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Students can go through Andhra Pradesh SCERT AP State Board Syllabus 6th Class Maths Notes Pdf in English Medium and Telugu Medium to understand and remember the concepts easily. Besides, with our AP State 6th Class Maths Notes students can have a complete revision of the subject effectively while focusing on the important chapters and topics. Students can also read AP Board 6th Class Maths Solutions for exam preparation.

AP State Board Syllabus 6th Class Maths Notes

• Chapter 1 Numbers All Around us Notes
• Chapter 2 Whole Numbers Notes
• Chapter 3 HCF & LCM Notes
• Chapter 4 Integers Notes
• Chapter 5 Fractions and Decimals Notes
• Chapter 6 Basic Arithmetic Notes
• Chapter 7 Introduction to Algebra Notes
• Chapter 8 Basic Geometric Concepts Notes
• Chapter 9 2D-3D Shapes Notes
• Chapter 10 Practical Geometry Notes
• Chapter 11 Perimeter and Area Notes
• Chapter 12 Data Handling Notes

These AP State Board Syllabus 6th Class Maths Notes provide an extra edge and help students to boost their self-confidence before appearing for their final examinations.

Students can go through AP Board 7th Class Maths Notes Chapter 15 Symmetry to understand and remember the concepts easily.

AP State Board Syllabus 7th Class Maths Notes Chapter 15 Symmetry

→ Line of symmetry: The line which divides a figure into two identical parts is called the line of symmetry or axis of symmetry.
Ex: In the adjacent figure the dotted lines are the line of symmetry.

→ An object can have one or more than one lines of symmetry or axes of symmetry.
Ex: In the above figure there are two lines of symmetry.

→ If we rotate a figure, about a fixed point by a certain angle and the figure looks exactly the same as before, we say that the figure has rotational symmetry.
Ex: An equilateral triangle; a square etc.

→ The angle of turning during rotation is called the angle of rotation (or) the minimum angle rotation of a figure to get exactly the same figure as original is called the angle of rotation.
Ex: i) Angle of rotation of an equilateral triangle = 120°.
ii) Angle of rotation of a square = 90°.

→ All figures having rotational symmetry of order 1, can be rotated completely through 360° to come back to their original position. So we say that an object has rotational symmetry only when the order of symmetry is more than 1.
Eg: The order of rotational symmetry for an equilateral triangle is 3.
ii) For a square is 4.

→ Some shapes only have line symmetry and some have only rotational symmetry and some have both. Squares, equilateral triangles and circles have both line symmetry and rotational symmetry.

Students can go through AP Board 7th Class Maths Notes Chapter 14 Understanding 3D and 2D Shapes to understand and remember the concepts easily.

AP State Board Syllabus 7th Class Maths Notes Chapter 14 Understanding 3D and 2D Shapes

→ A net is a sort of skeleton – outline in 2-D, which, when folded, results in a 3-D shape. Each shape can also have more than one net according to the way we cut it.
Eg:

→ 3-D shapes can be visualised by drawing their nets on 2-D surfaces.

→ Oblique sketches are drawn on a grid paper to visualise 3-D shapes.

→ Isometric sketches can be drawn on a dot isometric paper to visualise 3-D shapes.

Students can go through AP Board 7th Class Maths Notes Chapter 13 Area and Perimeter to understand and remember the concepts easily.

AP State Board Syllabus 7th Class Maths Notes Chapter 13 Area and Perimeter

→ The area of a parallelogram is equal to the product of its base (b) and corresponding height (h) A = bh.

Any side of the parallelogram can be taken as its base.

→ The area of a triangle is equal to half the product of its base and height.

A = \(\frac{1}{2}\) bh
A triangle = Half a parallelogram

→ The area of a Rhombus is equal to half the product of Its diagonals.

A = \(\frac{1}{2}\) d₁d₂

→ The circumference of a circle = 2πr = πd where π = \(\frac{22}{7}\) or 3.14, d = \(\frac{r}{2}\)

Students can go through AP Board 7th Class Maths Notes Chapter 12 Quadrilaterals to understand and remember the concepts easily.

AP State Board Syllabus 7th Class Maths Notes Chapter 12 Quadrilaterals

→ Quadrilateral: A closed figure bounded by four line segments is called a quadrilateral.
In the figure, ABCD is a quadrilateral.

