SPE (YEAR 8)
MATH REVISION HIGHLIGHTS
2022
5 UNITS:
UNIT 1: ARITHMETIC
UNIT 2: ALGEBRA
UNIT 3: GEOMETRY
UNIT 4: MENSURATION
UNIT 5: STATISTICS
BY: TEACHER ALIZAH ITA
UNIT 1 - ARITHMETIC (6):
1. SET OF NUMBER:
- Natural (N) = 1, 2, 3, 4…
- Real (R) = Irrational & Rational (Continuous, e.g. 5.625 & Recurring e.g. 0.272727…)
- Integers (Z) = ….-3, -2, -1, 0, 1, 2, 3… (Positive, zero, negative).
- Rational (Q) = x:x, x = c/d, c, d, ∈, Z, d≠0
- Whole (W) = 0, 1, 2, 3…
(Even: 2, 4, 6…), (Odd: 1, 3, 5…), (Prime: 2, 3, 5, 7, 11… Divisible by the number itself & by 1).
2. S.I. UNIT (UNIT CONVERSION):
A. LENGTH
B. AREA
1cm = 10mm (1mm =
1m = 100cm (1cm =
1km = 1000m (1m =
C. SQ & ROOT, RATIO
1
2
2
2
cm) 1cm = 10 mm
10
1
m)
100
1m2 = 104 cm2
SQUARE: X2
Square root: √X or X
D. MASS
CUBE: X3
Cube root: 3√X or X
1
2
km) 1km = 1000 m
1000
1 KG = 1000G (1G =
1
2
1
3
RATIO, a:b = a÷b = a
b
1
KG)
1000
1 TONNE = 1000KG (1G =
1
KG)
1000
E. VOLUME:
1 L = 1000ML = 1000CM3
1
4
3. FRACTION (e.g. ), DECIMAL (e.g. 0.25) & PERCENTAGE (e.g. 25﹪, Fraction w/ denominator of 100).
4. A. INVERSE PROPORTION:
B. DIRECT PROPORTION
15 workers = 4 days
(15 x 4 = 60)
30 workers = y days
(30 x y = 60)
y x 30 = 15 x 4
y = 15 x 4 ÷ 30
y = 2 days.
2 toys = $20
5 toys = $?
2 toys = $20
1 toy = $20 ÷ 2 = $10
5 toys = $10 x 5 = $50.
5. A. SIGNIFICANT FIGURES (S.F.)
VS B. DECIMAL PLACES (D.P)
- The rst number that is not zero.
- Moving the “point”.
- if the no. next right: 0-4 = maintain, if 5-10= +1. E.g. - E.g. 3 dec places, move 3 points right.
- if the number next right, is 0-4 = maintain.
243 = 200
(Correct to 1 sig. g)
- if the number next right, is 5 & above = +1. E.g.
0.0243 = 0.024 (Correct to 2 sig. g)
(C.P - S.P) x 100
C.P
I = PRT
100
S=D
T
S.P = Selling Price,
C.P = Cost Price
I = Interest , P = Principle S= Speed, D = Distance
T = Time. (e.g. S = 90km/h)
R = Rate ﹪, T = Time/
fi
(S.P - C.P) x 100
C.P
fi
D. AVERAGE SPEED
fi
C. SIMPLE INTEREST
fi
B. LOSS ﹪
fi
6. A. PROFIT ﹪
fi
3.14 = 3.1 (Correct to 1 D.P.).
0.9364 = 0.94 (Correct to 2 D.P.).
7.1302 = 7.130 (Correct to 3 D.P.).
0.00343 = 0.003 (Correct to 3 D.P.).
