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🇮🇳 ICSE Class 10 · subject
ICSE Class 10 Mathematics Syllabus
The Mathematics syllabus for ICSE Class 10 in full: 1 chapter and 5 topics, every one listed below, plus 50 Mathematics flashcards with answers.
Mathematics syllabus: 1 chapter, 5 topics
Expand any chapter to see its topics and sub-topics.
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ICSE Mathematics
5 topics- Commercial Mathematics
- Algebra
- Geometry
- Mensuration
- Statistics
ICSE Class 10 Mathematics flashcards — 50 questions with answers
In Compound Interest, what is the formula for the amount A when interest is compounded annually for n years at rate R% on principal P?
A = P(1 + R/100)^n. Compound Interest = A − P.
How do you compute compound interest when it is compounded half-yearly at R% per annum for n years?
Use A = P(1 + (R/2)/100)^(2n); i.e. halve the rate and double the number of conversion periods. CI = A − P.
What is the formula for the value of an article after n years if it depreciates at R% per annum?
Depreciated value = P(1 − R/100)^n, where P is the original cost.
How is GST (Goods and Services Tax) split, and how is it calculated on intra-state sale of an article of value V at rate r%?
For intra-state sale, GST = CGST + SGST, each at r/2%. Total GST = V × r/100. For inter-state sale, IGST = V × r/100 is charged instead.
In GST, what is Input Tax Credit (ITC) and how does it determine a dealer's net GST payable?
ITC is the GST a dealer already paid on purchases. Net GST payable = Output GST (on sales) − Input GST (on purchases / ITC).
What is the maturity value formula for a Recurring Deposit of monthly instalment P for n months at R% per annum simple interest?
Interest I = P × [n(n+1)/2] × (R/100) × (1/12); Maturity Value = P×n + I.
For shares: define Nominal (Face) Value, Market Value, and Dividend.
Nominal/Face Value (NV) is the printed value of a share. Market Value (MV) is the price it trades at. Dividend is the profit paid per share, calculated as a percentage of the FACE value, not the market value.
How do you find the annual income and the rate of return (yield) from shares?
Income = Number of shares × Face value × Dividend%. Number of shares = Investment ÷ Market value. Yield% = (Annual income ÷ Investment) × 100.
State the quadratic formula for solving ax² + bx + c = 0.
x = [−b ± √(b² − 4ac)] / (2a), valid for a ≠ 0.
What does the discriminant D = b² − 4ac tell you about the roots of a quadratic equation?
If D > 0: two distinct real roots; if D = 0: two equal (real, coincident) roots; if D < 0: no real roots (roots are imaginary).
State the Factor Theorem and the Remainder Theorem for a polynomial p(x).
Remainder Theorem: when p(x) is divided by (x − a), the remainder is p(a). Factor Theorem: (x − a) is a factor of p(x) if and only if p(a) = 0.
What is the condition for two ratios a:b and c:d to be in proportion, and what are the means and extremes?
They are in proportion if a:b :: c:d, i.e. a/b = c/d, equivalently ad = bc (product of extremes a, d = product of means b, c).
Define the third proportional, fourth proportional, and mean proportional.
Fourth proportional of a, b, c is x where a:b = c:x. Third proportional of a, b is x where a:b = b:x. Mean proportional of a and b is √(ab).
State the law of componendo and dividendo for a/b = c/d.
If a/b = c/d, then (a + b)/(a − b) = (c + d)/(c − d).
What is the order of a matrix, and when can two matrices A and B be multiplied?
Order is rows × columns (m × n). A (m×n) and B (p×q) can be multiplied as AB only if n = p; the product has order m × q.
What is the identity matrix and the additive identity (zero matrix) in matrix algebra?
The identity matrix I has 1s on the main diagonal and 0s elsewhere, satisfying AI = IA = A. The zero (null) matrix O has all entries 0, satisfying A + O = A.
State the formula for the nth term of an Arithmetic Progression (AP) with first term a and common difference d.
aₙ = a + (n − 1)d.
State the two formulas for the sum of the first n terms of an AP.
Sₙ = n/2 [2a + (n − 1)d], or equivalently Sₙ = n/2 (a + l) where l is the last term.
State the nth term and sum formulas for a Geometric Progression (GP) with first term a and common ratio r.
nth term aₙ = arⁿ⁻¹. Sum Sₙ = a(rⁿ − 1)/(r − 1) for r > 1, or a(1 − rⁿ)/(1 − r) for r < 1.
How do you solve a pair of linear equations in two variables by the method of cross-multiplication?
For a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0: x/(b₁c₂ − b₂c₁) = y/(c₁a₂ − c₂a₁) = 1/(a₁b₂ − a₂b₁).
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State the distance formula between points (x₁, y₁) and (x₂, y₂).
Distance = √[(x₂ − x₁)² + (y₂ − y₁)²].
State the section formula for the point dividing the join of (x₁, y₁) and (x₂, y₂) in ratio m:n internally.
Point = ((mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n)).
What is the midpoint formula, and the centroid of a triangle with vertices (x₁,y₁), (x₂,y₂), (x₃,y₃)?
Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2). Centroid = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3).
What is the slope (gradient) of a line through (x₁,y₁) and (x₂,y₂), and the conditions for parallel and perpendicular lines?
Slope m = (y₂ − y₁)/(x₂ − x₁). Parallel lines have equal slopes (m₁ = m₂); perpendicular lines satisfy m₁ × m₂ = −1.
State the slope-intercept and point-slope forms of the equation of a straight line.
Slope-intercept: y = mx + c (c = y-intercept). Point-slope: y − y₁ = m(x − x₁).