→ A quadrilateral divides a plane into three parts.
i) Interior of the quadrilateral
ii) Exterior of the quadrilateral
iii) Boundary of the quadrilateral

→ In the figure the points P, Q are in the interior of the quadrilateral. i3r In the figure the points R, S are in the exterior of the quadrilateral.

→ In the figure the points A, B, C, D are on the boundary of the quadrilateral.

→ A quadrilateral is said to be a convex quadrilateral if all line segments joining points in the interior of it also lie in its interior completely.
□ BELT is a convex quadrilateral.

→ A quadrilateral is said to be a concave quadrilateral if all line segments joining points in the interior of it do not necessarily lie in its interior completely.

In □ RING, the line segment \(\overline{\mathrm{AB}}\) does not lie completely in its interior, as such the quadrilateral RING is a concave quadrilateral.

→ Sum of the interior angles of a quadrilateral is 360°.
∠A + ∠B + ∠C + ∠D = 360°

→ A quadrilateral in which one pair of opposite sides are parallel is called a trapezium.
In □ ABCD ; AB // CD

→ A kite has four sides. There are exactly two distinct pairs of equal length.
In quadrilateral KITE,

KI = KE and IT = ET

→ A quadrilateral in which both pairs of opposite sides are parallel is called a parallelogram. In quadrilateral ABCD,
AB // CD and AD // BC. Hence □ ABCD is a parallelogram.

→ In a parallelogram,

• Opposite sides are parallel and equal [AB = CD and AD = BC]
• Diagonals bisect each other (AO = OC and BO = OD)
• Opposite angles are equal (∠A = ∠C and ∠B = ∠D)
• Adjacent angles are supplementary (∠A + ∠B = ∠B + ∠C = ∠C + ∠D = ∠D + ∠A = 180°)

→ A parallelogram in which adjaœnt sides are equal is called a Rhombus.
In quadrilateral ABCD,
AB = BC = CD = DA and hence □ ABCD is a Rhombus.

In a rhombus diagonals bisect each other at right angles,
(i.e.) AC ⊥ BD and AO = OC, BO = OD

→ A rectangle is a parallelogram with equal angles (OR)
A parallelogram in which one angle is a right angle is called a rectangle.

In fig. ∠A = ∠B = ∠C = ∠D = 90° and □ ABCD is a rectangle.
In a rectangle the diagonals are equal.
In a rectangle the diagonals bisect each other.

(AC = BD and AO = OC; BO = OD)

→ A square is a rectangle with equal adjacent sides.

In the figure AB = BC = CD = DA
∠A = ∠B = ∠C = ∠D = 90°
In a square the diagonals are equal and bisect at right angles. Also they are equal.
[(AO = OC ; BO = OD), (AC ⊥ BD) and (AC = BD)]

Flow chart of family of quadrilaterals

Students can go through AP Board 7th Class Maths Notes Chapter 11 Exponents to understand and remember the concepts easily.

AP State Board Syllabus 7th Class Maths Notes Chapter 11 Exponents

→ Very large numbers are easier to read, write and understand when expressed in exponential form.
Eg : 10000 = 10⁴
8 × 8 × 8 × 8 × 8 × ….. × 8 (16 times) = 8¹⁶.

→ When a number is multiplied by itself for many number of times (repeated multiplication) then we write it in exponential form.
Eg : 2 × 2 × 2 × 2 = 2⁴ Here 2 is base 4 is exponent.
3 × 3 × 3 × 3 × 3 = 3⁵ Here 3 is base 5 is exponent.

→ a . a . a . a ….. a (m times) = a^m.

→ Here ‘a’ is called the base and ‘m’ is called the exponent.

→ Laws of exponents

i) a^m × aⁿ = a^m+n

ii)  (a^m)ⁿ = a^mn

iii) (ab)^m = a^m . b^m

iv) a^m = aⁿ ⇒ m = n

v) a^-n = \(\frac{1}{a^{n}}\)

vi) \(\frac{\mathrm{a}^{\mathrm{m}}}{\mathrm{a}^{\mathrm{n}}}\) = a^m-n  if (m > n)
= \(\frac{1}{a^{n-m}}\)  if (m < n)
= 1 if (m = n)

vii) \(\left(\frac{a}{b}\right)^{m}\) = \(\frac{a^{m}}{b^{m}}\)

viii) a⁰ = 1 where a ≠ 0

Students can go through AP Board 7th Class Maths Notes Chapter 10 Algebraic Expressions to understand and remember the concepts easily.