fi
468 = 470
(Correct to 2 sig. g)
0.5002 = 0.500 (Correct to 3 sig. g)
7.049 = 7.05 (Correct to 3 sig. g)
7.049 = 7.0
(Correct to 3 sig. g)
UNIT 2 - ALGEBRA:
1. a. Indices
b. Useful Identities
2. FACTORIZATION
c. Standard Form
Examples:
a. Common Factor
b. Grouping
c. Inspection
d. Di erences of 2 squares
3. GRADIENT & EQUATION OF A STRAIGHT LINE:
a. GRADIENT
M = Y2-Y1
b. STRAIGHT LINE
y = mx+c
c. MID-POINT
MAB = ( X2+X1 , Y2+Y1 )
2
2
d. DISTANCE
AB = √ ( X2-X1)2 + (Y2-Y1)2
ff
X2-X1
(y = y-intercept , m = gradient)
UNIT 3 - GEOMETRY
A. POLYGON (2):
1. POLYGON INTERIOR ANGLES
2. POLYGON EXTERIOR ANGLES
Sum of interior angles: (2n-4)x900 or (n-2)x1800
Sum of exterior angles: 3600
B. ANGLES (5):
1. STRAIGHT LINE 2. INTERSECTS
3. AT A POINT
4. TRIANGLE
5. PARALLEL
a + b = 1800
a+b+c+d+e = 3600
a+b+c = 1800
∠ACD = ∠A + ∠B
∠x = ∠a + ∠b
a=b , c=b ,
b+d=1800 , a+c = 1800
a+c+d+e = 3600
2. PERPENDICULAR BISECTOR 3. PERPENDICULAR FROM
of line XY
P to line AB
4. PERPENDICULAR RAISED
at point P
a=b & c=d
C. GEOMETRICAL CONSTRUCTION (8):
1. BISECTION
of ∠ABC
5. 600 at point A
6. 900 at point X
7. CIRCUMCIRCLE
of triangle ABC
8. INCIRCLE
of triangle ABC
D. TRIGONOMETRY (2):
1. SOH CAH TOA
Sine A
(Hypotenuse)
(Opposite)
(Adjacent)
2. Pythogeras Theorem
= Opposite .
Hypotenuse
= BC
AC
Cosine A = Adjacent .
Hypotenuse
= AB
AC
.
.
Tangent A = Opposite . = BC.
Hypotenuse
AB
.
AC2 =
BC2 + AB2
AC = √ (BC2 + AB2)
UNIT 4 - MENSURATIONS:
A. PERIMETER & AREA (4):
Length (ℓ)
1. SQUARE:
Area
(A) = ℓ2
Perimeter
(P) = 4ℓ
Length
(ℓ) = √A or P÷4
2. RECTANGLE:
Area
(A) = ℓ x b
Perimeter
(P) = 2(ℓ x b)
Length
(ℓ) = (A÷b) or (P÷2-b)
Breadth
(b) = (A÷ℓ) or (P÷2-ℓ)
3. EQUILATERAL TRIANGLE:
Area
(A) = 1/2 (B x H)
Base
(P) = 2A÷h
Height
(H) = 2A÷b
4.i. SECTOR OF A CIRCLE:
Area
(A) = x/360 x πr2
Perimeter
(P) = x/360 x 2πr2 + 2r
4.ii. CIRCUMFERENCE OF A CIRCLE:
Area
(A) = πr2
Circumference (C) = 2πr or 2d
Diameter
(d) = 2r
or (c÷π)
Radius
(r) = (C÷2π) or (d÷2)
B. SURFACE AREA & VOLUME (4):
1. Cuboid:
Volume
(ℓ x b) x h
Height
Length
(H) = V ÷ ℓ x b
(ℓ) = v ÷ b x h
2. Cube:
Volume
Length
(V) = ℓ3
(ℓ) = 3√v
4. Prism:
Volume
(V) = base Area x height
3. Cylinder:
Surface Area
Volume
(A) = 2πrh + 2πr2
(V) = πr2 x h
(V) = Area of base x height =
UNIT 5 - STATISTICS:
1.
a) Which team performed the best in terms of the number of goals scored?
= Dragon = (4 x 4) + (4 x 1/2) = 18 goals
Horse = (2 x 4) + (4 x 3/4) = 11 goals
Lion
= (4 x 5) + (4 x 1/4) = 21 goals (The most goals)
Tiger = (4 x 4)
= 16 goals
.
. . Lion team performed the best. Lion team got the highest score with 21 goals.
b) Find the ratio of the number of goals scored by Dragon to that by Horse.
= Number of goals scored by Dragon : Number of goals scored by Horse
=
(4 x 4 + 2) : (4 x 2 + 3)
=
18 : 11
_______________________________________________________________________________________________________
2.
(a) Compare the sales of co ee over the 4 hours.
= The sales of co ee (30 cups) were highest at 8 a.m.
The sales of co ee (18 cups) were lowest at 10 a.m.
(b) During which period were the sales of tea more than those of co ee?
= The sales of tea were more than those of co ee at 10 a.m.
(c) How many cups of co ee were sold during the four hours?
= Total number of cups of co ee sold
= 30 + 26 + 18 + 20 = 94 cups of co ee.
_______________________________________________________________________________________________________
3.
(a) Find the value of x.
= 90° + 135° + x° + 75° = 360° (Zs at a point)
... x = 60°
(b) Find the percentage of interviewees who chose mango juice.
= 135/360 x 100﹪
= 37.5﹪
(c) If 40 interviewees selected apple juice, nd:
(i) the total number of interviewees,
= 40 ÷ 60/360
= 40 x 360/60
= 240 interviewees.
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ff
ff
ff
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(ii) the number of interviewees who chose orange juice.
= 240 x 90/360
= 60 interviewees.