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🇵🇰 COMSATS NTS-based Test · flashcards
COMSATS NTS-based Test Quantitative Reasoning Flashcards
50 question-and-answer cards covering Quantitative Reasoning as it is examined in COMSATS NTS-based Test. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Quantitative Reasoning deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
What does it mean if a system of linear equations has no solution or infinitely many solutions?
No solution: lines are parallel (same slope, different intercepts). Infinitely many: lines are identical (coincident).
What is the standard form of a quadratic equation?
ax² + bx + c = 0, where a ≠ 0.
State the quadratic formula for solving ax² + bx + c = 0.
x = [−b ± √(b² − 4ac)] / (2a).
What is the discriminant and what does it tell you about the roots?
Discriminant D = b² − 4ac. D > 0: two distinct real roots; D = 0: one repeated real root; D < 0: two complex (no real) roots.
What are the sum and product of the roots of ax² + bx + c = 0?
Sum of roots = −b/a; product of roots = c/a.
What does it mean to solve a quadratic by factoring?
Write ax² + bx + c = 0 as (px + q)(rx + s) = 0, then set each factor to zero (zero-product property) and solve for x.
What is the difference between an expression and an equation?
An expression is a combination of terms with no equals sign (e.g., 3x + 2). An equation states two expressions are equal (e.g., 3x + 2 = 8) and can be solved.
State the identity for the difference of two squares.
a² − b² = (a + b)(a − b).
State the expansions of (a + b)² and (a − b)².
(a + b)² = a² + 2ab + b²; (a − b)² = a² − 2ab + b².
How do you factor a quadratic trinomial x² + bx + c?
Find two numbers whose product is c and whose sum is b; then x² + bx + c = (x + p)(x + q) where p + q = b and pq = c.
State the sum and difference of cubes factorization formulas.
a³ + b³ = (a + b)(a² − ab + b²); a³ − b³ = (a − b)(a² + ab + b²).
What happens to an inequality when you multiply or divide both sides by a negative number?
The inequality sign reverses (e.g., −2x > 6 becomes x < −3).
How do you express the solution set of a linear inequality on a number line?
Use an open circle for strict inequalities (< or >) and a closed/filled circle for inclusive ones (≤ or ≥), shading toward the satisfying values.
How do you solve a compound inequality such as a < x + b < c?
Perform the same operation on all three parts simultaneously to isolate x while keeping the inequalities aligned.
State the basic laws of exponents for multiplication, division, and power of a power.
a^m · a^n = a^(m+n); a^m / a^n = a^(m−n); (a^m)^n = a^(mn).
What do a⁰, a^(−n), and a^(1/n) equal?
a⁰ = 1 (a ≠ 0); a^(−n) = 1/a^n; a^(1/n) = ⁿ√a (the nth root of a).
What is a surd, and what does it mean to rationalize the denominator?
A surd is an irrational root that cannot be simplified to a rational number (e.g., √2, √5). Rationalizing means removing the surd from the denominator, e.g., multiply by the conjugate so the denominator becomes rational.
How do you simplify √(ab) and √(a/b)?
√(ab) = √a · √b and √(a/b) = √a / √b (for a, b ≥ 0, b ≠ 0).
What is the sum of interior angles of a triangle, and of a polygon with n sides?
Triangle: 180°. Polygon with n sides: (n − 2) × 180°.
State the Pythagorean theorem.
In a right-angled triangle, the square of the hypotenuse equals the sum of squares of the other two sides: a² + b² = c² (c is the hypotenuse).
What are the area formulas for a triangle, rectangle, and circle?
Triangle = ½ × base × height; Rectangle = length × width; Circle = πr².
What is the circumference of a circle and the relationship between radius and diameter?
Circumference = 2πr = πd, where diameter d = 2r.
What is the distance formula between two points (x₁, y₁) and (x₂, y₂)?
Distance = √[(x₂ − x₁)² + (y₂ − y₁)²].
What are the midpoint and slope formulas for a line segment between (x₁, y₁) and (x₂, y₂)?
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2); Slope m = (y₂ − y₁)/(x₂ − x₁).
What this deck covers
The Quantitative Reasoning deck follows the COMSATS NTS-based Test Quantitative Reasoning syllabus — 6 chapters and 26 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 8.3 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 84 characters, which is long enough to carry the reasoning and short enough to say out loud.
A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.
Quantitative Reasoning flashcards FAQ
How many Quantitative Reasoning flashcards are in this COMSATS NTS-based Test deck?
50 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these COMSATS NTS-based Test flashcards free?
Yes. The preview here is free to read with no signup, and the full 50-card deck is free inside the Examius app.
What do the Quantitative Reasoning cards cover?
They follow the COMSATS NTS-based Test Quantitative Reasoning syllabus — 6 chapters and 26 topics — so the questions track what is actually examinable.
How should I use these flashcards?
Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.