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MCQs (12)

Standard form of ax²+bx+c=0 is: Number of methods to solve: Pure quadratic equation if: Solution of x²-49=0: 5x²=30x has solution: Equation 2^x + 64.2^-x - 20 = 0 is: Reciprocal equation remains unchanged when x replaced by: x²-5x+6=0 roots are: ax²+bx+c=0 is linear if: Solution set of x²-9=0: The degree of quadratic equation is: Quadratic formula is:

Shorts (13)

Define Quadratic Equation. Define Reciprocal Equation. Define Radical Equation. Define Exponential Equation. Solve x²-x-20=0 by factorization. Write in standard form: (x+7)(x-3)=-7 Solve by formula: 2-x²=7x Find solution set: x²-5x+6=0 Solve 3x²-6x=x+20 Solve x²+4x-2=0 Name 3 methods to solve quadratic equation. Convert to standard form: 1/(x+4) + 1/(x-4) = 3 Is x(x+7)=(2x-1)(x+4) a pure quadratic?

Longs (7)

Solve by Completing Square: 2x²-5x-3=0 Solve by Quadratic Formula: (x+1)/(x+2) + (x+2)/(x+3) = 25/12 Solve the equation: x⁴-13x²+36=0 Solve the reciprocal eq: 2x⁴+x³-6x²+x+2=0 Solve radical eq: √(3x+100) - x = 4 Solve exponential: 4.2^(2x+1) - 9.2^x + 1 = 0 Solve: (x²+1)/(x+1) + (x+2)/(x+1) = 5/2

MCQs (10)

Discriminant of ax²+bx+c=0: Cube roots of -1: Sum of cube roots of unity: Product of cube roots of unity: If Disc > 0 and perfect square, roots are: If Disc = 0, roots are: 1+ω+ω² = ? α+β = ? αβ = ? ω^4 = ?

Shorts (13)

Find Discriminant: 2x²-7x+1=0 Find Discriminant: x²-3x+3=0 Evaluate: (1-ω-ω²)⁷ Evaluate: (1-3ω-3ω²)⁵ Find sum and product of roots: 3x²+7x-11=0 Find sum and product: x²-5x+3=0 Define Synthetic Division. Using synthetic division, find quotient: (x²+7x-1)÷(x+1) Find h if sum of roots is 3 times product. If α,β are roots of x²-5x+3=0, find α-β. Write quadratic equation with roots 3, 4. Evaluate ω⁻¹³ + ω⁻¹⁷ Define Simultaneous Equations.

Longs (7)

Solve using Synthetic Division: (x³+x²-3x+2)/(x-2) Prove that x³+y³=(x+y)(x+ωy)(x+ω²y) Find p if roots of x²+3x+p-2=0 differ by 2. If α,β are roots of 4x²-5x+6=0, find equation with roots 2α+1, 2β+1. Solve simultaneous equations: x+y=7, x²-xy+y²=13 Use synthetic division to find l and m if x-1 and x+1 are factors of x³+3lx²+mx-1. Prove (1+ω)(1+ω²)(1+ω⁴)... = 1

MCQs (10)

In a:b, a is called: In a:b, b is called: y=kx is: y=k/x is: Third proportional to 6, 12 is: Find x if 4:x :: 5:15 Mean proportional of 4, 16 is: If u ∝ v then: If u ∝ 1/v then: Ratio has unit:

Shorts (13)

Define Ratio. Define Proportion. Define Direct Variation. Define Inverse Variation. Define Joint Variation. Find 3rd proportional to 6, 12. Find 4th proportional to 8, 4, 2. Find mean proportional to 20, 45. If y ∝ x, and y=8 when x=2, find y when x=5. If y ∝ 1/x, and y=4 when x=3, find x when y=12. Find Fourth proportional to 5, 8, 15. Express in simplest form: 4kg : 2kg. Solve 3(4x-5y) = 2x-7y for x:y.

