Mixed Practice
Mixed practice builds exam readiness by exposing you to all algebra topic types in random order, mimicking real aptitude exam conditions.
Essential Formulation Tips
- Quickly identify the topic of each question before starting.
- Use elimination for linear systems, factoring for quadratics.
- Apply Vieta's formulas when sum/product of roots are needed without solving.
- For word problems: define variable → write equation → solve → verify.
Shortcut Execution Techniques
- AM ≥ GM: (a+b)/2 ≥ √ab for all non-negative a, b.
- If f(a) = f(b) for a symmetric function, then a = ±b.
- (a+b)² - (a-b)² = 4ab.
- For any linear system: if lines are parallel, no solution; if same line, infinite solutions.
Contextual Inquiries (FAQs)
Q: How should I approach a mixed test?
A: Scan all questions first, answer the ones you know quickly, then spend more time on harder ones.
Q: What is the most tested algebra topic in aptitude exams?
A: Linear equations and quadratic equations appear most frequently, followed by word problems.
No structural solved cases documented for this level module.
Mixed Practice Set 1
A balanced mix of all algebra topics — basic to intermediate level.
Q1. Solve: 4x - 3 = 2x + 9.
Q2. Find the roots of x² - 8x + 15 = 0.
Q3. Expand (2x + 3)².
Q4. If p(x) = x³ - 2x + 1, find the remainder when divided by (x - 1).
Q5. Solve: -4x + 5 > 13.
Q6. If f(x) = x² - 1 and g(x) = x + 2, find (g ∘ f)(3).
Q7. A father is 30 years older than his son. In 5 years, he will be twice as old. Find son's current age.
Q8. If a + b = 8 and ab = 15, find a² + b².
Q9. Which of these is always true for any real a: a² + 1 > ?
Q10. Find the inverse of f(x) = 4x - 7.