Advanced level 2026 south west regional mock mathematics with statistics 1

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Mathematics Mock Exam – Paper 1 (Section Extract)

1. If $f(x) = 3x^2 – 2x + 5$, then $f(x – 1)$ is

• A. $3x^2 – 8x + 6$

• B. $3x^2 – 8x + 10$

• C. $3x^2 – 8x – 6$

• D. $3x^2 – 8x – 10$

2. If $x^2 – mx + 16 = 0$ has equal roots, the value of $m$ is

• A. $\pm 8$

• B. $\pm 4$

• C. $\pm 2$

• D. $\pm 16$

3. The expression $\frac{x^2-4}{x^2-x-6}$ when simplified gives

• A. $\frac{x-2}{x+3}$

• B. $\frac{x+2}{x+3}$

• C. $\frac{x+2}{x-3}$

• D. $\frac{x-2}{x-3}$

4. Given that $y = e^{x^3+2}$, $\frac{dy}{dx}$ is equal to

• A. $3x^2 e^{x^3+1}$

• B. $(x^3+2)e^{x^2+1}$

• C. $3x^2 e^{x^3+2}$

• D. $e^{x^3+1}$

5. A linear relationship between the logs of the variables $x$ and $y$ which is connected by the relation $y = p(x-2)^n$ is

• A. $\log y = np(\log x) – 2$

• B. $\log y = n(\log x – 2) + p$

• C. $\log y = \log p + n(\log x – 2)$

• D. $\log y = np(\log x – 2)$

6. What is the value of $n$ given that $0.000029 = 2.9 \times 10^n$?

• A. $5$

• B. $6$

• C. $-4$

• D. $-5$

7. Evaluating $\int_{0}^{\pi} (\sin 2y + \cos y) dy$ gives

• A. $-2$

• B. $1$

• C. $2$

• D. $\frac{1}{2}$

8. At the point $(1, 5)$, the function $f: \mathbb{R} \to \mathbb{R}; f(x) = 6x – x^2$ is

• A. Monotonic decreasing

• B. Monotonic decreasing and increasing

• C. Monotonic increasing

• D. Monotonic bounded

9. Which of the lines is/are perpendicular?

• $L1: 2y = x + 5$

• $L2: y + 2x = 0$

• $L3: y = 7 + 2x$

  • A. $L1$ and $L2$ only

  • B. $L2$ and $L3$ only

  • C. $L1, L2$ and $L3$

  • D. $L1$ and $L3$ only

10. The sum of the series $4 – 2 + 1 – \frac{1}{2} + \dots$ is

• A. $\frac{5}{2}$

• B. $8$

• C. $\frac{8}{3}$

• D. $\frac{16}{3}$

11. The function $y = f(x)$ has a maximum value at $x = a$ if

• A. $\frac{d^2y}{dx^2} > 0$

• B. $\frac{dy}{dx} < 0$ and $\frac{dy}{dx} > 0$

• C. $\frac{d^2y}{dx^2} = 0$

• D. $\frac{d^2y}{dx^2} < 0$

12. Given that $p: x^2$ is even, $q: x$ is even. Which of the following statements is true?

• A. $p \Rightarrow q$

• B. $p \Leftarrow q$

• C. $p \Leftrightarrow q$

• D. $p = q$

13. The series $1 + 3x + 9x^2 + 27x^3 + \dots$ will converge if

• A. $-3 < x < 3$

• B. $-1 < x < 3$

• C. $-1 < x < 1$

• D. $-\frac{1}{3} < x < \frac{1}{3}$

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