Longs (7)

Using Componendo-Dividendo solve: √(x+3)+√(x-3) / √(x+3)-√(x-3) = 4/3 If y varies inversely as x² and y=3 when x=4, find y at x=4. Using K-Method prove a:b=c:d implies (a²+b²)/(a²-b²) = (c²+d²)/(c²-d²). Solve using theorem of componendo-dividendo: (x-2)²-(x-4)² / (x-2)²+(x-4)² = 12/13 If y varies jointly as x² and z, and y=6 when x=4, z=9. Find y when x=-8, z=12. Prove that a:b = c:d if (3a+5b):(7a-5b) = (3c+5d):(7c-5d). Find mean proportional to x²-y² and (x-y)/(x+y).

MCQs (10)

Degree of numerator < degree of denominator is: Degree of numerator >= degree of denominator is: Partial fractions of 1/(x²-1): Identity holds for: Conditional equation holds for: x³/(x²+1) is: Number of partial fractions of x³/(x+1)(x-1): Form of A/(x+a) + B/(x+b) is for: How many constants in (Ax+B)/(x²+1)? Rational Fraction is P(x)/Q(x) where Q(x) is:

Shorts (13)

Define Rational Fraction. Define Proper Fraction. Define Improper Fraction. Define Identity. How to make x²/(x-1) proper? Resolve 1/(x-1)(x+1) into form. Diff Conditional Eq vs Identity. Resolve 7x+25/(x+3)(x+4). Convert improper to proper: (x²+1)/(x+1). Write Identity form for 1/(x²+1)(x-1). Define Partial Fractions. Is 2x/(x-1) proper or improper? Resolve x/(x-a)(x-b).

Longs (7)

Resolve into partial fractions: (7x+4)/(3x+2)(x+1)² Resolve: 1/(x²-1)(x+1) Resolve: (x²+1)/(x³+1) Resolve: (x⁴+1)/(x²(x-1)) Resolve: 3x-11 / (x+3)(x²+1) Resolve: (2x+1)/(x-1)(x+2)(x+3) Resolve: 1 / (x-1)²(x+1)

MCQs (10)

Set of natural numbers: If A has 3 elements, P(A) has: AUB = BUA is: A∩B = B∩A is: Point (-1, 4) is in quadrant: A function A->B is onto if Range f = ? A function is one-one if: Binary relations in AxB if A has 2, B has 2 elements: Intersection of disjoint sets is: U - A is called:

Shorts (13)

Define De Morgan Laws. Define Bijective Function. Define Onto Function. Define One-One Function. If A={1,2}, B={2,3}, find AxB. If A={a,b}, find P(A). Find a,b if (a-4, b-2)=(2,1). Diff Domain and Range. Define Binary Relation. Find AUB if A={1}, B={2}. Verify distributive law for A={1}, B={2}, C={3}. Define Complement of a set. Write two binary relations from AxA if A={a,b}.

Longs (7)

Verify De Morgan Law (AUB)'=A'∩B' for U={1..10}, A={1,3,5}, B={2,4,6}. Verify AUB = BUA and A∩B = B∩A for given sets. If U={1..10}, A={1,3,5,7}, B={2,4,6,8}, verify (A∩B)' = A' U B'. If A={1,3}, B={2,4}, find 3 binary relations in AxB. Given L={a,b,c}, M={3,4}. Find two binary relations in LxM. Prove A U (B ∩ C) = (A U B) ∩ (A U C). Verify Associativity of Union for A, B, C.

MCQs (10)

Most frequent value is: Middle value of data is: Sum of deviations from mean is: Mean of 1,2,3: Xmax - Xmin is: Data in classes is called: Formula for HM: Mean is affected by: Standard Deviation is square root of: Mode of 2,2,3,3,3,4 is:

Shorts (13)

Define Arithmetic Mean. Define Geometric Mean. Define Harmonic Mean. Define Mode. Define Median. Define Range. Define Variance. Define Standard Deviation. Find Range: 11, 13, 2, 5, 20. Calculate Mean of 12, 14, 17, 20. Define Histogram. Define Cumulative Frequency. What is Grouped Data?

