NTS NAT-IE Quantitative Reasoning Syllabus

Define Cost Price (CP), Selling Price (SP), Profit and Loss.

CP is the price at which an item is bought; SP is the price at which it is sold. Profit = SP − CP (when SP > CP); Loss = CP − SP (when CP > SP).

What are the formulas for Profit% and Loss%?

Profit% = (Profit ÷ CP) × 100; Loss% = (Loss ÷ CP) × 100. Both percentages are always calculated on the Cost Price.

How do you find SP from CP given a profit or loss percentage?

SP = CP × (100 + Profit%)/100 for a profit; SP = CP × (100 − Loss%)/100 for a loss.

What is the formula for discount and the relationship between Marked Price, Discount and Selling Price?

Discount = Marked Price × Discount%/100, and Selling Price = Marked Price − Discount. Discount is always calculated on the Marked (list) Price.

State the simple interest formula and the total amount formula.

Simple Interest (SI) = (P × R × T) ÷ 100, where P = principal, R = rate per year, T = time in years. Amount A = P + SI.

State the compound interest formula for the final amount, compounded annually.

A = P(1 + R/100)^T, where P = principal, R = annual rate, T = time in years. Compound Interest = A − P.

What is the key difference between simple 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.

How is the compound interest formula adjusted when interest is compounded n times per year?

A = P(1 + R/(100n))^(nT), where n is the number of compounding periods per year (e.g., n = 2 for half-yearly, 4 for quarterly).

State the fundamental relationship between speed, distance and time.

Speed = Distance ÷ Time; Distance = Speed × Time; Time = Distance ÷ Speed.

How do you convert km/h to m/s and m/s to km/h?

km/h → m/s: multiply by 5/18. m/s → km/h: multiply by 18/5.

What is the average speed for a journey covering different distances at different speeds?

Average speed = (total distance) ÷ (total time taken), not the simple average of the individual speeds.

For two objects moving toward each other vs. in the same direction, what relative speed do you use?

Toward each other (opposite directions): relative speed = sum of speeds. Same direction: relative speed = difference of speeds.

What is a like term in algebra, and can like terms be combined?

Like terms have identical variable parts with the same exponents (e.g., 3x² and −5x²). They can be combined by adding/subtracting their coefficients; unlike terms cannot.

State the identity 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).

(a + b)(a − b) = a² − b² (the difference of two squares).

State the identities for a³ + b³ and a³ − b³.

a³ + b³ = (a + b)(a² − ab + b²); a³ − b³ = (a − b)(a² + ab + b²).

State the expansion of (a + b + c)².

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.

What is a linear equation in one variable and what does its solution represent?

An equation of the form ax + b = 0 (a ≠ 0) where the highest power of the variable is 1. Its solution x = −b/a is the single value that makes the equation true.

What does the slope-intercept form y = mx + c tell you about a line?

m is the slope (rate of change / steepness) and c is the y-intercept (where the line crosses the y-axis at x = 0).

How many solutions can a system of two linear equations in two variables have, and what does each case mean graphically?

One solution (lines intersect at a point), no solution (parallel lines), or infinitely many solutions (the same line / coincident lines).

What is the standard (general) form of a quadratic equation?

ax² + bx + c = 0, where a, b, c are constants and a ≠ 0.

State the quadratic formula for solving ax² + bx + c = 0.

x = [−b ± √(b² − 4ac)] ÷ (2a).

What is the discriminant of a quadratic, and what do its values reveal about the roots?

Discriminant D = b² − 4ac. If D > 0: two distinct real roots; D = 0: one real (repeated) root; D < 0: no real roots (two complex 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.

State the laws of exponents for a^m × a^n, a^m ÷ a^n, and (a^m)^n.

a^m × a^n = a^(m+n); a^m ÷ a^n = a^(m−n); (a^m)^n = a^(mn).

What do a^0 and a^(−n) equal (a ≠ 0)?

a^0 = 1 and a^(−n) = 1/a^n (a negative exponent gives the reciprocal).

How is a fractional exponent a^(m/n) expressed as a radical?

a^(m/n) = the n-th root of a^m = (ⁿ√a)^m. For example, a^(1/2) = √a and a^(3/2) = √(a³).

State the rules for multiplying and dividing radicals (same index).

√a × √b = √(ab) and √a ÷ √b = √(a/b), provided a, b ≥ 0 (and b ≠ 0 for division).

Define complementary, supplementary, and vertically opposite angles.

Complementary angles sum to 90°; supplementary angles sum to 180°; vertically opposite angles are formed by two intersecting lines and are equal to each other.

When a transversal cuts two parallel lines, what is the relationship between corresponding angles, alternate angles, and co-interior angles?

Corresponding angles are equal; alternate (interior and exterior) angles are equal; co-interior (allied) angles are supplementary (sum to 180°).