functions
• Maximum of expressions under a quadratic constraint and splitting into odd piles for maximum product

Algebra rules useful for this set

• Reciprocal log: \( \dfrac{1}{\log_{a}N}=\log_{N}a \)
• Log sum: \( \log_{N}a+\log_{N}b=\log_{N}(ab) \)
• Integer polynomial: \( (a-b) \) divides \( P(a)-P(b) \)
• Unique solution of two lines: \( a_{1}b_{2}-a_{2}b_{1}\neq 0 \)
• If \( f(x)=ax+b \): \( f(f(x))=a^{2}x+ab+b \)

Revision tips for advanced CAT algebra

• Draw modulus regions on rough paper; most turn out to be squares, rhombuses or hexagons.
• To minimise the sum of distances from points on a line, place the point at the median.
• For integers a and b and a whole number n, the nth power of a plus root b added to the nth power of a minus root b is always an integer; use this to find the integer part of a surd's power.

Who should take Test 6

Suited to CAT and OMET aspirants in the final practice phase who want to stress-test algebra on less routine problems.