Đề Toán Tiếng Anh tham khảo thi vào Raffles Singapore

If x varies directly as the cube of y and the square of y varies inversely as the cube of z, prove that x2z9 is a constant... In each of the following, the graph of fx is given.. On the

SECTION A (50 marks) Answer all questions in this section

1 Solve the follwing equations

(a) (2x + 3)(2x - 1) = 5(5 - x)

(b) 12x2 - kx = 15, where k is a constant, leaving your answers in terms of k and in surd form if necessary

Answer (a)………[2]

(b)………[2]

1 8

2

2

2 2

2

=

−

+

b a

b ab

, find the value of 2

2

4

b a

3 Given that 1 - 5x 2 2

2

and 1 2y 6, find the range in which y

x

must lie

Answer ………[4]

4 If x varies directly as the cube of y and the square of y varies inversely as the cube of z, prove that x2z9 is a constant

Answer ………[4]

5 In each of the following, the graph of f(x) is given On the same axes, sketch and label the graph of g(x) Indicate clearly the x-intercept(s), y-intercept and

asymptote, where applicable

(a) f(x) = x 2 g(x) = f(x) + 2 [1]

(b) f(x) = x(x - 2)(x - 4) g(x) = f(2x) [2]

(c) f(x) = x

1

g(x) = f(x - 1) [2]

y

6 The line 5y + 4x = 20 cuts the x-axis at P and the y-axis at Q The point R is the midpoint of PQ and O is the origin

Find the equation of

(a) the line through R which is parallel to the y-axis,

(b) the line which is the reflection of the line PQ in the x-axis

Answer (a)………[2] (b)………[1]

7 In the diagram, AD is the diameter of circle, centre O The points B and C lie on the circumference of the circle such that BC is parallel to AD Given that reflex

∠ AOB = 3200, find

(a) ∠ ACB,

(b) ∠ ADC

Answer (a)………[1]

8 The graph below shows how the speed of a car changes as it starts from rest The four sections of the graph indicate the speeds in the four gears

(a) Calculate the distance travelled in the fifst 10s

(b) On the axes in the answer space, sketch the acceleration-time graph of the car in the first 26 seconds [3]

Answer (a)………[2]

9 AD and CD are tangents to the circle, center O Given that ∠ADC = 360, calculate

(a) ∠ACD

(b) ∠ABC

Answer (a)………[1]

(b)………[3]

10 In triangle ABC, ∠BAC = 1200, AB = 3cm and AC = 5cm, caculate (a) the area of ABC,

(b) the height h, of ABC,

[sin 600 = 0.87, cos 600 = 0.5, tan 600 = 1.73]

Answer (a)………[2] (b)………[3]

C

11 A group of 60 pupils took a test 5

1

of the students obtained not more than 5

2

of the maximum score 4

1

of the pupils obtained more than or equal to 10

7

of the maximum score The minimum and maximum scoreres were 0 and 100 respectively

(a) Complete the frequency table below and use it to complete the histogram

[4]

Class (score) Base (Class size) Frequency Frequency Density

Frequency density

10 20 30 40 50 60 70 80 90 100

Score

(b) Identify the modal class

Answer (b)………[1]

12 A strange chessboard has 4 rows and 2 columns There are eight 1 x 1 squares and three 2 x 2 squares on it

(a) If the chessboard has 5 rows and 3 columns, how many 1 x 1, 2 x 2 and 3 x 3 squares are there on the chessboard?

(b) Complete the table below [2]

Chessboard of squares

5 x 3

6 x 4

7 x 5

(c) By using the observed pattern in (b), find the total number of squares of all sizes

on the chessboard if the chessboard has 10 rows and 8 columns

Answer (a) Number of 1 x 1 squares =………

Number of 2 x 2 squares =………

Number of 3 x 3 squares =………

[1]

(c)………[2]

End of selection A