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Table of contents
Chapter 1: Quadratic Equations
In this unit, students will learn how to:
- define quadratic equation
- solve a quadratic equation in one variable by factorization.
- solve a quadratic equation in one variable by completing square.
- derive quadratic formula by using method of completing square.
- solve a quadratic equation by using quadratic formula.
- solve the equations of the type ax4 + bx2 + c = 0 by reducing it to the quadatic form.
- solve exponential equations involving variables in exponents.
- solve equations of the type (x+a) (x+b) (x+c) (x+d) = k where a+b = c+d
Chapter 2: Theory of Quadratic Equations
After solving this unit, you will be able to:
- define discriminant of the quadratic expression ax2 + bx + c
- find discriminant of a given quadratic equation.
- discuss the nature of roots of a quadratic equation through discriminant.
- determine the nature of roots of a given quadratic equation and verify the result by solving the equation.
- determine the value of an unknown involved in a given quadratic equation when nature of its roots is given.
- find cube roots of unity
- find the sum and product of roots of a given quadratic equation without solving it.
Chapter 3: Variations
After solving this unit, you will be able to:
- define ratio, proportions and variations (direct and inverse).
- find 3rd, 4th, mean and continued proportion.
- apply theorems of invertendo, alternendo, compnendo, dividendo and componendo & dividendo to find proportions.
- define joint variation.
- solve problems related to joint variation.
- use k-method to prove conditional equalities involving proportions.
- solve real life problems based on variations.
Chapter 4: Partial Fractions
After solving this chapter, you will be able to:
- define proper, improper and rational fraction.
- resolve an algebraic fraction into partial fractions when its denomination consists of
- non-repeated linear factors,
- repeated linear factors,
- non-repeated quadratic factors,
- repeated quadratic factors.
Chapter 5: Sets and Functions
After solving this chapter, you will be able to:
- recall the sets denoted by N, W, Z, E, O, P and Q.
- perform operations on sets union, intersection, difference and complement.
- give formal proofs of the following fundamental properties of union and intersection of two or three sets.
- commutative property of union,
- commutative property of intersection,
- associative property of union,
- associative property of intersection,
- De Morgan's laws.
- verify the fundamental properties for given sets.
- use venn diagram to represent
- union and intersection of sets,
- complement of a set.
Chapter 6: Basic Statistics
After studying this chapter, you will learn how to:
- construct grouped frequency table.
- construct histograms with equal and unequal class intervals.
- draw a cumulative frequency polygon.
- calculate median, mode, geometric mean, harmonic mean.
- recognize properties of arithmetic mean.
Chapter 7: Introduction to Trignometry
After solving this chapter, you will be able to:
- measure an angle in degree, minute and second.
- convert an angle given in degrees, minutes and seconds into decimal form and vice versa.
- establish the rule l = r0, where r is the radius of the circle, l the length of circular arc and 0 the central angle measured in radians.
- recognize quadrants and quadrantel angles.
- solve real life problems involving angle of elevation and depression.
Chapter 8: Projection of a side of a Triangle
After solving this chapter, you will be able to prove the following theorems along with corollaries and apply them to solve appropriate problems.
- In an obtuse-angled triangle, the square on the side opposite to the obtuse angle is equal to the sum of the squares on the sides containing the obtuse angle together with twice the rectangle contained by one of the sides, and the projection on it of the other.
- In any triangle, the sum of the squares on any two sides is equal to twice the square on half the third side together with twice the square on the median which bisects the third side (Apollonius' Theorem).
Chapter 9: Chords of a Circle
After studying this chapter, you will be able to prove the following theorems alongwith corollaries and apply them to solve appropriate problems.
- One and only one circle can pass through three non collinear points.
- A straight line, drawn from the centre of a circle to bisect a chord (which is not a diameter) is perpendicular to the chord.
- Two chords of a circle which are equidistant from the centre are congruent.
Chapter 10: Tangent to a circle
After studying this chapter, you will learn how to prove the following theorems alongwith corollariesw and apply them to solve appropriate problems.
- If a line is drawn perpendicular to a radial segment of a circle at its outer end point, it is tangent to the circle at that point.
- The tangent to a circle and the radial segment joining the point of contact and the centre are perpendicular to each other.
- The two tangents drawn to a circle from a point outside it, are equal in the length.
Chapter 11: Chords and arcs
After studying this unit, you will learn:
- If two arcs of a circle (or of congruent circles) are congruent, then the corresponding chords are equal.
- If two chords of a circle (or of congruent circles) are equal, then their corresponding arcs (minor, major or semi-circular) are congruent.
Chapter 12: Angle in a segment of circle
In this unit, you will learn:
- Any two angles in the same segment of a circle are equal.
- The circum angle
- in a semi-circle is a right angle,
- in a segment less than a semi-circle is greater than a right angle,
- in a segment less than a semi-circle is less than a right angle,
- The opposite angles of any quadrilateral inscribed in a circle are supplementary.
Chapter 13: Practical geometry circles
After studying this chapter, you will learn how to:
- locate the centre of a given circle.
- draw a circle passing through three given non-collinear points.
- circumscribe a circle about a given triangle.
- inscribe a circle in a given triangle.
- escribe a circle in a given triangle.
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