form2_maths mind maps

8/4/2019 Form2_maths Mind Maps

1/13

Chapter 1: Directed Numbers

DIRECTED NUMBERS

Integers Fractions Decimals

Positive and negative Positive and negative

fractions decimals

Multiplication Division(+) (+) = + (+) (+) = + Addition Subtraction Division

(+) () = (+) () = + () = () = + (+) (+) = +

() (+) = () (+) = + (+) = + (+) (+) () =

() () = + () () = + () (+) =

() () = +

Combined Operation

Follow the order as follows when solving Multiplication

combined operations. (+) (+) = +

1 Operations in the brackets. (+) () =

2 Multiplication or division from left to right. () (+) =

3 Addition or subtraction from left to right. () () = +


2/13

SQUARES, SQUARE ROOTS,

CUBES AND CUBE ROOTS

Cubes

1 A number when multiplied by itself twice.

2 The cube ofx=xxx=x3.

3 The cube of any positive number is always

positive.4 The cube for any negative number is always

negative.

Cube Roots

1 A number which, when multiplied by itself

twice, produces the given number.

2 Finding cube roots is the inverse of

cubing.

3 The cube root of any positive number is

always positive.

4 The cube root of any negative number is

always negative.

Squares

1 A number when multiplied by itself.

2 The square ofx=xx=x2.

3 A square of any number is equal to zero or

greater than zero (always positive).

Square Roots

1 A number which when multiplied by itself,

produces the given number.

2 Finding square roots is the inverse of

squaring.

3 x2 = x

4 x x = ( x)2 = x

x x5 = y y

6 x y = xy

7 x+y x + y

Chapter 2: Squares, Square Roots, Cubes and Cube Roots


3/13

Chapter 3: Algebraic Expressions

Simplify Algebraic Expressions

1 Arrange the like terms together.

2 Remove the brackets.

3 Add or subtract the numerical

coefficient of the like terms.

Evaluate Expressions

1 Substitute letters with numbers.

2 Find the value.

Remove the Brackets

+(x+y) = +x+y

+(xy) = +xy

+(x+y) = x+y

+(xy) = xy

(x+y) = xy

(xy) = x+y

(x+y) = +xy

(xy) = +x+y

Quotient of Two Terms

1 Divide the numbers and

the unknowns.

2 Simplify the terms using

the elimination method.

36x2y3 = 6xy2

6xy

Product of Two Terms

1 Multiply the numbers

and the unknowns.

2 Write the unknowns in

alphabetical order.

6xy ( 4xy)

= 24x2y2

ALGEBRAIC EXPRESSIONS

Algebraic Expressions

An expression consist of one or more terms

joined together by a plus or minus symbol.

6

Algebraic Terms

Combination of a number (coefficient)

and one or more unknowns.

Unknown Coefficient

A quantity that is The term in front

not known and of an unknown in

usually represented an algebraic term.

by a letter.

Like Terms Unlike Terms

Terms that have the Terms with different

same unknown unknowns.

with the samepower.


4/13

Chapter 4: Linear Equations I

LINEAR EQUATIONS I

Linear

Algebraic Terms

A term with

unknowns to the

power of 1.

81y, 4s

Linear Equations

An equation

consisting of linear

algebraic terms and

numbers or linear

algebraic expressions

and numbers.3x+ 9y= 36

Solutions of Linear Equations

in One Unknown

1 Subtracting a number from both

sides.

y+ 2 = 6 y+ 2 2 = 6 2

y = 4

2 Adding a number to both sides.

y 2 = 6

y 2 + 2 = 6 + 2

y = 8

3 Dividing both sides by the

number.

2y = 6

2y 2 = 6 2

y = 3

4 Multiply both sides with a

number. y

= 62

y 2 = 6 22

y = 12

5 Mixed operations.

3x + 2 = 8

43x

= 8 24

3x 4 = 6 4

4

24 x = 3

x = 8

Equality

1 A relationship between

two quantities which

have the same value.

2 = means equal to.

3 means not equal to.

Linear Equations in

One Unknown

Equations with only one

unknown to the power of

one.

Linear Algebraic

Expressions

Combination of one or

more linear terms

connected by addition

or subtraction or both.

2x 5y


5/13

Chapter 5: Ratios, Rates and Proportions

Ratios

A relationship that is used

to compare two or more

quantities with the same

unit of measurement.

Proportions

1 A relationship between two

quantities or two ratios.

2 Ifp and q are two values for

quantity Yand rand s are two

values for quantityZ, YandZis a proportion if

p r = or p : q = r: s.

q s

(q 0, s 0)Equivalent Ratio

Two or more ratios

which have the same

value.

Ratio of Three Quantities

1 Comparison of three

quantities with the same unit.

2 IfP: Q : R =x:y:z, then

(i) P: Q = x:y

(ii) Q : R = y:z

(iii) R : P = z :x

(iv) P: P+ Q + R =x:x+y+z

Simplify Ratio to

Lowest Terms

The ratio a : b is

in lowest terms if

a and b are whole

numbers that have

no other common

factor except 1.

Rates

The change in a quantity

with respect to another

quantity.

