Topics
Rational and Irrational Numbers
- Rational Numbers
- Properties of Rational Numbers
- Decimal Representation of Rational Numbers
- Irrational Numbers and Proof of Irrationality
- Concept of Real Numbers
- Surds
- Rationalisation of Surds
- Simplifying an Expression by Rationalization of the Denominator
Compound Interest [Without Using Formula]
- Calculation of Interest
- Concept of Compound Interest
- Compound Interest as a Repeated Simple Interest Computation with a Growing Principal
- Concept of Compound Interest
Compound Interest [Using Formula]
- Concept of Compound Interest
- Inverse Formula
- Miscellaneous Problem
- When the Interest is Compounded Half Yearly
- When the Time is Not an Exact Number of Years and the Interest is Compounded Yearly
- Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years
Expansions
- Algebraic Identities
- Expansion of (a + b)3
- Expansion of Formula
- Special Product
- Methods of Solving Simultaneous Linear Equations by Cross Multiplication Method
Factorisation
- Factorisation by Taking Out Common Factors
- Factorisation by Taking Out Common Factors
- Factorisation by Taking Out Common Factors
- Factorisation by Grouping
- Factorisation of a Quadratic Trinomial by Splitting the Middle Term
- Method of Factorisation : Difference of Two Squares
- Method of Factorisation : the Sum Or Difference of Two Cubes
Simultaneous (Linear) Equations [Including Problems]
- Methods of Solving Simultaneous Linear Equations by Elimination Method
- Methods of Solving Simultaneous Linear Equations by Elimination Method
- Method of Elimination by Equating Coefficients
- Equations Reducible to Linear Equations
- Simultaneous linear equations
- Methods of Solving Simultaneous Linear Equations by Cross Multiplication Method
- Word Problems on Linear Equations
- Pair of Linear Equations in Two Variables
Indices [Exponents]
- Laws of Exponents
- Handling Positive, Fraction, Negative and Zero Indices
- Simplification of Expressions
- Solving Exponential Equations
Logarithms
- Introduction of Logarithms
- Interchanging Logarithmic and Exponential Forms
- Logarithmic to Exponential
- Exponential to Logarithmic
- Laws of Logarithm
- Product Law
- Quotient Law
- Power Law
- Expansion of Expressions with the Help of Laws of Logarithm
- More About Logarithm
Triangles [Congruency in Triangles]
- Basic Concepts of Triangles
- Relation Between Sides and Angles of Triangle
- Important Terms of Triangle
- Congruence of Triangles
- Criteria for Congruence of Triangles
Isosceles Triangles
- Classification of Triangles based on Sides
- Isosceles Triangles Theorem
- Converse of Isosceles Triangle Theorem
Inequalities
- Inequalities in a Triangle
- If two sides of a triangle are unequal, the greater side has the greater angle opposite to it.
- If Two Angles of a Triangle Are Unequal, the Greater Angle Has the Greater Side Opposite to It.
- Of All the Lines, that Can Be Drawn to a Given Straight Line from a Given Point Outside It, the Perpendicular is the Shortest.
Mid-point and Its Converse [ Including Intercept Theorem]
- Theorem of Midpoints of Two Sides of a Triangle
- Equal Intercept Theorem
Pythagoras Theorem [Proof and Simple Applications with Converse]
- Right-angled Triangles and Pythagoras Property
- Right-angled Triangles and Pythagoras Property
- Advanced Regular Polygon
Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
- Introduction of Rectilinear Figures
- Classification of Polygons
- Diagonal Properties of Different Kinds of Parallelograms
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Property: The diagonals of a rhombus are perpendicular bisectors of one another.
- Property: The Diagonals of a Rectangle Are of Equal Length.
- Property: The diagonals of a square are perpendicular bisectors of each other.
Construction of Polygons (Using Ruler and Compass Only)
- Constructing a Quadrilateral
- Construction of Parallelograms
- Construction of Trapezium
- Construction of a Rectangle When Its Length and Breadth Are Given.
