Advanced level 2025 BAEBOC Further mathematics 1

Advanced level 2025 BAEBOC Further mathematics 1

Advanced level 2025 BAEBOC Further mathematics 1

Here’s the extracted data from the image:

1. x2−x−62x2−3​ expressed in partial fractions, where p, q and r are constants, is: A. x−3p​+x+2q​ B. p+x−3q​+x+2r​ C. x−3p​−(x−3)2q​ D. p+x+2q​+(x−3)2r​

2. If $\sinh x=2$, then $x=$ A. ln(2−3​) B. ln(2+3​) C. ln(−2+5​) D. ln(2+5​)

3. The integrating factor for dxdy​+3y=x+1 is A. $3x$ B. ex C. e3x D. $\ln (3x)$

4. $(\mathbf{i}-\mathbf{j}-\mathbf{k})\times (\mathbf{j}-2\mathbf{k})=$ A. $3\mathbf{i}-2\mathbf{j}+\mathbf{k}$ B. $3\mathbf{i}+2\mathbf{j}+\mathbf{k}$ C. $-\mathbf{i}+2\mathbf{j}+\mathbf{k}$ D. $-\mathbf{i}-2\mathbf{j}-\mathbf{k}$

5. The polar curves $r=2\sec \theta$ and $r=\cos \theta$ intersect at A. $(2,0)$ B. (1,3π​) C. (21​,3π​) D. $(1,0)$

6. The slope of the tangent to the curve y=3x2−4x+5 at the point $(1,4)$ is A. 6 B. 2 C. -2 D. -6

7. ∫x2+3x+52x+3​dx= A. ln∣x2+3x+5∣+c B. 21​ln∣x2+3x+5∣+c C. 2ln∣x2+3x+5∣+c D. x2+3x+51​+c

8. One of the tangents at the pole to the polar curve $r=1-2\cos \theta$ is $\theta =$ A. 4π​ B. 3π​ C. 2π​ D. 32π​

9. The oblique asymptote to the curve y=x−1x2​ is A. $y=x+1$ B. $y=x+2$ C. $y=x-2$ D. $y=x-1$

10. The random variable X has variance 2. Var$(2X – 1) =$ A. 6 B. 3 C. 4 D. 9

11. The parabola y2−4y=4(x+1) has as focus the point A. $(0,2)$ B. $(-1,0)$ C. $(0,-1)$ D. $(0,0)$