Ordinary level 2026 South West regional mock additional mathematics 1

Based on the image provided, here is the extraction of the math problems and their multiple-choice options.

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Mathematics Worksheet Extraction

1. Rational Exponents

$(a)^{\frac{m}{n}}$ is the same as:

• A. $a^{mn}$

• B. $a^{m+n}$

• C. $a^{m-n}$

• D. $\sqrt[n]{a^m}$

2. Logarithm Rules

$\log_a \left(\frac{M}{N}\right) =$

• A. $\log_a M + \log_a N$

• B. $\frac{\log_a M}{\log_a N}$

• C. $\log_a M – \log_a N$

• D. $M \log_a N$

3. Difference of Two Squares

$(1 – \sqrt{2})(1 + \sqrt{2}) =$

• A. $3 + 2\sqrt{2}$

• B. $1$

• C. $3 – 2\sqrt{2}$

• D. $-1$

4. Forming Quadratic Equations

The quadratic equation with roots $2$ and $3$ is:

• A. $x^2 – 5x + 6 = 0$

• B. $x^2 – 5x + 3 = 0$

• C. $x^2 + 5x + 6 = 0$

• D. $x^2 – 2x – 3 = 0$

5. Nature of Roots (Discriminant)

Given that $ax^2 + bx + c = 0, a, b, c \in \mathbb{R}$, and $c \neq 0$ has imaginary roots. Then the correct statement below is:

• A. $b^2 – 4ac = 0$

• B. $b^2 – 4ac > 0$

• C. $b^2 – 4ac < 0$

• D. $b^2 – 4ac \geq 0$

6. Solving Quadratics

The set of roots of the quadratic equation $2x^2 – 5x + 2 = 0$ are:

• A. $\{-5, 2\}$

• B. $\{-\frac{5}{2}, 1\}$

• C. $\{-\frac{1}{2}, -2\}$

• D. $\{\frac{1}{2}, 2\}$

7. Factor Theorem

Given that $(x – 1)$ is a factor of the polynomial $x^3 – 3x^2 + k$, where $k$ is a constant, then the value of $k$ is:

• A. $1$

• B. $-2$

• C. $2$

• D. $-1$

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8. Remainder Theorem

The remainder when the polynomial $x^3 – x^2 + 3x – 1$ is divided by $(x – 1)$ gives:

• A. $2$

• B. $-6$

• C. $-2$

• D. $6$

9. Sequences

Let the $n^{th}$ term, $U_n$, of a sequence be given by $U_n = -2(-1)^{n+1}$. Then $U_2$ is equal to:

• A. $-8$

• B. $2$

• C. $-2$

• D. $8$

10. Geometric Progression (GP)

The sum of all the terms of the geometric progression $a, 9, 3, 1, \dots$ is $40.5$. Then the value of $a$ is:

• A. $27.3$

• B. $18.5$

• C. $27$

• D. $81$

11. Arithmetic Progression (AP)

The $n^{th}$ term of an arithmetic progression with first term $2$ and common difference $-1$ is:

• A. $3 + n$

• B. $3 – n$

• C. $3 + 2n$

• D. $3 – 2n$

12. Sum to Infinity

The sum to infinity of a geometric progression with first term $1$ is equal to $6$. Then its common ratio is equal to:

• A. $-\frac{5}{6}$

• B. $\frac{1}{6}$

• C. $\frac{5}{6}$

• D. $-\frac{1}{6}$

13. Binomial Expansion

The first three terms of the binomial expansion $(1 – 2x)^{-2}$ are:

• A. $1 – 4x – 12x^2$

• B. $1 – 4x – 24x^2$

• C. $1 + 4x + 12x^2$

• D. $1 + 4x + 24x^2$

14. Binomial Terms

The number of terms in the binomial expansion of $(1 + x)^n$, where $n \in \mathbb{N}$ is:

• A. $n$

• B. $n + 1$

• C. $n + 2$

• D. $n – 1$