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NTS NAT-IGS Quantitative Reasoning Flashcards
53 question-and-answer cards covering Quantitative Reasoning as it is examined in NTS NAT-IGS. 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.
State the compound interest amount formula for annual compounding.
A = P(1 + R/100)^T, and Compound Interest = A − P.
How is the compound interest formula adjusted for half-yearly and quarterly compounding?
Half-yearly: A = P(1 + R/200)^(2T). Quarterly: A = P(1 + R/400)^(4T) — the rate is divided and the period multiplied by the number of compounding intervals per year.
For the same P, R and T, how do simple and compound interest compare, and what is the 2-year difference?
Compound interest is greater than simple interest (equal only in the first period). For 2 years, CI − SI = P(R/100)².
Expand the identity (a + b)² and (a − b)².
(a + b)² = a² + 2ab + b²; (a − b)² = a² − 2ab + b².
State the identity for a² − b² and for (a + b)(a − b).
a² − b² = (a + b)(a − b); equivalently (a + b)(a − b) = a² − b².
Expand (a + b)³ and (a − b)³.
(a + b)³ = a³ + 3a²b + 3ab² + b³; (a − b)³ = a³ − 3a²b + 3ab² − b³.
State the identities for a³ + b³ and a³ − b³.
a³ + b³ = (a + b)(a² − ab + b²); a³ − b³ = (a − b)(a² + ab + b²).
Expand (x + a)(x + b).
(x + a)(x + b) = x² + (a + b)x + ab.
What is the identity for a² + b² + c² when a + b + c and ab+bc+ca are known?
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca), so a² + b² + c² = (a+b+c)² − 2(ab+bc+ca).
How do you solve a single linear equation in one variable?
Isolate the variable by performing the same operations on both sides (collect variable terms on one side, constants on the other) until the variable is alone.
Name the three algebraic methods for solving a pair of linear equations in two variables.
Substitution, elimination (addition/subtraction), and cross-multiplication.
For two lines a1x+b1y+c1=0 and a2x+b2y+c2=0, what conditions give one, none, or infinitely many solutions?
Unique solution: a1/a2 ≠ b1/b2 (intersecting). No solution: a1/a2 = b1/b2 ≠ c1/c2 (parallel). Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident).
State the standard form of a quadratic equation and the quadratic formula.
Standard form: ax² + bx + c = 0 (a ≠ 0). Roots: x = [−b ± √(b² − 4ac)]/(2a).
What does the discriminant D = b² − 4ac tell you about the roots of a quadratic?
D > 0: two distinct real roots; D = 0: two equal (real) roots; D < 0: no real roots (two complex conjugate roots).
State the sum and product of the roots of ax² + bx + c = 0.
Sum of roots = −b/a; product of roots = c/a.
How do you build a quadratic equation from a given sum S and product P of its roots?
x² − Sx + P = 0, i.e. x² − (sum)x + (product) = 0.
What happens to an inequality when both sides are multiplied or divided by a negative number?
The direction of the inequality sign reverses (e.g. −2x < 6 becomes x > −3).
How do you solve the absolute-value inequality |x| < a (a > 0) and |x| > a?
|x| < a means −a < x < a; |x| > a means x < −a or x > a.
State the product rule, quotient rule, and power rule for exponents.
a^m · a^n = a^(m+n); a^m / a^n = a^(m−n); (a^m)^n = a^(mn).
What are a^0, a^(−n), and a^(1/n) equal to?
a^0 = 1 (a ≠ 0); a^(−n) = 1/a^n; a^(1/n) = the n-th root of a (ⁿ√a).
How do you rationalize a denominator of the form 1/(√a + √b)?
Multiply numerator and denominator by the conjugate (√a − √b), giving (√a − √b)/(a − b).
State the angle sum of a triangle and the exterior angle theorem.
The three interior angles of a triangle sum to 180°. The exterior angle equals the sum of the two non-adjacent (remote) interior angles.
Define complementary, supplementary, and vertically opposite angles.
Complementary angles sum to 90°; supplementary angles sum to 180°; vertically opposite angles (formed by two intersecting lines) are equal.
When a transversal cuts two parallel lines, which angle pairs are equal and which are supplementary?
Corresponding angles and alternate (interior/exterior) angles are equal; co-interior (allied) angles are supplementary, summing to 180°.
What this deck covers
The Quantitative Reasoning deck follows the NTS NAT-IGS Quantitative Reasoning syllabus — 4 chapters and 20 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 13.3 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 89 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 NTS NAT-IGS deck?
53 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these NTS NAT-IGS flashcards free?
Yes. The preview here is free to read with no signup, and the full 53-card deck is free inside the Examius app.
What do the Quantitative Reasoning cards cover?
They follow the NTS NAT-IGS Quantitative Reasoning syllabus — 4 chapters and 20 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.