What strong algebra looks like in TMUA
The \(CF\) Maths algebra notes emphasise structural moves before calculation: rewrite composite bases in primes, substitute a repeated rational power, use a discriminant for parameter conditions, factor in the substituted variable and preserve every domain restriction.
Questions with modulus or radicals often become much easier after identifying the breakpoints or the non-negative quantity. Polynomial questions often reward factor/remainder structure or a root-count argument rather than full expansion.
Common traps
Do not add \(a \pm \) sign to a principal square root; do not keep extraneous roots after squaring; do not clear a denominator without recording where it is zero; and do not assume a condition on the original exponents before fully simplifying a prime-factor expression.
For functions, distinguish the equation \(f(f(x))=0\) from \(f(x)=0\), and remember that a transformation such as \(f(|x|)\) samples only the non-negative input side of the original graph.
FREE PRACTICE
Try these TMUA-style questions
These questions now draw from the current reviewed CF Maths banks, including image and diagram items where appropriate. Open the solution only after you have committed to a route.
QUESTION 1 · Algebraic modelling & equationsShow answer & route
Answer: B
Correct answer: \(B\). This item is marked from the validated final 200-question answer key. Revision method: Algebraic modelling & equations. Rework the displayed question carefully and compare your algebra with the keyed option.
Show answer & route
Answer: B
Correct answer: \(B\). This item is marked from the validated final 200-question answer key. Revision method: Polynomial roots & factors. Rework the displayed question carefully and compare your algebra with the keyed option.
Show answer & route
Answer: C
Correct answer: \(C\). This item is marked from the validated final 200-question answer key. Revision method: Functions & transformations. Rework the displayed question carefully and compare your algebra with the keyed option.
Show answer & route
Answer: C
Correct answer: \(C\). This item is marked from the validated final 200-question answer key. Revision method: Floor & ceiling functions. Rework the displayed question carefully and compare your algebra with the keyed option.
Show answer & route
Answer: D
Correct answer: \(D\). This item is marked from the validated final 200-question answer key. Revision method: Algebraic modelling & equations. Rework the displayed question carefully and compare your algebra with the keyed option.
Show answer & route
Answer: C
Correct answer: \(C\). This item is marked from the validated final 200-question answer key. Revision method: Algebraic modelling & equations. Rework the displayed question carefully and compare your algebra with the keyed option.
Show answer & route
Answer: C
Correct answer: \(C\). This item is marked from the validated final 200-question answer key. Revision method: Algebraic modelling & equations. Rework the displayed question carefully and compare your algebra with the keyed option.
Show answer & route
Answer: B
Correct answer: \(B\). This item is marked from the validated final 200-question answer key. Revision method: Polynomial roots & factors. Rework the displayed question carefully and compare your algebra with the keyed option.