Longs (7)

Calculate Mean, Median, Mode: 4,6,7,4,8,9,7,10. Calculate Standard Deviation: 9,3,8,8,9,8,9,18. Compute Arithmetic Mean for frequency distribution. Calculate Variance for the data. Find Harmonic Mean for 12, 5, 8, 4. Find Geometric Mean for 2, 4, 8. Make a Frequency Distribution table for data.

MCQs (10)

1+tan²θ = ? 1-sin²θ = ? π radians = ? degrees Reciprocal of sinθ: Tanθ = ? Angle < 90 is: Sec²θ - Tan²θ = ? Cotθ = ? 1 degree = ? min Sin(90) = ?

Shorts (13)

Define Radian. Convert 30° to radians. Convert π/4 to degrees. Find l when r=2, θ=180°. Prove tanθ+cotθ=secθcosecθ. Convert 12°15' to decimal. Define Angle of Elevation. Define Angle of Depression. Verify sin²θ+cos²θ=1. Find r when l=5, θ=1/2 rad. Evaluate sin(45)+cos(45). Define Coterminal Angles. Find θ when l=4, r=2.

Longs (7)

Prove: (1-sinθ)/(1+sinθ) = (secθ-tanθ)² Prove: (tanθ+secθ-1)/(tanθ-secθ+1) = tanθ+secθ A ladder makes 60° with wall... find length. Verify identity: sinθ(tanθ+cotθ)=secθ Find height of a cliff if angle of elevation is 30° at 100m distance. Prove: cos⁴θ-sin⁴θ = cos²θ-sin²θ Find the angle subtended by an arc of length 10cm on circle of radius 5cm.

MCQs (10)

In right triangle, square of hypotenuse equals: In acute triangle, square opp to acute angle is: In obtuse triangle, square opp to obtuse angle is: Projection of a point on a line is: Projection of line segment perpendicular to line is: Apollonius Theorem relates to: Angle > 90 is: Angle < 90 is: Zero dimension projection is: Pythagoras theorem is for:

Shorts (13)

Define Projection. Define Obtuse Angle. Define Acute Angle. Define Right Angle. State Pythagoras Theorem. State Apollonius Theorem. Define Zero Dimension. What is projection of vertical stick on ground? Find x if sides are 3,4,x (Right Angled). Diff between Acute and Obtuse triangle. In triangle ABC, if C=90, what is c²? Does projection imply shadow? Condition for Acute Triangle (sides).

Longs (7)

Theorem: In obtuse triangle, square on side opposite to obtuse angle is sum of squares of other two + 2(rect). Theorem: In acute triangle, square on side opposite to acute angle is sum - 2(rect). Theorem: Apollonius Theorem. Calculate projection of a side of length 5 making 60 degree angle. In triangle with sides 17, 8, 15, prove it is right angled. Calculate length of median using Apollonius theorem. Prove Pythagoras theorem using projection.

MCQs (10)

Chord passing through center is: Distance from center to chord bisects it: One and only one circle passes through: Radii of same circle are: Longest chord is: Circle is locus of points equidistant from: Line cutting circle at 2 points: Points on same circle are: Angle in semi-circle: Two chords equidistant from center are:

Shorts (13)

Define Circle. Define Chord. Define Diameter. Define Radius. Define Secant. Define Concyclic Points. Define Circumference. Define Arc. Diff Chord vs Diameter. Define Locus. What are collinear points? What are Non-collinear points? How many circles pass through 3 collinear points?

Longs (7)

Theorem: One and only one circle can pass through three non-collinear points. Theorem: A straight line, drawn from the centre of a circle to bisect a chord (which is not a diameter) is perpendicular to the chord. Theorem: Perpendicular from the centre of a circle on a chord bisects it. Theorem: Two chords of a circle which are equidistant from the centre, are congruent. Theorem: Two congruent chords of a circle are equidistant from the centre. Write steps to find center of a circle. Prove that diameter is the longest chord.

MCQs (10)

Tangents from outside point are: Tangent touches circle at: Radius is perpendicular to: Number of tangents from external point: Angle between tangent and radius: Tangents at ends of diameter are: Distance between centers of touching circles (external): Distance (internal touch): Common tangents to 2 disjoint circles: Touching circles have common tangent:

Shorts (13)

Define Tangent. Define Point of Contact. Define Secant. Define Length of Tangent. How many tangents from point on circle? How many tangents from point outside? Condition for touching circles externally. Condition for touching circles internally. Diff Tangent vs Secant. Define Common Tangent. Angle between radius and tangent? Draw two touching circles. Define Normal to circle.

