LUMS LCAT Quantitative Reasoning — Advanced Mathematics
Advanced Mathematics is a Quantitative Reasoning topic on the LUMS Admission Test, covering 6 subtopics. We hold 311 practice MCQs on it, each with a written explanation of why the right answer is right. The subtopics, how often it appears in the sample papers, and worked questions are below.
Subtopics (6)
- Exponents and Radicals 56
- Logarithms 54
- Nonlinear Functions 32
- Polynomial Expressions 32
- Quadratic Equations and Functions 80
- Rational Expressions and Equations 54
How Advanced Mathematics is tested
Across the 8 LCAT sample papers on ParhaiKrlo, Advanced Mathematics accounts for 80 questions. It appears in all 8, about 10 questions a paper. The heaviest was LUMS Sample Paper 1, with 11 questions.
| Paper | Questions |
|---|---|
| LUMS Sample Paper 1 | 11 |
| LUMS Sample Paper 2 | 11 |
| LUMS Sample Paper 3 | 11 |
| LUMS Sample Paper 4 | 11 |
| LUMS Sample Paper 5 | 11 |
| LUMS Sample Paper 6 | 11 |
| LUMS Sample Paper 7 | 11 |
| LUMS Sample Past Paper | 3 |
Advanced Mathematics MCQs from the LCAT sample papers
Try each one before opening the answer. Each comes with a short explanation.
- Q1 · LUMS Sample Past Paper · Advanced Mathematics
A company models its profit, P, in thousands of dollars, based on the number of products sold, x, in thousands, with the equation P(x) = x² - 3x + 2. Determine the number of thousands of products the company must sell to break even (profit of 0).
- A.1 thousand products
- B.2 thousand products
- C.3 thousand products
- D.Both options A) and B) are correct
Show answer
Answer: D. Both options A) and B) are correct — Break-even means P(x)=0. Factoring x²-3x+2=(x-1)(x-2)=0 gives x=1 or x=2, so D (both A and B) is correct.
- Q2 · LUMS Sample Paper 1 · Advanced Mathematics
If x² - 13x + 40 = 0 factors as (x - p)(x - q), what is the value of p + q?
- A.13
- B.-13
- C.40
- D.-40
Show answer
Answer: A. 13 — (A): the factored roots are 5 and 8, so p + q = 13.
- Q3 · LUMS Sample Paper 2 · Advanced Mathematics
The equation x² + kx + 63 = 0 has roots 7 and 9. What is the value of k?
- A.-16
- B.16
- C.-63
- D.63
Show answer
Answer: A. -16 — k = -16 (A).