- Construction of Rhombus
- Square: Properties and Construction
- To Construct a Regular Hexagon
Area Theorems [Proof and Use]
- Concept of Area
- Figures Between the Same Parallels
- Triangles with the Same Vertex and Bases Along the Same Line
Circle
Statistics
- Concepts of Statistics
- Constants and Variables in Mathematics
- Tabulation of Data
- Frequency
- Frequency Distribution Table
- Frequency Distribution Table
- Class Intervals and Class Limits
- Cumulative Frequency and Cumulative Frequency Table
- Frequency Distribution and Its Applications
- Graphical Representation of Continuous Frequency Distribution
Mean and Median (For Ungrouped Data Only)
- Mean of Grouped Data
- Properties of Mean
Area and Perimeter of Plane Figures
Solids [Surface Area and Volume of 3-d Solids]
- Solid Figures
- Surface Area of a Cuboid
- Surface Area of a Cube
- Mensuration of Cylinder
- Cost of an Article
- Cross Section of Solid Shapes
- Flow of Water ( or any other liquid )
Trigonometrical Ratios [Sine, Consine, Tangent of an Angle and Their Reciprocals]
- Concept of Perpendicular, Base, and Hypotenuse in a Right Triangle
- Notation of Angles
- Trigonometric Ratios
- Relation Among Trigonometric Ratios
Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
- Trigonometric Ratios of Specific Angles
- Trigonometric Equation Problem and Solution
Solution of Right Triangles [Simple 2-d Problems Involving One Right-angled Triangle]
- Solution of Right Triangles
Complementary Angles
- Trigonometrical Ratios of Complementary Angles
- Trigonometric Ratios of Complementary Angles
- Trigonometrical Ratios of Complementary Angles
- Complimentary Angles for Tangent ( Tan ) and Contangency ( Cot )
- Complimentary Angles for Secant ( Sec ) and Cosecant ( Cosec )
Co-ordinate Geometry
- Dependent and Independent Variables
- Ordered Pair
- Cartesian Coordinate System
- Co-ordinate Geometry
- Quadrants and Sign Convention
- Plotting of Points
- Concept of Graph
- Graphs of Linear Equations
- Equally Inclined lines
- Forms of the Equation of a Straight Line
Graphical Solution (Solution of Simultaneous Linear Equations, Graphically)
Distance Formula
Profit , Loss and Discount
- Concept of Discount
- To Find C.P., When S.P. and Gain (Or Loss) Percent Are Given
- To Find S.P., When C.P. and Gain (Or Loss) Percent Are Given
- Profit or Loss as a Percentage
- Overhead Expenses
Construction of Triangles
- Construction of Triangles
- Construct Isosceles Triangle
Changing the Subject of a Formula
- Changing the Subject of a Formula
Similarity
Shaalaa.com | Statistics - Ex.5.1 Part 2
Related QuestionsVIEW ALL [16]
Use the table given below to find:
(a) The actual class limits of the fourth class.
(b) The class boundaries of the sixth class.
(c) The class mark of the third class.
(d) The upper and lower limits of the fifth class.
(e) The size of the third class.
| Class Interval | Frequency |
| 30 - 34 | 7 |
| 35 - 39 | 10 |
| 40 - 44 | 12 |
| 45 - 49 | 13 |
| 50 - 54 | 8 |
| 55 - 59 | 4 |
A frequency distribution table for the production of oranges of some farm owners is given below. Find the mean production of oranges by ‘assumed mean’ method.
|
Production (Thousand rupees)
|
25-30 | 30-35 | 35-40 | 40-45 | 45-50 |
| No. of Customers | 20 | 25 | 15 | 10 | 10 |
In the following table, the toll (in ₹) paid by drivers and the number of vehicles is shown. Find the mean of the toll by 'assumed mean' method.
| Toll (Rupees) | 300 - 400 | 400 - 500 | 500 - 600 | 600 - 700 | 700 - 800 |
| No. of vehicles | 80 | 110 | 120 | 70 | 40 |
The following data shows the number of students using different modes of transport:
| Modes of Transport | Number of Students |
| Bicycle | 140 |
| Bus | 100 |
| Walk | 70 |
| Train | 40 |
| Car | 10 |
From this table, find the central angle (θ) for the Mode of Transport ‘Bus’.
The following frequency distribution table shows the distances travelled by some rickshaws in a day. Observe the table and answer the following questions
| Class (Daily distance travelled in km) |
Continuous Classes |
Frequency (no.of. rickshaws) |
Cumulative frequency less than type |
| 60 – 64 | 59.5 – 64.5 | 10 | 10 |
| 65 – 69 | 64.5 – 69.5 | 34 | 10 + 34 = 44 |
| 70 – 74 | 69.5 – 74.5 | 58 | 44 + 58 = 102 |
| 75 – 79 | 74.5 – 79.5 | 82 | 102 + 82 = 184 |
| 80 – 84 | 79.5 – 84.5 | 10 | 184 + 10 = 194 |
| 85 – 89 | 84.5 – 89.5 | 6 | 194 + 6 = 200 |
- Which is the modal class? Why?
- Which is the median class and why?
- Write the cumulative frequency (C.F) of the class preceding the median class.
- What is the class interval (h) to calculate median?
A milk centre sold milk to 50 customers. The table below gives the number of customers and the milk they purchased. Find the mean of the milk sold by direct method.
| Milk Sold (Litre) | 1 – 2 | 2 – 3 | 3 – 4 | 4 – 5 | 5 – 6 |
| No. of Customers | 17 | 13 | 10 | 7 | 3 |
