SING YIN SECONDARY SCHOOL

F.2 FIRST EXAMINATION 2024-2025

MATHEMATICS — Question-Answer Book

75 minutes — FULL MARKS: 84

This paper must be answered in English

After the announcement of the start of the exam, write your name, class and class number in the spaces provided.
Attempt ALL questions in this paper. Write your answers in the spaces provided in this Question-Answer Book. Do not write in the margins.
There are TWO sections, A and B. You are advised to finish Section A in about 25 minutes.
In Section A, choose the best answer and write the appropriate letter in the box provided.
In Section B, unless otherwise specified, all working must be clearly shown.
Unless otherwise specified, numerical answers should be either exact or correct to 3 significant figures.
The diagrams in this paper are not necessarily drawn to scale.
No calculators are allowed.

Name:

Class:

Class Number:

Go on to the next page

Section A (2 marks each)

(You are advised to finish Section A in about 25 minutes.)

1. (2c)³(3c²)² =

A. 108c⁷

B. 54c⁶

C. 72c⁸

D. 108c⁸

2. (5y³ − 2y²) − (3y³ + 7y²) =

A. 2y³ − 9y²

B. 8y³ + 5y²

C. −2y³ − 9y²

D. −8y³ + 5y²

3. The coefficient of x² in (2 − x)(4x − 3 + x²) is

A. −2

B. −4

C. 2

D. 4

4. 3(a − 5)² =

A. 3a² − 30a + 75

B. 3a² − 15a + 25

C. 6a² − 30a + 150

D. 3a² − 30a + 25

5. 9.02 × 10⁶ − 7.95 × 10⁵ =

A. 8.225 × 10⁶

B. 1.07 × 10⁶

C. 8.225 × 10⁵

D. 1.07 × 10⁵

6. In which of the following does the digit “0” have the greatest place value?

A. 23015₆

B. 14027₈

C. 101010₂

D. 120304₅

7. ((−1)/81)⁸ × 3²⁴ =

A. 1/9⁸

B. −1/9⁸

C. 1/3⁸

D. −1/3⁸

8. (4m)²n⁴ ÷ (mn⁻³) =

A. 16n⁷/m

B. 4n⁷/m

C. 16m n⁷

D. 16n/m

9. Which of the following is/are identity(ies)?
I. 6(p + 1) − 6 = 6p
II. (2q − 3)(q + 3) − 2q² + 9 = 0
III. (5r − 1)² − (25r² − 1) = 0

A. I only

B. II only

C. I and II only

D. I and III only

10. 8ux − 24uy − 6vx + 18vy =

A. (8u − 6v)(y − 3x)

B. (8u − 6v)(3y − x)

C. (8u + 6v)(x − 3y)

D. (8u + 6v)(3y − x)

11. 16 − (a − 4b)² =

A. (4 + a − 4b)(4 − a − 4b)

B. (4 − a + 4b)(4 + a − 4b)

C. (16 + a − 4b)(16 − a − 4b)

D. (4 − a − 4b)(4 + a + 4b)

12. (4p² − 12pq) / (9q² − 3pq) =

A. 4p / 9q

B. (4p²) / (9q²)

C. 4(p − 3q) / (3q(3q − p))

D. (4p) / (3q)

13. 5/(3k − 8) − k/(8 − 3k) + (2 − k)/(3k − 8) =

A. 1

B. −1

C. (7 − 2k)/(3k − 8)

D. (k − 7)/(3k − 8)

14. If N = T(2a + b/3), then a =

A. (N/T)/2 − b/6

B. (3N − Tb) / (6T)

C. (N − Tb/3) / (2T)

D. 2N/T − b/3

15. If 0.6051 < x < 0.6059, which of the following is true?

A. x = 0.61 (correct to 2 decimal places)

B. x = 0.61 (correct to 2 significant figures)

C. x = 0.606 (correct to 3 decimal places)

D. x = 0.606 (correct to 3 significant figures)

End of Section A — Go on to the next page

Section B: Conventional Questions (54 marks)

(6 marks)

1. Simplify the following expressions and express answers with positive indices.

(a) (−3a²b)³ × (ab⁻²) × (2b³)²

(b) (x²y⁻¹z)³ ÷ (x⁻¹y²z⁻²)

(5 marks)

2. (a) Expand (m − 7)(m + 7).

(b) Hence, or otherwise, expand (p + q − 7)(p + q + 7).

(3 marks)

3. Let C and D be constants. Find the values of C and D if (4x + C)(x − 3) = 4x² + Dx − 3C.

(5 marks)

4. (a) Simplify (5y² − 3y + 4) − (2y² + 7y − 1).

(b) Hence, find the value of the expression in (a) when y = −2.

(5 marks)

5. Expand and simplify:

(a) −3(u v − 2)

(b) t²(3t − s) + (t² + 9)(3t + s)

(5 marks)

6. (a) Factorize: pq + 7q − 5p − 35.

(b) Hence, factorize: (q − 5)² + pq + 7q − 5p − 35.

(4 marks)

7. (a) Convert 1010110₂ to a denary number. Show your steps.

(b) Convert 73₁₀ to a binary number. Show your steps.

(6 marks)

8. (a) Make w the subject of the formula z = (200 − 5w)/(t − 3w).

(b) If z = 1/5 and t = 250, find the value of w.

(9 marks)

9. Simplify the following:

(a) (3x − 12y)/(9x − 36y)

(b) (2p + 6)/(p² − 9) ÷ (p + 3)/(2p − 6)

(6 marks)

10. It is given that the mass of a sodium atom is approximately 3.8 × 10⁻²³ g and the mass of a chlorine atom is approximately 5.9 × 10⁻²³ g. A molecule of sodium chloride (NaCl) consists of one sodium atom and one chlorine atom.

(a) Express the mass of one NaCl molecule in scientific notation.

(b) How many NaCl molecules are there in 2.0 kg of NaCl? Express your answer in scientific notation, correct to 3 significant figures.

END OF PAPER