Longs (7)

Theorem: If a line is drawn perpendicular to a radial segment of a circle at its outer end, it is tangent to the circle. Theorem: The tangent to a circle and the radial segment joining the point of contact and the centre are perpendicular to each other. Theorem: The two tangents drawn to a circle from a point outside it, are equal in length. Theorem: If two circles touch externally, the distance between their centres is equal to the sum of their radii. Theorem: If two circles touch internally, distance is diff of radii. Construct transverse common tangent. Construct direct common tangent.

MCQs (10)

Equal chords subtend equal angles at: Congruent arcs subtend equal angles at: Angle subtended by major arc is: Angle subtended by minor arc is: Equal chords are equidistant from: In equal circles, equal chords cut: Corresponding arcs of equal chords are: Semi-circle angle: Ratio of circumference to diameter: Sector area formula:

Shorts (13)

Define Sector. Define Segment. Define Chord. Define Arc. Define Subtended Angle. Diff Minor vs Major Arc. Define Central Angle. Define Congruent Circles. Condition for equal arcs. Diff Sector vs Segment. What is semi-circumference? Define Cyclic Points. Relation between arc and angle.

Longs (7)

Theorem: If two arcs of a circle are congruent, then the corresponding chords are equal. Theorem: If two chords of a circle are equal, then their corresponding arcs are congruent. Theorem: Equal chords subtend equal angles at the centre. Theorem: Equal angles at center are subtended by equal chords. Theorem: Congruent arcs subtend equal angles at the center. Prove that internal bisector of angle of a triangle bisects circumcircle. Prove that diagonals of a cyclic parallelogram are equal.

MCQs (10)

Angle in semi-circle is: Angles in same segment are: Cyclic quadrilateral opposite angles are: Central angle is ___ of circum-angle. Angle in major segment is: Angle in minor segment is: Sum of opposite angles of cyclic quad: Vertices of cyclic quad lie on: External angle of cyclic quad equals: Quad inscribed in circle is:

Shorts (13)

Define Cyclic Quadrilateral. Define Central Angle. Define Circum-Angle. Define Angle in Segment. Property of Cyclic Quad angles. Angle in Semi-circle property. Condition for Concyclic points. Define Segment of Circle. Diff Major vs Minor Segment angle. What are supplementary angles? Sum of angles of quad? Draw a Cyclic Quad. Theorem of central angle statement.

Longs (7)

Theorem: The measure of a central angle of a minor arc of a circle, is double that of the angle subtended by the corresponding major arc. Theorem: The angle in a semi-circle is a right angle. Theorem: The angle in a segment greater than a semi-circle is less than a right angle. Theorem: The angle in a segment less than a semi-circle is greater than a right angle. Theorem: The opposite angles of any quadrilateral inscribed in a circle are supplementary. Prove: Angles in same segment are equal. Construct a cyclic quadrilateral.

MCQs (10)

Circle passing through vertices: Circle touching sides internally: Circle touching one side externally: Intersection of medians is: Intersection of altitudes: Intersection of angle bisectors: Intersection of perp bisectors of sides: Number of escribed circles: Geometry means measurement of: Point of concurrency means:

Shorts (13)

Define Circum Circle. Define In-Circle. Define Escribed Circle. Define Centroid. Define Ortho-center. Define Circum-center. Define In-center. Define Geometry. What are Concurrent Lines? Diff Circum vs In-circle. Define Polygon. Define Regular Hexagon. Steps to bisect an angle.

Longs (7)

Construct a circle of radius 2cm. Draw tangents at angle 60°. Circumscribe a circle about triangle with sides 3,4,5 cm. Inscribe a circle in a triangle ABC. Escribe a circle opposite to vertex A. Construct a triangle and draw its altitudes. Construct a triangle and draw its medians. Draw two common tangents to two touching circles.