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SNAP Quantitative Ability Syllabus
The Quantitative Ability syllabus for SNAP in full: 5 chapters, 27 topics and 43 sub-topics, every one listed below, plus 53 Quantitative Ability flashcards with answers.
Quantitative Ability syllabus: all 5 chapters
Expand any chapter to see its topics and sub-topics.
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Arithmetic
7 topics- Percentages
- Successive percentage change
- Applications in profit and population
- Profit, Loss and Discount
- Cost price, selling price and marked price
- Successive discounts
- Simple and Compound Interest
- Difference between SI and CI
- Equated installments
- Ratio, Proportion and Variation
- Direct and inverse proportion
- Componendo and dividendo
- Averages, Mixtures and Alligation
- Weighted averages
- Alligation rule
- Time, Speed and Distance
- Relative speed
- Trains, boats and streams
- Circular and linear races
- Time and Work
- Work efficiency and rate
- Pipes and cisterns
- Percentages
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Algebra
6 topics- Linear and Quadratic Equations
- Roots, nature and sum-product relations
- Word problems on equations
- Inequalities and Modulus
- Functions and Graphs
- Domain, range and composite functions
- Logarithms
- Laws of logarithms
- Progressions
- Arithmetic progression
- Geometric and harmonic progression
- Surds and Indices
- Linear and Quadratic Equations
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Geometry and Mensuration
5 topics- Lines, Angles and Triangles
- Properties of triangles and congruence
- Similarity and theorems
- Polygons and Circles
- Quadrilateral properties
- Tangents, chords and arcs
- Coordinate Geometry
- Distance, section and midpoint formulae
- Equation of a line and slope
- Mensuration
- Areas of 2D figures
- Surface area and volume of solids
- Trigonometry Basics
- Trigonometric ratios and identities
- Heights and distances
- Lines, Angles and Triangles
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Number System
5 topics- Classification of Numbers
- Natural, integer, rational and real numbers
- Factors and Multiples
- HCF and LCM
- Number of factors and their sum
- Divisibility and Remainders
- Divisibility rules
- Remainder theorems and cyclicity
- Unit Digit and Last Digits
- Base System
- Conversion between bases
- Classification of Numbers
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Modern Mathematics
4 topics- Permutations and Combinations
- Arrangements and selections
- Circular permutations
- Probability
- Classical probability
- Conditional probability and events
- Set Theory
- Venn diagrams
- Union, intersection and complement
- Binomial Theorem
- Permutations and Combinations
SNAP Quantitative Ability flashcards — 53 questions with answers
How do you convert a percentage increase from value A to value B into a formula, and what is the result if a price rises from 80 to 100?
Percentage change = ((B − A)/A) × 100. From 80 to 100: ((100−80)/80)×100 = 25% increase.
If a quantity increases by x% and then decreases by x%, what is the net percentage change?
A net decrease of (x²/100)%. The two changes never cancel; the result is always lower than the original.
What is the formula for Profit %, and what does it tell you?
Profit % = (Profit / Cost Price) × 100. It expresses gain as a fraction of the cost price (not the selling price).
How are Selling Price (SP), Marked Price (MP) and Discount related?
SP = MP × (1 − Discount%/100). Discount is always calculated on the Marked Price, not on the Cost Price.
A shopkeeper gives two successive discounts of a% and b%. What single equivalent discount do they represent?
Equivalent discount = a + b − (ab/100) percent.
What is the Simple Interest formula, and what does each symbol mean?
SI = (P × R × T)/100, where P = principal, R = rate % per annum, T = time in years.
What is the Compound Interest amount formula for annual compounding?
A = P(1 + R/100)^T, and CI = A − P, where P = principal, R = annual rate %, T = years.
For 2 years, by how much does Compound Interest exceed Simple Interest on the same principal and rate?
CI − SI (2 years) = P × (R/100)². This difference equals the interest earned on the first year's interest.
What does the ratio a : b mean, and how do you find the value of each part if a:b = 3:5 and the total is 64?
a:b means a/b = 3/5. Total parts = 3+5 = 8; each part = 64/8 = 8, so a = 24 and b = 40.
State the relationship in a proportion a : b :: c : d and the property it satisfies.
a/b = c/d, meaning the product of the means equals the product of the extremes: a × d = b × c.
Define direct variation and inverse variation.
