Advanced Level – Combined Mathematics (Model Paper - 005)

 

Advanced Level – Combined Mathematics (Model Paper)

Time: 3 Hours
Total Marks: 100

Instructions to Candidates

1. Answer all questions.

2. Show all workings.

3. Use π ≈ 3.14 unless otherwise stated.

4. Calculators may be used where permitted.

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Section A — Multiple Choice Questions (MCQs)

(10 × 1 = 10 marks)

Section B — Short Answer Questions

(10 × 4 = 40 marks)

(10 × 4 = 40 marks)

11. Expand and simplify $(x+2)(x−3)(x+4)$
    

12. Solve the equation:
    $3\sin x −1=0$
    for $0\mathrm{°}\le x\le 360\mathrm{°}$

13. Find the derivative of $y=5x^4−3x+7$
    

14. Find the equation of the tangent to the curve $y=x^2+2x−3$ at $x=1$

15. A box contains 5 red and 7 blue balls. One ball is chosen at random. Find the probability it is blue.

16. Find the inverse of the matrix $\begin{pmatrix} 2 & 1 \\ 5 & 3\end{pmatrix}$.

17. Evaluate $\int (4x-1)dx$

18. Solve $\log_2 (x+1)=3$
    

19. A sequence has general term $T_n=2n+3$. Find $T_{10}$ the sum $S_{10}$.

20. Determine whether the vectors $\vec{u}=(4,1)$ and $\vec{v}=(1,−2)$ are perpendicular.

Section C — Structured Questions

(5 × 10 = 50 marks)