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TRANSCRIPT
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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. () () = +
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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
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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.
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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
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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
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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
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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
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Chapter 8: Coordinates
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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)
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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.
Locus of points that
are equidistant from
two intersecting lines
is a pair ofangle
bisectors.
Locus of points that
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.
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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
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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
A type of transformation in
which all points are moved in
the same direction through
the same distance
Rotation
A type of transformation in
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
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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
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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