📘 MATHEMATICS

1) Simplify each expression: 1.a) Simplify $3 \times \left(\frac{1}{2} - \frac{1}{3}\right)$

1. The quadratic formula: $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ 2. Pythagorean theorem: $$a^2+b^2=c^2$$

1. **Multiple Choice Questions (6 marks)** 1. The slope of the line passing through points $(1,2)$ and $(3,6)$ is:

1. The Riemann Hypothesis is a famous unsolved problem in mathematics. 2. It concerns the zeros of the Riemann zeta function, which is defined for complex numbers $s$ with real par

1. **Understanding Percentages** A percentage is a way to express a number as a fraction of 100. The symbol for percentage is **%**.

1. Buktikan bahwa $ (A \cup B)^c = A^c \cap B^c $ dengan dua langkah: 1.1. Tunjukkan $ (A \cup B)^c \subseteq A^c \cap B^c $:

1. The problem asks to identify the name that describes the numbers highlighted on the number line. 2. The highlighted numbers are 0, 1, 2, 3, 4, and 5.

1. **Problem 5.1:** Write down the domain of $g(x) = \frac{-4}{x-3} + 8$. The function $g$ has a vertical asymptote at $x=3$, so $x=3$ is excluded from the domain.

1. The problem asks to write a mathematical explanation in a paragraph format. 2. Writing math in paragraph form means combining the explanation and the math expressions smoothly.

1. Define Rank of a matrix. The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. It represents the dimension of the vector space spanne

1. The problem involves understanding continuous functions on an interval, polynomials, and the set of $m \times n$ matrices, focusing on a specific question labeled as number 5b.

1. The arrows pointing to the right typically indicate the direction of a process, movement, or flow in diagrams or equations. 2. In mathematics, arrows can represent functions map

1. The problem is to generate typical GCSE Maths Higher paper questions. 2. Here are some example questions:

1. Let's clarify why rounding to 0 might happen: when a number is very close to zero, rounding to the nearest whole number results in 0 because the decimal part is less than 0.5. 2

1. Paper 2 Problem: Solve the quadratic equation $2x^2 - 5x + 3 = 0$. Step 1: Identify coefficients: $a=2$, $b=-5$, $c=3$.

1. **Compound Interest Problem:** Given principal $P$, annual interest rate $r$ (as a decimal), number of times interest applied per year $n$, and number of years $t$, the compound

1. Let's consider a real-life scenario involving permutations: Suppose you have 5 different books and want to arrange 3 of them on a shelf. The number of ways to arrange 3 books ou

1. Let's start by understanding what it means for a number to be "valid" in mathematics. 2. A valid number typically means it is a well-defined number within a given context, such

1. The problem is to understand why there are 3 brackets in the expression or context you are referring to. 2. Brackets are used in mathematics and programming to group terms, clar

1. The RMS (Root Mean Square) value of a function $f(x)$ over the interval $a \leq x \leq b$ is defined as the square root of the average of the square of the function over that in

1. **Problem Statement:** This worksheet covers understanding real numbers and their subsets through examples, definitions, true/false questions, multiple choice, and classificatio