Direct: y = kx (y increases as x increases, ratio constant). Inverse: y = k/x (y decreases as x increases, product constant).
What is the formula for the average (arithmetic mean) of n quantities?
Average = (Sum of all quantities) / (Number of quantities). Equivalently, Sum = Average × n.
State the alligation rule for mixing two ingredients to get a desired mean price.
(Quantity of cheaper)/(Quantity of dearer) = (Price of dearer − Mean price)/(Mean price − Price of cheaper).
A vessel has milk and water in ratio. What is the formula for milk left after one of n repeated replacements of x from a volume V?
Milk left = V × (1 − x/V)^n, after each operation removing x and replacing with water.
What is the basic relationship between speed, distance and time, including the unit conversion from km/h to m/s?
Speed = Distance/Time. To convert km/h to m/s, multiply by 5/18; m/s to km/h, multiply by 18/5.
What is the formula for average speed when equal distances are covered at speeds u and v?
Average speed = 2uv/(u + v), the harmonic mean of the two speeds (not the simple average).
For two trains crossing each other, how does relative speed differ for same vs opposite directions?
Opposite directions: relative speed = sum of speeds. Same direction: relative speed = difference of speeds.
In Time and Work, if A completes a job in n days, what is A's one-day work, and how is combined work found?
A's one-day work = 1/n. If A does 1/a and B does 1/b per day, together they do (1/a + 1/b) per day; time = 1/(1/a+1/b).
State the relationship between the roots and coefficients of ax² + bx + c = 0.
Sum of roots = −b/a; Product of roots = c/a.
What is the quadratic formula and what does the discriminant indicate?
x = (−b ± √(b²−4ac))/2a. Discriminant D = b²−4ac: D>0 two real distinct roots, D=0 equal real roots, D<0 complex roots.
Show the other 33 Quantitative Ability flashcards
When solving inequalities, what operation reverses the inequality sign?
Multiplying or dividing both sides by a negative number reverses the inequality sign (e.g. −2x > 6 becomes x < −3).
How do you solve the modulus inequality |x| < a (a > 0) and |x| > a?
|x| < a means −a < x < a. |x| > a means x < −a or x > a.
What is the definition of a function, and how do you determine if a graph represents one?
A function maps each input to exactly one output. The vertical line test: any vertical line meets the graph at most once.
What do f(x) + k, f(x + k), and f(−x) do to the graph of f(x)?
f(x)+k shifts up by k; f(x+k) shifts left by k; f(−x) reflects across the y-axis.
State the definition of a logarithm: what does log_b(x) = y mean?
log_b(x) = y means b^y = x, where b > 0, b ≠ 1, and x > 0.
State the three core logarithm laws (product, quotient, power).
log(mn) = log m + log n; log(m/n) = log m − log n; log(m^k) = k·log m.
What is the change of base formula for logarithms?
log_b(x) = log_c(x) / log_c(b), allowing conversion to any convenient base c (commonly 10 or e).
What is the nth term and sum of an Arithmetic Progression with first term a and common difference d?
nth term: a_n = a + (n−1)d. Sum: S_n = (n/2)[2a + (n−1)d] = (n/2)(first + last term).
What is the nth term and sum of a Geometric Progression with first term a and common ratio r?
nth term: a_n = a·r^(n−1). Sum (r≠1): S_n = a(r^n − 1)/(r − 1). Infinite sum (|r|<1): S = a/(1 − r).
What is the sum of the first n natural numbers, their squares, and their cubes?
Σn = n(n+1)/2; Σn² = n(n+1)(2n+1)/6; Σn³ = [n(n+1)/2]².
State the key laws of indices 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). Also a^0 = 1 and a^(−n) = 1/a^n.
How do you rationalise a denominator of the form 1/(√a + √b)?
Multiply numerator and denominator by the conjugate (√a − √b): 1/(√a+√b) = (√a−√b)/(a − b).
State the angle-sum property of a triangle and the exterior angle theorem.
The three interior angles of a triangle sum to 180°. An exterior angle equals the sum of the two non-adjacent (remote) interior angles.
State the Pythagorean theorem and name three common Pythagorean triples.
In a right triangle, hypotenuse² = base² + height². Triples: (3,4,5), (5,12,13), (8,15,17).
What is the formula for the sum of interior angles of a polygon with n sides, and each interior angle if regular?
