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NTS NAT-IM Quantitative Reasoning Flashcards
50 question-and-answer cards covering Quantitative Reasoning as it is examined in NTS NAT-IM. 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 is the formula for compound interest amount, and how is CI found?
Amount A = P(1 + R/100)ⁿ, where n is the number of compounding periods. Compound Interest = A − P.
What is the key difference between simple interest and compound interest?
Simple interest is calculated only on the original principal each period. Compound interest is calculated on the principal plus accumulated interest, so it grows faster than simple interest.
For compound interest compounded half-yearly, how do you adjust rate and time?
Halve the annual rate and double the number of periods: rate becomes R/2 per period and time becomes 2T periods, so A = P(1 + R/200)^(2T).
For the same P, R, and T = 2 years, what is the difference between CI and SI?
CI − SI for 2 years = P × (R/100)². The extra amount equals the interest on the first year's interest.
What is the difference between a term, a coefficient, and a constant in an algebraic expression?
A term is a single number/variable or their product (e.g., 3x²). A coefficient is the numerical factor of a term (3 in 3x²). A constant is a term with no variable (a fixed number).
What are like terms, and why do they matter in simplification?
Like terms have the same variables raised to the same powers (e.g., 4x and 7x). Only like terms can be combined (added or subtracted) when simplifying expressions.
State the algebraic identities for (a+b)² and (a−b)².
(a+b)² = a² + 2ab + b². (a−b)² = a² − 2ab + b².
State the identity for (a+b)(a−b) and for a³+b³, a³−b³.
(a+b)(a−b) = a² − b². a³ + b³ = (a+b)(a² − ab + b²). a³ − b³ = (a−b)(a² + ab + b²).
Expand (a+b)³ and (a−b)³.
(a+b)³ = a³ + 3a²b + 3ab² + b³. (a−b)³ = a³ − 3a²b + 3ab² − b³.
What is a linear equation in one variable, and how is it solved?
A linear equation in one variable has the form ax + b = 0 (highest power of x is 1). Solve by isolating x: x = −b/a, performing the same operations on both sides.
What does the graph of a linear equation in two variables represent, and what is slope-intercept form?
It represents a straight line. Slope-intercept form is y = mx + c, where m is the slope (rate of change) and c is the y-intercept (where the line crosses the y-axis).
What are the methods to solve a pair of simultaneous linear equations?
Substitution, elimination, cross-multiplication, and graphical methods. Substitution solves one equation for a variable; elimination adds/subtracts equations to remove a variable.
How many solutions does a pair of linear equations have based on their coefficients a₁/a₂, b₁/b₂, c₁/c₂?
Unique solution if a₁/a₂ ≠ b₁/b₂ (intersecting lines). Infinitely many if a₁/a₂ = b₁/b₂ = c₁/c₂ (coincident). No solution if a₁/a₂ = b₁/b₂ ≠ c₁/c₂ (parallel).
What is the standard form of a quadratic equation?
ax² + bx + c = 0, where a, b, c are constants and a ≠ 0. The highest power of the variable is 2.
State the quadratic formula for solving ax² + bx + c = 0.
x = [−b ± √(b² − 4ac)] ÷ (2a). The roots are the two values of x that satisfy the equation.
What is the discriminant of a quadratic, and what does it reveal about the roots?
Discriminant D = b² − 4ac. If D > 0: two distinct real roots. If D = 0: two equal real roots. If D < 0: no real roots (complex roots).
For ax² + bx + c = 0, what are the sum and product of the roots?
Sum of roots = −b/a. Product of roots = c/a. (For roots α and β: α+β = −b/a, αβ = c/a.)
State the product, quotient, and power rules of exponents.
Product: aᵐ × aⁿ = aᵐ⁺ⁿ. Quotient: aᵐ ÷ aⁿ = aᵐ⁻ⁿ. Power of a power: (aᵐ)ⁿ = aᵐⁿ.
What do a negative exponent and a fractional exponent mean?
Negative exponent: a⁻ⁿ = 1/aⁿ. Fractional exponent: a^(m/n) = ⁿ√(aᵐ), the nth root of a raised to the m power.
How do you simplify or rationalize a radical such as 1/√a?
Multiply numerator and denominator by √a: 1/√a = √a/a. Rationalizing removes the radical from the denominator. Also, √a × √b = √(ab).
What happens to the inequality sign when both sides are multiplied or divided by a negative number?
The inequality sign reverses (flips) direction. E.g., if −2x < 6, dividing by −2 gives x > −3.
What is the difference between the symbols <, ≤, and the open vs closed circle on a number line?
< (strictly less than) and > use an open circle (endpoint excluded). ≤ and ≥ use a closed/filled circle (endpoint included). Open means the boundary value is not part of the solution.
What is the relationship between 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 always equal.
When a transversal cuts two parallel lines, what is the relationship between corresponding, alternate, and co-interior angles?
Corresponding angles are equal. Alternate (interior and exterior) angles are equal. Co-interior (allied/same-side interior) angles are supplementary (sum to 180°).
What this deck covers
The Quantitative Reasoning deck follows the NTS NAT-IM Quantitative Reasoning syllabus — 5 chapters and 22 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 10.0 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 127 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-IM 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 NTS NAT-IM 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 NTS NAT-IM Quantitative Reasoning syllabus — 5 chapters and 22 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.