State the three main similarity criteria for triangles.
AA (two pairs of equal angles), SSS (all three pairs of sides proportional), and SAS (two pairs of sides proportional with included angles equal).
State the Basic Proportionality Theorem (Thales' Theorem).
If a line is drawn parallel to one side of a triangle to intersect the other two sides, it divides those two sides in the same ratio.
How do the perimeters, areas, and volumes of two similar figures relate to the ratio of corresponding sides k?
Ratio of perimeters (or any corresponding lengths) = k; ratio of areas = k²; ratio of volumes = k³.
State the theorem about the angle subtended by an arc at the centre versus at the circumference.
The angle subtended by an arc at the centre is twice the angle subtended by the same arc at any point on the remaining part of the circumference.
State the cyclic quadrilateral angle theorem.
The opposite angles of a cyclic quadrilateral are supplementary (each pair sums to 180°).
What is the relationship between the tangent to a circle and the radius at the point of contact, and the equal-tangents property?
A tangent is perpendicular to the radius at the point of contact. Two tangents drawn from an external point to a circle are equal in length.
State the alternate segment theorem for a circle.
The angle between a tangent to a circle and a chord drawn from the point of contact equals the angle subtended by that chord in the alternate segment.
State the angle in a semicircle theorem and the equal-chords property.
The angle in a semicircle is a right angle (90°). Equal chords of a circle are equidistant from the centre, and chords equidistant from the centre are equal.
State the relationship sin θ, cos θ, and tan θ have via the basic identity, and give the reciprocal ratios.
tan θ = sin θ / cos θ, and sin²θ + cos²θ = 1. Reciprocals: cosec θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ.
State the two trigonometric identities (besides sin²θ + cos²θ = 1) involving sec and cosec.
sec²θ − tan²θ = 1 (i.e. 1 + tan²θ = sec²θ) and cosec²θ − cot²θ = 1 (i.e. 1 + cot²θ = cosec²θ).
Give the values of sin, cos, and tan for 0°, 30°, 45°, 60°, and 90°.
sin: 0, ½, 1/√2, √3/2, 1. cos: 1, √3/2, 1/√2, ½, 0. tan: 0, 1/√3, 1, √3, undefined (∞).
In heights and distances, define the angle of elevation and the angle of depression.
Angle of elevation is the angle above the horizontal when looking up at an object; angle of depression is the angle below the horizontal when looking down at an object. They are equal (alternate angles).
State the curved (lateral) surface area, total surface area, and volume of a right circular cylinder of radius r and height h.
CSA = 2πrh; TSA = 2πr(h + r); Volume = πr²h.
State the slant height, curved surface area, total surface area, and volume of a right circular cone (radius r, height h, slant l).
l = √(r² + h²); CSA = πrl; TSA = πr(l + r); Volume = (1/3)πr²h.
State the surface area and volume of a sphere and a hemisphere of radius r.
Sphere: surface area = 4πr², volume = (4/3)πr³. Hemisphere: CSA = 2πr², TSA = 3πr², volume = (2/3)πr³.
How do you find the surface area and volume of a combination/solid (e.g. a cone mounted on a cylinder)?
Total surface area = sum of the exposed surface areas of each part (excluding hidden joined faces); total volume = sum of the individual volumes of the component solids.
Give the formula for the length of an arc and the area of a sector of a circle with radius r and central angle θ°.
Arc length = (θ/360) × 2πr; Sector area = (θ/360) × πr².
State the formula for the mean of grouped data using the direct method.
Mean x̄ = Σfᵢxᵢ / Σfᵢ, where xᵢ are class marks (midpoints) and fᵢ are the corresponding frequencies.
What are the two main methods, besides direct, to calculate the mean of grouped data?
Assumed mean (short-cut) method: x̄ = A + Σfd/Σf, where d = x − A. Step-deviation method: x̄ = A + (Σfu/Σf) × h, where u = (x − A)/h and h is the class size.
State the formula for the median of grouped (continuous) data.
Median = l + [(N/2 − cf)/f] × h, where l = lower boundary of median class, N = total frequency, cf = cumulative frequency before median class, f = frequency of median class, h = class size.
State the formula for the mode of grouped data.
Mode = l + [(f₁ − f₀)/(2f₁ − f₀ − f₂)] × h, where l = lower boundary of modal class, f₁ = modal class frequency, f₀ = preceding frequency, f₂ = following frequency, h = class size.
State the empirical relationship between mean, median, and mode.
Mode = 3 × Median − 2 × Mean.
What are an ogive and the two types of cumulative frequency curves, and how is the median found graphically?
An ogive is a cumulative frequency curve: the 'less than' ogive (rising) and 'more than' ogive (falling). The median is the x-coordinate of the point where the two ogives intersect (or where the less-than ogive reaches N/2).
State the classical (theoretical) definition of probability of an event E.
P(E) = (Number of favourable outcomes) / (Total number of equally likely outcomes). It always satisfies 0 ≤ P(E) ≤ 1.
What is the probability of the complement of an event, and the probability of a sure and an impossible event?
P(not E) = 1 − P(E). The sum P(E) + P(not E) = 1. P(sure event) = 1 and P(impossible event) = 0.
ICSE Class 10 Mathematics FAQ
What is in the ICSE Class 10 Mathematics syllabus?
ICSE Class 10 Mathematics is split into 1 chapter: ICSE Mathematics. Together they contain 5 topics.
How many chapters are in ICSE Class 10 Mathematics?
1 chapter, containing 5 topics.
Are there flashcards for ICSE Class 10 Mathematics?
Yes — a 50-card Mathematics 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.