Sum of interior angles = (n − 2) × 180°. Each interior angle of a regular polygon = (n−2)×180°/n.
State the inscribed angle theorem and the angle in a semicircle.
The angle subtended by an arc at the centre is twice that subtended at any point on the remaining circumference. The angle in a semicircle is 90°.
What is the distance formula and the midpoint formula between points (x₁,y₁) and (x₂,y₂)?
Distance = √[(x₂−x₁)² + (y₂−y₁)²]. Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2).
What is the slope of a line through two points, and the condition for two lines to be perpendicular?
Slope m = (y₂−y₁)/(x₂−x₁). Two lines are perpendicular when m₁ × m₂ = −1; parallel when m₁ = m₂.
State the area and circumference/perimeter formulas for a circle.
Area = πr²; Circumference = 2πr, where r is the radius.
State the formulas for the volume and total surface area of a cylinder.
Volume = πr²h; Total Surface Area = 2πr(r + h), where r = radius, h = height.
State the volume and total surface area of a sphere of radius r.
Volume = (4/3)πr³; Surface Area = 4πr².
State the three basic trigonometric ratios in a right triangle.
sin θ = Opposite/Hypotenuse; cos θ = Adjacent/Hypotenuse; tan θ = Opposite/Adjacent = sin θ/cos θ.
State the fundamental Pythagorean trigonometric identity and the values of sin and cos at 0°, 30°, 45°, 60°, 90°.
sin²θ + cos²θ = 1. sin: 0, 1/2, 1/√2, √3/2, 1. cos: 1, √3/2, 1/√2, 1/2, 0.
Classify numbers: what distinguishes rational, irrational, prime, and composite numbers?
Rational: expressible as p/q (q≠0). Irrational: not expressible as a fraction (e.g. √2, π). Prime: exactly two factors. Composite: more than two factors.
How do you find the total number of factors of a number from its prime factorisation p^a · q^b · r^c?
Number of factors = (a+1)(b+1)(c+1). Their sum = (p^(a+1)−1)/(p−1) × similar terms for each prime.
State the relationship between HCF, LCM, and the product of two numbers.
HCF × LCM = Product of the two numbers (holds only for exactly two numbers).
State the divisibility rules for 3, 9, and 11.
Divisible by 3: digit sum divisible by 3. By 9: digit sum divisible by 9. By 11: difference of sums of alternate digits is 0 or divisible by 11.
What is the unit (last) digit cycle of powers of 2, and how do you find the unit digit of 2^n?
Powers of 2 cycle every 4: 2,4,8,6. Find n mod 4 (using 4 if remainder is 0) and pick the corresponding digit.
In a base system, what is the place value of a digit, and how do you convert a base-b number to decimal?
Each digit's value = digit × b^(position index from right, starting at 0). Sum these products to get the decimal value.
What is the difference between Permutations and Combinations, with their formulas?
Permutations (order matters): nPr = n!/(n−r)!. Combinations (order doesn't matter): nCr = n!/[r!(n−r)!].
State the classical probability formula and the addition rule P(A∪B).
P(E) = favourable outcomes / total outcomes. P(A∪B) = P(A) + P(B) − P(A∩B); for mutually exclusive events P(A∩B)=0.
State the Set Theory inclusion-exclusion formula for n(A∪B) and n(A∪B∪C).
n(A∪B) = n(A) + n(B) − n(A∩B). n(A∪B∪C) = n(A)+n(B)+n(C) − n(A∩B) − n(B∩C) − n(A∩C) + n(A∩B∩C).
State the general term in the Binomial Theorem expansion of (a + b)^n.
The (r+1)th term: T_(r+1) = nCr · a^(n−r) · b^r, for r = 0 to n. Total number of terms = n + 1.
SNAP Quantitative Ability FAQ
What is in the SNAP Quantitative Ability syllabus?
SNAP Quantitative Ability is split into 5 chapters: Arithmetic, Algebra, Geometry and Mensuration, Number System and Modern Mathematics. Together they contain 27 topics and 43 sub-topics.
How many chapters are in SNAP Quantitative Ability?
5 chapters, containing 27 topics and 43 sub-topics. The largest chapter is Arithmetic, with 7 topics.
Are there flashcards for SNAP Quantitative Ability?
Yes — a 53-card Quantitative Ability deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.