There is one paper of two and a half hours duration carrying 80 marks and Internal Assessment of 20 marks. The paper is divided into two sections: Section I (40 marks) and Section II (40 marks).
Section I consists of compulsory short answer questions. In Section II, you are required to answer four out of seven questions.
(i) Compound Interest
(a) Compound interest as a repeated Simple Interest computation with a growing Principal. Use of this in computing Amount over a period of 2 or 3-years.
(b) Use of formula A = P(1+ r/100)n. Finding CI from the relation CI=A–P.
Note: Paying back in equal installments, being given rate of interest and installment amount, not included.
(ii) Sales Tax and Value Added Tax
Computation of tax including problems involving discounts, list-price, profit, loss, basic/cost price including inverse cases.
(a) Savings Bank Accounts. Types of accounts. Idea of savings Bank Account, computation of interest for a series of months.
(b) Recurring Deposit Accounts: computation of interest using the formula:
SI = P x [n(n+1)/2x12] x r/100
(iv) Shares and Dividends
(a) Face/Nominal Value, Market Value, Dividend, Rate of Dividend, Premium.
Note: Brokerage and fractional shares not included
(i) Linear Inequations
Linear Inequations in one unknown for x ε N, W, Z, R. Solving
(ii) Quadratic Equations
(a) Quadratic equations in one unknown. Solving by:
(b) Nature of roots
(c) Solving problems.
(a) Reflection of a point in a line: x=0, y=0, x=a, y=a, the origin.
(b) Reflection of a point in the origin.
(c) Invariant points.
(iv) Ratio and Proportion
(a) Duplicate, triplicate, sub-duplicate, sub-triplicate, compounded ratios.
(b) Continued proportion, mean proportion
(c) Componendo and dividendo, alternendo and invertendo properties.
(d) Direct applications.
(a) Factor Theorem.
(b) Remainder Theorem.
(c) Factorizing a polynomial completely after obtaining one factor by factor theorem. Note: f(x) not to exceed degree 3.
(a) Order of a matrix. Row and column matrices.
(b) Compatibility for addition and multiplication.
(c) Null and Identity matrices.
(d) Addition and subtraction of 2x2 matrices.
(e) Multiplication of a 2x2 matrix by
(vii) Co-ordinate Geometry
Co-ordinates expressed as (x,y) Distance between two points, section, and Midpoint formula, Concept of slope, equation of a line, Various forms of straight lines.
(a) Distance formula.
(b) Section and Mid-point formula (Internal section only, co-ordinates of the centroid of a triangle included).
(c) Equation of a line:
Geometric understanding of ‘m’ as slope/ gradient/ tanθ where θ is the angle the line makes with the positive direction of the x axis.
Geometric understanding of c as the y-intercept/ the ordinate of the point where the line intercepts the y axis/ the point on the line where x=0.
Conditions for two lines to be parallel or perpendicular. Simple applications of all of the above.
(a) Lines of symmetry of an isosceles triangle, equilateral triangle, rhombus, square, rectangle, pentagon, hexagon, octagon (all regular) and diamond shaped figure.
(b) Being given a figure, to draw its lines of symmetry. Being given part of one of the figures listed above to draw the rest of the figure based on the given lines of symmetry (neat recognizable free hand sketches acceptable).
Axioms of similarity of triangles. Basic theorem of proportionality.
(a) Areas of similar triangles are proportional to the squares on corresponding sides.
(b) Direct applications based on the above including applications to maps and models.
Loci: Definition, meaning, Theorems based on Loci.
(a) The locus of a point equidistant from a fixed point is a circle with the fixed point as centre.
(b) The locus of a point equidistant from two interacting lines is the bisector of the angles between the lines.
(c) The locus of a point equidistant from two given points is the perpendicular bisector of the line joining the points.
(a) Chord Properties:
(b) Arc and chord properties:
(c) Cyclic Properties:
(d) Tangent Properties:
Note: Proofs of the theorems given above are to be taught unless specified otherwise.
(a) Construction of tangents to a circle from an external point.
(b) Circumscribing and inscribing a circle on a triangle and a regular hexagon.
Area and circumference of circle, Area and volume of solids – cone, sphere.
(a) Circle: Area and Circumference. Direct application problems including Inner and Outer area.
(b) Three-dimensional solids - right circular cone and sphere: Area (total surface and curved surface) and Volume. Direct application problems including cost, Inner and Outer volume and melting and recasting method to find the volume or surface area of a new solid. Combination of two solids included.
Note: Frustum is not included. Areas of sectors of circles other than quarter circle and semicircle are not included.
(a) Using Identities to solve/prove simple algebraic trigonometric expressions
(b) Trigonometric ratios of complementary angles and direct application:
(c) Heights and distances: Solving 2-D problems involving angles of elevation and depression using trigonometric tables.
Note: Cases involving more than two right angled triangles excluded.
Statistics - basic concepts, , Histograms and Ogive, Mean, Median, Mode.
(a) Graphical Representation. Histograms and ogives.
(b) Computation of:
(tossing of one or two coins, throwing a die and selecting a student from a group)