Here are the solutions to the remaining questions: 1a. (i) Two common misconceptions in learning number and algebra are: 1. Misconception about the equals sign: Students often perceive the equals sign (=) as an instruction to "find the answer" or "perform the calculation" rather than representing a balance or equivalence between two expressions. Explanation:* For example, when presented with $3 + 4 = \_ + 2$, a student might incorrectly fill the blank with 7, thinking the equals sign means the result of $3+4$. They fail to understand that both sides of the equation must have the same value, which would make the correct answer 5. 2. Misconception about variables: Students frequently view letters in algebra as representing specific objects or labels rather than unknown numerical values or quantities that can vary. Explanation:* For instance, in an expression like $2a + 3b$, students might believe 'a' stands for "apples" and 'b' for "bananas," leading them to conclude that these terms cannot be combined. They struggle with the abstract nature of variables as placeholders for numbers. 1a. (ii) Given the set of numbers, $S = \{-3, -1, 0, 2, 4\}$: ($\alpha$) Identify which numbers are natural numbers, which are whole numbers, and which are integers. Natural numbers:* These are positive integers starting from 1. From S: $\{2, 4\}$ Whole numbers:* These include zero and all natural numbers. From S: $\{0, 2, 4\}$ Integers:* These include all whole numbers and their negative counterparts. From S: $\{-3, -1, 0, 2, 4\}$ ($\beta$) Represent the set on a number line. ` <---•---•---•---•---•---•---•---•---•---> -3 -2 -1 0 1 2 3 4 5 ^ ^ ^ ^ ^ ` ($\gamma$) Determine if the set is closed under addition. A set is closed under addition if the sum of any two elements (including an element added to itself) in the set is also an element of the set. Let's test some sums: $$ 2 + 4 = 6 $$ Since $6 \notin S$, the set is not closed under addition. 1b. (i) You need $\frac{5}{6}$ cup of milk to make a cake, but you only have $\frac{1}{4}$ cup. How much more milk do you need? To find out how much more milk is needed, subtract the amount you have from the amount you need. $$ \text{Milk needed} = \frac{5}{6} - \frac{1}{4} $$ Find a common denominator for 6 and 4, which is 12. $$ \frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12} $$ $$ \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} $$ Now subtract: $$ \frac{10}{12} - \frac{3}{12} = \frac{10 - 3}{12} = \frac{7}{12} $$ You need $\boxed{\frac{7}{12} \text{ cup}}$ more milk. 1b. (ii) Express the number $987531.342$ in standard form. Standard form (scientific notation) requires the number to be expressed as $a \times 10^n$, where $1 \le |a| < 10$. Move the decimal point to the left until there is only one non-zero digit before it. $$ 987531.342 \rightarrow 9.87531342 $$ The decimal point moved 5 places to the left, so $n=5$. The number in standard form is $\boxed{9.87531342 \times 10^5}$. 1b. (iii) Round the number $3826.117$ to the nearest tenth and the nearest hundredth. Nearest tenth: The tenths digit is 1. The digit to its right is 1. Since $1 < 5$, we keep the tenths digit as it is. $$ 3826.117 \approx \boxed{3826.1} $$ Nearest hundredth: The hundredths digit is 1. The digit to its right is 7. Since $7 \ge 5$, we round up the hundredths digit. $$ 3826.117 \approx \boxed{3826.12} $$ 1b. (iv) Find the sum of $5\sqrt{2}$ and $3\sqrt{2}$. These are like terms because they both have $\sqrt{2}$. Add their coefficients. $$ 5\sqrt{2} + 3\sqrt{2} = (5+3)\sqrt{2} = \boxed{8\sqrt{2}} $$ 2b. Let the universal set be $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ and let sets $A = \{2, 4, 6, 8