Làm quen toán tiếng Anh

Các em hãy làm quen với các bài toán bằng tiếng Anh sau đây.. Chúc các em học tốt.. The tangents TA and TD are drawn from a point T to the circle, centre O.. The diameter DB and the tang

Các em hãy làm quen với các bài toán bằng tiếng Anh sau đây Chúc các em học tốt.

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1 (a) It is given that  = {1, 2, 3, 4, 5, , k} where k is a positive integer.} where k} where k is a positive integer is a positive integer.

P is a subset where P = {x: x is a prime number}

Q is another subset and Q = {x: the unit digit is 9}

(i) List all the members of Q given that k} where k is a positive integer = 100

(ii) If n(P  Q) = 4, list the elements of the set P  Q and hence state the largest possible value of k} where k is a positive integer

(b) It is given that n() = 23, n(A  B) = x, n(A) = y, n(B) = 2y and n(A'  B') = 7

(i) Use a Venn diagram and show that 3y = 16 + x

(ii) Hence find the least possible value of y

2 Find the equation of the perpendicular bisector of AB where A is (3, 10) and B is (7, 2)

3 The roots of the quadratic equation x2 - 6x + x = 0 are  and 

Without using a calculator, show that



1

+ 1 = 3

4 The tangents TA and TD are drawn from a point T to the circle, centre O The diameter

DB and the tangent TA when produced meet at E Given that  ADO = 26o, find

(a)  ADT

(b)  ATD

(c)  BAE

(d)  ACD ( C is a point on the cirlce, centre O)

Tôn Nữ Bích Vân giới thiệu

1 (a) (i) Q = {9, 19, 29, 39, 49, 59, 69, 79, 89, 99}

(ii) P  Q = {19, 29, 59, 79} ; k} where k is a positive integer = 88 (b)

least value of y = 6 [when x = 2]

2 The mid-point of AB is (5, 6) The gradient of the line AB is 27--103 = -2 The perpendicular is the

line with gradient 21 and passing through the

point (5, 6) Equation of the perpendicular of AB is:

y - 6 =

2

1

(x - 5)

y = 21 x +

2 7

Alternative method

Let P(x, y) lie on the perpendicular of AB

Therefore PA = PB

 (x - 3) 2  (y - 10) 2 = (x - 7) 2  (y - 2) 2

 x2 - 6x + 9 + y2 - 20y + 100 = x2 - 14x + 49 + y2 - 4y + 4

Simplifying, 8x - 16y + 56 = 0

2

7

3 The quadratic equation whose roots are  and  is (x - ) (x - ) = 0

x2 - ( + )x +  = 0

By inspection:  +  = 6

 = 2

2

6 1

1



















4 (a) ODT = 90o (tan  rad )

ADT = 90o - 26o

= 64o (b) TA = TD (tangents from an external point)

TDA = TAD (base s of isos )

ATD = 180o - 64o - 64o ( sum of )

= 52o (c) BAE = ADB ( in alt segment) = 26o



7

(y-x) x (2y-x)

26 o

O

E

A B

C

D

T

(d) ACD = ADT ( in alt segment) = 64o