AP State Board Syllabus 7th Class Maths Notes Chapter 10 Algebraic Expressions

→ Variable: It takes different values.
Ex: x, y, z, a, b, c, m etc.
Constant: The value of constant is fixed.
Ex: 1, 2, \(\frac{-2}{3}\), \(\frac{4}{5}\) etc.

→ Algebraic Expression: An algebraic expression is a single term or a combination of terms connected by the symbols ‘+’ (plus) or(minus).
Ex: 2x + 3, \(\frac{2}{5}\)p, 3x – 1 etc.

→ Numerical Expression : If every term of an expression is a constant term, then the expression is called a Numerical expression.
Ex: 2 + 1, -5 × 3, (12 + 4) ÷ 3.
Note: In the expression 2x + 9, ‘2x’ is an algebraic term. ‘9’ is called numeric term.

→ Like terms are terms which contain the same variables with the same exponents.
Ex: 12x, 25x, -7x are like terms.
2xy², 3xy², 7xy² are like terms.

→ Coefficient: In a.xⁿ, ‘a’ is called the numerical coefficient and ‘x’ is called the literal coefficient.
Types of algebraic expressions.

→ Degree of a monomial: The sum of all exponents of the variables present in a monomial is called the degree of the term or degree of the monomial.
Ex: The degree of 9x²y² is 4 [∵ 2 + 2 = 4]
Note: Degree of constant term is zero.
The highest of the degrees of all the terms of an expression is called the degree of the expression.
Ex: The degree of the expression ax + bx² + cx³ + dx⁴ + ex⁵ is 5.

→ The difference between two like terms is a like term with a numerical coefficient equal to the difference between the numerical coefficients of the two like terms.
Note:

1. If no two terms of an expression are alike then it is said to be in the simplified form.
2. In an expression, if the terms are arranged in such a way that the degrees of the terms are in descending order then the expression is said to be in standard form.
3. Addition (or) subtraction of expressions should be done in two methods, they are
   i) Column or Vertical method.
   ii) Row or Horizontal method.

Students can go through AP Board 7th Class Maths Notes Chapter 9 Construction of Triangles to understand and remember the concepts easily.

AP State Board Syllabus 7th Class Maths Notes Chapter 9 Construction of Triangles

→ A triangle can be drawn of any three of its elements are known.

→ To construct a triangle, we need

1. Three sides
2. Any two sides and the angle included between them.
3. Two angles and the side included between them.
4. Hypotenuse and one adjacent side of a right angled triangle.
5. Two sides and a non-included angle.

Students can go through AP Board 7th Class Maths Notes Chapter 8 Congruency of Triangles to understand and remember the concepts easily.

AP State Board Syllabus 7th Class Maths Notes Chapter 8 Congruency of Triangles

→ Two figures are said to be identical if their shapes are same.
Eg: Any two squares, circles or equilateral triangles.

→ Two figures are said to be congruent if they are identical in shape and equal in size.

→ Two line segments are congruent if they have same lengths.

→ Two triangles are congruent if the corresponding angles are equal.

→ We establish the congruency of the triangles by following criteria.

→ S.S.S. criterion: If three sides of a triangle are equal to the corresponding three sides of another triangle, then the triangles are congruent.

FA = TI; AN = IN; FN = TN then △FAN ≅ △TIN

→ S.A.S. criterion: If two sides and the angle included between the two sides of a triangle are equal to the corresponding two sides and the included angle of another triangle, then the two triangles are congruent.

CA = PI; ∠C = ∠P; CT = PG
then, △CAT ≅ △PIG

→ A.S.A. criterion : If two angles and the included side of a triangle are equal to the corresponding two angles and included side of another triangle then the triangles are congruent.

∠A = ∠I; AT = IM; ∠T = ∠M then △MAT ≅ △DIM.

→ R.H.S. criterion: In two right angled triangles, if the hypotenuse and one corresponding side are equal then they are congruent.

