Advanced level 2026 south west regional mock further mathematics 1

Mathematics Mock Exam – Paper 1 (Section Extract)

1. The structure $(\mathbb{N}^*, +)$ is not a group because

• A. closure does not hold

• B. associativity holds

• C. no identity element exists in $\mathbb{N}^*$ under addition

• D. commutativity holds

2. A group with underlying set $H$ has subgroups $\{a, b\}$, $\{a, d\}$ and $\{a, b, c, d\}$. The identity element of $H$ is

• A. $a$

• B. $b$

• C. $c$

• D. $d$

3. Given that $p$ and $q$ are statements, $\sim(\sim p \implies \sim q) \equiv$

• A. $p \wedge q$

• B. $\sim p \wedge q$

• C. $p \wedge \sim q$

• D. $q \implies \sim p$

4. Given the statements $P: \cosh(x) = \cosh(y)$ and $Q: x = y$,

• A. $Q \implies \sim P$

• B. $P \iff Q$

• C. $P \implies Q$

• D. $Q \implies P$

5. The partial fractions form of $\frac{7x}{(x+4)(x^2-16)}$ where $p, q$ and $r$ are real constants is

• A. $\frac{p}{x+4} + \frac{q}{x-4} + \frac{r}{(x-4)^2}$

• B. $\frac{p}{x+4} + \frac{q}{(x+4)^2} + \frac{r}{x-4}$

• C. $\frac{p}{x+4} + \frac{qx+r}{x^2-16}$

• D. $\frac{p}{x+4} + \frac{qx+r}{x^2+16}$

6. A curve that is symmetrical about $\theta = \frac{\pi}{2}$ is

• A. $r = 5\sin 3\theta$

• B. $r = 5\cos 3\theta$

• C. $r = 15\cos \theta$

• D. $r = 15\cos 5\theta$

7. The polar curve $r = 1 + \sin \theta$ and the line $r \sin \theta = 2$ intersect at

• A. $(\frac{\pi}{2}, 2)$

• B. $(2, \frac{\pi}{2})$

• C. $(0, 2)$

• D. $(2, 0)$

8. Given that $(MN)x = y$, where $M$ and $N$ are non-singular square matrices; $x$ and $y$ are non-zero column vectors, $x =$

• A. $yM^{-1}N^{-1}$

• B. $yN^{-1}M^{-1}$

• C. $M^{-1}N^{-1}y$

• D. $N^{-1}M^{-1}y$

9. Let $W$ be a matrix of order 3 and $|W| = 2k$. $|3W| =$

• A. $54k$

• B. $24k$

• C. $18k$

• D. $6k$

10. The remainder when $-37$ is divided by 5 is

• A. $-3$

• B. $-2$

• C. $2$

• D. $3$

11. The unit digit of $(19)^{1983} + (11)^{1983} + (9)^{1983}$ is

• A. $9$

• B. $7$

• C. $3$

• D. $0$

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