| Topic | Problem | Solution |
|---|---|---|
| None | 8. Express the equation of the line passing throu… | First, we find the slope of the line. Since the x-coordinates of both points are the same, the line… |
| None | Question 4 (2 marks) The following facts are know… | Since the function is neither even nor odd, we cannot use the properties of even or odd functions t… |
| None | $\frac{1}{2}+\frac{1}{3}$ | Find a common denominator for the two fractions: \(\text{lcm}(2, 3) = 6\) |
| None | 2) Find the interval of convergence if \[ \sum_{n… | Rewrite the series as \(\sum_{n=1}^\infty a_n\), where \(a_n = (-1)^n \frac{(x-1)^n \cdot 3^n}{4^n(… |
| None | Solve the following: \[ \begin{aligned} 2 x+y & =… | Substitute the expression for y from the second equation into the first equation: \(2x + (6x + 4) =… |
| None | A train is made up of 10 carriages. The mean numb… | Find the total number of passengers by multiplying the mean number of passengers per carriage by th… |
| None | $d=\frac{\left|a x_{0}+b y_{0}+c\right|}{\sqrt{a^… | Let \(x = \sqrt{a^2 + b^2}\). Then \(x^2 = a^2 + b^2\), so \(d = \frac{|ax_0 + by_0 + c|}{x}\) |
| None | Example-4: It has been estimated that $43 \%$ of … | Let n be the number of students, p be the probability of changing major, and threshold be the numbe… |
| None | Let $f(x)=3 x^{2}$ a) Find the linearization $L(x… | The linearization of a function \(f(x)\) at a point \(a\) is given by \(L(x) = f(a) + f'(a)(x-a)\). |
| None | Example-1: A basketball player makes 80 percent o… | Given that the basketball player makes 80 percent of his free throws, we have p = 0.8 and n = 8. |
| None | If $\log _{C} A=1.214$ and $\log _{C} B=1.415$, w… | Rewrite the expression using properties of logarithms: \(\log _{C}\left(\frac{B^{2}}{A}\right) = \l… |
| None | Harrison has a rectangular plank of wood that is … | Use Pythagorean theorem: \(29^2 = 14^2 + x^2\) |
| None | Rationalise and simplify $\frac{\sqrt{3}-7}{\sqrt… | Multiply the numerator and denominator by the conjugate of the denominator: \(\frac{(-7 + \sqrt{3})… |
| None | 17 There are 3 cinemas $\mathbf{A}, \mathbf{B}$ a… | Total number of seats = Mean number of seats per cinema * Total number of cinemas = \(380 * 3 = 114… |
| None | Charles wants to verify the identity $\csc x \tan… | Find the values of \(\csc x\), \(\tan x\), and \(\sec x\) when \(x = \frac{\pi}{6}\) rad |
| None | QUESTION FOUR Suppose on January 1 you deposit $\… | Given the initial deposit P = $100, annual interest rate r = 11.33463%, daily compounding n = 365, … |
| None | A fruit vendor had a certain number of apples for… | Let x be the number of apples at the beginning. After the first customer's purchase, the vendor had… |
| None | Prove each identity using an algebraic approach. … | Rewrite the given expression in terms of sine and cosine functions: \(\frac{1/\sin x}{(1/\cos^2 x) … |
| None | Consider the data set below: \[ \begin{array}{lll… | Given the data set: \(26, 33, 37, 44, 46, 47, 50, 52, 55, 63, 67, 72\) |
| None | Find the slope of the tangent line to the curve \… | Given the curve equation: \(x - 3\sin(x)\cos(y) + 5\sin(x) + 4\cos(y) - 7\pi = 0\) |
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