∠B = ∠E = 90°
BC = EF
AC = DF
then △ABC ≅ △DEF

→ If by any criterion two triangles are congruent then all the corresponding parts are equal.

Students can go through AP Board 7th Class Maths Notes Chapter 7 Data Handling to understand and remember the concepts easily.

AP State Board Syllabus 7th Class Maths Notes Chapter 7 Data Handling

→ Data: Information which is in the form of numbers or words and helps in taking decisions or drawing conclusions is called data. Tables and graphs are the ways in which data is presented.
The numerical entries in the data are called ‘observations’.

→ The average or Arithmetic Mean or Mean
A.M = \(\frac{\text { Sum of all observations }}{\text { Number of observations }}\)

→ (i.e.,) A.M. is equal to sum of all the observations of a data set divided by the number of observations. It lies between the lowest and highest values of the data.

→ Mode: An observation of data that occurs most frequently is called the mode of the data. A data may have one or more modes and sometimes none.

→ Median: Median is simply the middle observation, when all observations are arranged in ascending or descending order. In case of even number of observations median is the average of middle observations.

→ Mean, mode, median are representative values for a data set.

→ When all values of data set are increased or decreased by a certain number, the mean also increases or decreases by the same number.

→ Data can be presented in bar graphs / double bar graphs or pie chart.

→ Bar graph: Bar graph are made up of bars of uniform width which can be drawn horizontally or vertically with equal spacing between them. The length of each bar tells us the frequency of the particular item. We take convenient scale for the length of bar graph.

→ Double bar graph: It presents two observations side by side.

→ Pie chart: A circle is divided into sectors to represent the given data.
Angle subtended by the sector at the centre of the circle is directly proportional to each observation.

Students can go through AP Board 7th Class Maths Notes Chapter 6 Ratio – Applications to understand and remember the concepts easily.

AP State Board Syllabus 7th Class Maths Notes Chapter 6 Ratio – Applications

→ Ratio: A ratio is an ordered comparison of quantities of the same units.
We use the symbol ‘:’ to represent a ratio. The ratio of two quantities ‘a’ and ‘b’ is a : b and we read it as “a is to b”. The two quantities ‘a’ and ‘b’ are called the terms of the ratio. The first quantity ‘a’ is called first term or antecedent and the second quantity ‘b’ is called consequent.

→ Proportion: If two ratios are equal, then the four terms of the ratios are said to be in proportion. We use the symbol : : (is as)
If two ratios a : b and c : d are equal, we write a : b :: c : d or a : b = c : d
Here ‘a’, ‘d’ are called extremes and b, c are called means.

→ Unitary Method: The method in which we first find the value of one unit and then the value of the required number of units is known as unitary method.
Eg: If the cost of 5 pens is Rs. 85; then the cost of 12 pens is ……… ?
Solution. Cost of 5 pens = Rs. 85
Cost of 1 pen = \(\frac{85}{5}\) = Rs. 17
∴ Cost of 12 pens = 12 × 17 = Rs. 204

→ Direct proportion: If in two quantities, when one quantity increases, the other also increase or vice-versa then the two quantities are said to be in direct proportion.
Eg: The number of books and their cost are in direct proportion.
As the number of books increases, the cost also increases.

→ Ratios also appear in the form of percentages.

→ The word percent means “per every hundred” or for a hundred. The symbol % is used to denote percentage.

→ To convert a quantity into its equivalent percentage

• express it as a fraction.
• multiply it with 100.
• assign % symbol.

Eg: A man purchased an article for Rs. 80 and sells it for Rs. 100. Find his gain percent.
Solution. Cost price = Rs. 80
Selling price = Rs. 100
gain = Rs. 20
gain as a fraction = \(\frac{20}{80}\)
gain as percent = \(\frac{20}{80}\) × 100 = 25%

→ When C.P > S.P there incurs loss.

→ When C.P < S.P there is gain.

→ When C.P = S.P neither loss nor gain.

→ Loss = C.P – S.P gain = S.P – C.P

→ Discount is always expressed as some percentage of marked price.

→ In general when P is principle; R% is rate of interest per annum and I is the interest, then
I = R% of P
I = R% of P for T years