RATIOS, RATES AND PROPORTIONS


6/13

Chapter 6: Pythagoras Theorem

Pythagoras Theorem

In a right-angled triangle, the

square of the hypotenuse is equal

to the sum of the squares of the

other two sides.

c2 = a2 + b2

c = a2 + b2

a2 = c2 b2

a = c2 b2

b2 = c2 a2

b = c2 a2

PYTHAGORAS THEOREM

Converse of

Pythagoras Theorem

Used to determine

whether a triangle is a

right-angled triangle.

If c2 = a2 + b2,

thenC = 90.

Pythagorean Triples

A combination of three

positive integers for a

right-angled triangle that

fulfils Pythagoras Theorem.

3, 4, 5 6, 8, 10

7, 24, 25

B

C A

ca

b

B C

A

cb

a


7/13

Chapter 7: Geometrical Constructions

GEOMETRICAL CONSTRUCTIONS

Line Segments

Triangle with

given sides

Perpendicular Parallel lines

Parallel lines

M N

P

Q

M N

P

Q

120

60

Perpendicular

bisector of a line

Perpendicular

to a line passing

through a point

not on the line

Perpendicular to a

line passing through a

point on the line

Angles

Angles of 60

Angles of 120

Angle bisector

Parallelogram

60

M N

P

Q


8/13

Chapter 8: Coordinates

-

COORDINATES

Cartesian Plane

y-axis

x-axis

0 Origin

y

x

20

10

10 5 5 10 15

Scales of Coordinate Axes

The ratio which shows the values

represented by one unit on an axis.

Scale on thex-axis 1 : 5

Scale on they-axis 1 : 10

Midpoint of a Straight Line

Joining Two Points

1 The point in the middle of a line

segment

2 Midpoint of a straight line with:

(i) commony-coordinate = mean of

the twox-coordinates

(ii) commonx-coordinate = mean of

the twoy-coordinates

(iii) differentx-coordinates and

differenty-coordinates

Midpoint between (x1,y

1) and (x

2,y

2)

x1

+x2 y

1+y

2( , )2 2

Distance between Two Points

(i) commony-coordinate = difference

between thex-coordinates

(ii) commonx-coordinate = difference

between they-coordinates

(iii) differentx-coordinates and different

y-coordinatesDistance between (x

1,y

1) and (x

2,y

2)

Using Pythagoras theorem,

(x2

x1)2 + (y

2y

1)2

Coordinates of Points

(x, y)

(x-coordinate) (y-coordinate)

Distance fromy-axis Distance fromx-axis

y

(negative, positive) (positive, positive)

(Second quandrant) (First quadrant)

x(negative, negative) (positive, negative)

(Third quadrant) (Fourth quadrant)


9/13

Chapter 9: Loci in Two Dimensions

LOCI IN TWO DIMENSIONS

Locus of points

that are a constant

distance from a fixed

point is a circle.

Intersection of

Two Loci

The intersection point

satisfies the conditions

of both loci.

Locus of points that

are a constant

distance from a

straight line is a pair

ofparallel lines.


are equidistant from

two intersecting lines

is a pair ofangle

bisectors.


are equidistant from

two fixed points is the

perpendicular

bisector of the line

joining the two points.

Path formed by a set

of points that satisfy

a certain condition.


10/13

Chapter 10: Circles I

Circumferene of a Circle

Circumference = dor 2r22

= or 3.1427

Parts of a Circle

CIRCLES I

Circle

Completely

round flat

shape.

Area of Circle

Area of circle = r2

Area of circler =

Area of Sector

Area of sector Angle of sector = Area of circle 360

Area of sector = r2

360

Length of the Arc of a Circle

Length of arc Angle at centre = Circumference 360

Length of arc = 2r

360

centre

circumference

diameter

radiuschord

minor arc

major arc

majorsegment

minorsegment

major sector

minor sector


11/13

Chapter 11: Transformations I

TRANSFORMATIONS I

Reflection

A type of transformation in

which all points on a plane

are flipped over in the

same plane at a line called

the axis of reflection

Translation


which all points are moved in

the same direction through

the same distance

Rotation


which all points on a plane are

rotated about a point in the

same direction through the

same angle

Isometry

A transformation that preserves the

shape and size of the object

Congruence

Two figures are congruent if they

have the same shape and size under

any orientation


12/13

Chapter 12: Solid Geometry II

SOLID GEOMETRY II

Geometric solids and their nets

(i) Prism

(ii) Pyramid

(iii) Cylinder

(iv) Cone

Total surface area of geometric solids

(i) Cube (iv) Sphere

Surface area Surface area

= 6 l2 = 4r2

(ii) Cylinder (v) Pyramid

Surface area Total surface area

= 2r2 + 2rh = area of base +

area of slant faces

(iii) Cone

Surface area

= r2 + rl

l

h

l


13/13

Chapter 13: Statistics

Pictograms

Graphic representation of data

using symbols or pictures

Bar graphsA representation of data using a

graph with horizontal or vertical

bars of equal width

Line graphs

A graph in which points are joined

by line segments to represent data

collected over a period of time

Data

A collection of information or facts

Frequency

The number of times an event orvalue occurs in given data

Frequency tables

A table which shows how many times

an item or event occurs in a set of

data

STATISTICS

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