Các em hãy làm quen với các bài toán bằng tiếng Anh sau đây.. Chúc các em học tốt.[r]
(1)Các em làm quen với toán tiếng Anh sau Chúc em học tốt ***
1. (a) It is given that = {1, 2, 3, 4, 5, , k} where k 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 = 100
(ii) If n(P Q) = 4, list the elements of the set P Q and hence state the largest possible value of k
(b) It is given that n() = 23, n(A B) = x, n(A) = y, n(B) = 2y and n(A' B') = (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 -
√6 x + √x = are and Without using a calculator, show that 1α + 1β = √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)
Tơn Nữ Bích Vân giới thiệu
(2)1. (a) (i) Q = {9, 19, 29, 39, 49, 59, 69, 79, 89, 99} (ii) P Q = {19, 29, 59, 79} ; k = 88
(b)
least value of y = [when x = 2]
2. The mid-point of AB is (5, 6) The gradient of the line AB is - 107 - 3 = -2 The perpendicular is the
line with gradient 12 and passing through the point (5, 6) Equation of the perpendicular of AB is:
y - = 12 (x - 5) y = 12 x + 72 Alternative method
Let P(x, y) lie on the perpendicular of AB Therefore PA = PB
y - 10¿2
x - 3¿2+¿ ¿
√¿
=
y - 2¿2
x - 7¿2+¿ ¿
√¿
x2 - 6x + + y2 - 20y + 100 = x2 - 14x + 49 + y2 - 4y + Simplifying, 8x - 16y + 56 =
y = 12 x + 72
3. The quadratic equation whose roots are and is (x - ) (x - ) = x2 - (
+ )x + = By inspection: + = √6
= √2
Now 1α+1
β= α+β
αβ =√
6
√2=√3 [Hence shown]
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 (d) ACD = ADT ( in alt segment) = 64o
A B
7
(y-x) x (2y-x)
26o O E
A B
C
D