Area of square-SxS

Area of right-angled triangle-1/2 x base x height

Area of trapezium-1/2 x (Sum of parallel sides) x height

Area of rhombus – ½ x d1 x d2

Perimeter of rectangle=2(L+B)

Area of 4 walls-2 (L+B) h

 

VOLUME:

Cube-s3

Cuboid – lbh

Cylinder- πr2h

 

Surface area-

Cube-6a2

Cuboid – 2 (lb+bh+hl)

Cylinder - 2π(r+h)

 

Curved surface area of cylinder=2πrh
PI CHART-They are  circles that are divided into segments or categories which reflect the proportion of the variables in relation to the whole. Percentages are used to compare the segments, with the whole being equal to 100%.
BAR GRAPH-A Bar Graph (also called Bar Chart) is a graphical display of data using bars of different heights.
HISTOGRAM- A GRAPH consisting of rectangles whose area is proportional to the frequency of a variable and whose width is equal to the class interval.
LINE GRAPH-Line graphs compare two variables. Each variable is plotted along an axis. A line graph has a vertical axis and a horizontal axis. So, for example, if you wanted to graph the height of a ball after you have thrown it, you could put time along the horizontal, or x-axis, and height along the vertical, or y-axis.

CONVERSION
1cm= 10 mm
1 km = 1000m
1 km = 100000 cm
1 cubic m= 1000000 cubic cm

laws of exponents

x¹ = x
x⁰ = 1        7⁰ = 1
x^-1 = 1/x     4^-1 = 1/4

x^mxⁿ = x^m+n       | x²x³ = x²⁺³ = x⁵
x^m/xⁿ = x^m-n      | x⁶/x² = x^6-2 = x⁴
(x^m)ⁿ = x^mn        | (x²)³ = x^2×3 = x⁶
(xy)ⁿ = xⁿyⁿ        | (xy)³ = x³y³
(x/y)ⁿ = xⁿ/yⁿ       (x/y)² = x² / y²
x^-n = 1/xⁿ

 

3168 ÷ 10 × 500= 158,400m sq

Area of right-angle triangle-1/2 b*h

Area of trapezium-1/2*h(a+b)

Area of rhombus – ½ x d1 x d2

Perimeter of rectangle=2(L+B)

Perimeter of 4 walls-
2h(l+b)

question 11
 2πr
2 × 22 ÷ 7 × 42 ÷ 100 × 120
=316.8
=316

3168 ÷ 10 × 500= 158400 sq meter

Area of square-SxS

Area of right-angled triangle-1/2 x base x height

Area of trapezium-1/2 x (Sum of parallel sides) x height

Area of rhombus – ½ x d1 x d2

Perimeter of rectangle=2(L+B)

Area of 4 walls-
Rectangle - 2h(L+B) 

 Square - 4a^2

VOLUME:

Cube-s^3

Cuboid – l*b*h

Cylinder- πr^2h

 

Surface area-

Cube-6a^2

Cuboid – 2 (lb+bh+lh)

Cylinder - 2π(r+h)

 

Curved surface area of cylinder=2πrh

CONVERSION
1cm= 10 mm
1 km = 1000m
1 km = 100000 cm
1 cubic m= 1000000 cubic cm

laws of exponents

x^1 = x
x^0 = 1       
x^-3= 1/x^3
x^m * x^n = x^m+n     
x^m\ x^n = x^m-n     
(x^m)^n = x^mn     
(xy)^n = x^n * y^n       
(x/y)^n = x^n/y^n
Definitions of different types of graph-
Histogram - a histogram is a visual way to display frequency data using bars. A feature of histograms is that they show the frequency of continuous data.

Bar graph - A bar graph is a chart that uses bars to show comparisons between categories of data.
 
Double bar graph - A double bar graph is a graphical display of information using two bars besides each other at various heights.We can use a double bar graph to compare two data groups.

Pie chart - a circular statistical graphic, which is divided into slices to illustrate numerical proportion.

Line graph - a type of chart which displays information as a series of data points called 'markers' connected by straight line segments. It is a basic type of chart common in many fields.

 

1. Factorize using identities

a) 4x^2– 4x +4​ = (2x - 2)^2
b)  25x^2 - 30x + 9​ 
Ans. FT = 5x
LT = 3
MT = 2 * FT * LT 
= (5x - 3)^2
c)  169x^2 – 196y^2
Ans. 13x^2 - 14x^2
c) a^4 - b^4
(a^2 + b^2)(a+b)(a-b)
d)  a^8 - b^8
(a^4+b^4)(a^2+b^2)(a+b)(a-b)

e)  a^16 - b^16
(A^8+b^8)(a^4+b^4)(a^2+b^2)(a+b)(a-b)
​​f) 5x^3 + 70x^2 + 245x 
5x[(x+14x+7)(x+7)]
  g)  3x^3 - 48x
3x[(x-4)(x-4)]
Q2) (x-8)(x-9)\(x-9) = x-8
Q3) (x+6)(x+5)\(x+6) = (x+5)