DSE MATHEMATICS TAK SUN SECONDARY SCHOOL 151112

Last Minutes Review II [1]

Mathematics Last Minutes Review II

Revision – Straight lines and locus Horizontal line: ky , Vertical line: hx

Intercept-slope form: cmxy Point-slope form: mxx

yy

1

1

Slope of a line (2 points): 12

12

xx

yy

Two-point form: 12

12

1

1

xx

yy

xx

yy

General form: 0 CByAx B

Cx

B

Ay x-intercept =

A

C (Put y = 0)

Slope = B

A y-intercept =

B

C (Put x = 0)

Relationship between two lines: overlapping (same slope 21 mm & y-intercept 21 cc )

parallel ( 21 mm )

perpendicular ( 121 mm )

intersecting ( 21 yy find the point) Linear programming:

1. Let x and y be the amount of those items Note: 0x , 0y , integer / number? Set up equations according to the questions

2. DRAW lines! (Get 2 points solid vs. dotted) SHADE area! (Try a point (0,0) shade / plot integral points)

3. Write down the Cost function of x and y Set Cost = 0 Plot the line move in parallel to the max/min

4. Get max/min point and find Cost (or get the point from all extremes)

Intersection of 2 lines

)2(0

)1(0

rqypx

cbyax Sub (1) into (2)

For any two points 11 , yxA and 22 , yxB , Distance formula: 212

212 yyxxAB

Mid-point formula:

2,

22121 yyxx

Section formula (r : s):

sr

rysy

sr

rxsx 2121 ,

Distance of A to line ky : ky 1 or 1yk Distance of A to line hx : hx 1 or 1xh

Finding locus: 1. Let yxP , be the movable point of the locus 2. Use distance formula, slope properties, … to set up a relationship 3. Express the equation as 022 FEyDxByAx

Description of locus: Fixed distance to a point Circle Fixed distance to a line 2 parallel lines Equal distance to parallel lines A line in the midway Equal distance to 2 points A perpendicular bisector Equal distance from 2 crossing lines A pair of angle bisectors Equal distance to a point and a line Parabola

DSE MATHEMATICS TAK SUN SECONDARY SCHOOL 151112

Last Minutes Review II [2]

Revision – Circle properties

DSE MATHEMATICS TAK SUN SECONDARY SCHOOL 151112

Last Minutes Review II [3]

Revision – Tangent properties

Revision – Equation of circle Given Centre kh, and radius r 222 rkyhx

Given 022 FEyDxyx Centre =

2,

2

ED, Radius = F

ED

22

22

Given 3 points Let 022 FEyDxyx Sub 3 points 3 equations 3 unknowns

Relationship between a circle and a straight line:

)2(

)1(22

cmxy

FEyDxyxy

Sub (2) into (1) Quadratic equation in x 0 2 intersections 0 1 intersection (line is tangent to circle) 0 0 intersections

Revision – Trigonometry functions For a right-angled triangle

c

asin ,

c

bcos ,

b

atan

For yxP , on a rectangular plane

r

ysin ,

r

xcos ,

x

ytan , 22 yxr

Properties: 1sin1 , 1cos1 tan has no max/min sin and cos are periodic of 360 tan are periodic of 180

Identities: 1cossin 22 ,

cos

sintan

ff

o

o

360

180,

coff

o

o

270

90

tan

1tan

sincos

cossin*

coff

coff

coff

a c

b

DSE MATHEMATICS TAK SUN SECONDARY SCHOOL 151112

Last Minutes Review II [4]

Revision – Graph of the functions 0 90 180 270 360 sin 0 1 0 – 1 0 cos 1 0 – 1 0 1 tan 0 +/– 0 –/+ 0

Translation of yxP , Reflection of yxP , Rotation of yxP ,

Translation of xfy Reflection of xfy Enlargement/ Reduction of

Revision – 3-D problem Draw triangles from side and top views Find projection of a point to a plane

Triangle properties: Pythagoras’ theorem: 222 cba

Sine law: C

c

B

b

A

a

sinsinsin

Cosine law: Cabbac cos2222

Area: of △: Cabsin2

1

Or Heron’s formula Direction:

True bearing: 045 200 Compass bearing: N45E S70W

(x, y+k)

(x, y–k)

(x+h, y) (x–h, y)

(x, y)

(x, –y)

(x, y) (–x, y)

(–y, x)

(y, –x)

(x, y)

(–x, –y)

y–k = f(x)

y+k = f(x)

y = f(x–h) y = f(x+h)

y = f(x)

–y = f(x)

y = f(x) y = f(–x)

y/k = f(x)

yk = f(x)

y = f(x/k) y = f(xk)

xfy