| Topic | Problem | Solution |
|---|---|---|
| None | Question 1 Level 2 Show that $x=\frac{1}{\sqrt{3}… | Substitute the given value of x into the equation: \(2\left(\frac{1}{\sqrt{3}-1}\right)^{2}-2\left(… |
| None | Question 2 For a certain polynomial $P(x), P(3)=2… | By the Remainder Theorem, we have $P(3) = 2$ and $P(-1) = -1$. |
| None | a) $\frac{2 n}{3}=4$ | Multiply both sides of the equation by 3: \(3 \times \frac{2n}{3} = 3 \times 4\) |
| None | $2 \cos ^{2} x-\cos x=0$ | Factor out \(\cos x\) from the equation: \(2 \cos ^{2} x - \cos x = 0\) becomes \((2\cos x - 1)\cos… |
| None | 2. Keith has $\$ 500$ in a savings account at the… | Keith starts with $500 and wants to have at least $210 left. This means he can spend $500 - $210 = … |
| None | (a) $x^{2}-5 x+2=0$ | Given the quadratic equation: \(x^2 - 5x + 2 = 0\) |
| None | 5. Mauna Kea is a m A company made a profit of $\… | Find the total profit or loss: \(8 + (-12) = -4\) |
| None | Find the slope of the line that goes through the … | Let the given points be \((-4,2)\) and \((-1,8)\). |
| None | A car is purchased for $\$ 26,500$. After each ye… | Calculate the resale value using the formula: \(Resale Value = Initial Value * (1 - Depreciation Ra… |
| None | Multiply. \[ (c-3)(6 c+1) \] Simplify your answer. | (c-3)(6c+1) = c(6c+1) - 3(6c+1) |
| None | Evaluate the integral. \[ \int \frac{4}{\sqrt{x}(… | First, we can make a substitution to simplify the integral. Let \(u = 1 + 4\sqrt{x}\). Then, \(du =… |
| None | 2. Given the function $f(x)=-3(x+1)^{2}-2$ : a) D… | We are given the function \(f(x)=-3(x+1)^{2}-2\) |
| None | \( x^{2}+3 x+7=0 \) | \(x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}\) |
| None | \( =6 \times 8 \) | \( 6 \times 8 \) |
| None | What are the coordinates of the point on the dire… | Let the point be P(x, y) and use the section formula. |
| None | What is the surface area of the cylinder with hei… | \(A_{base} = \pi r^2 = \pi(4)^2 = 16\pi\) |
| None | A clothing business finds there is a linear relat… | We are given two points on the line: (24000, 76) and (41000, 25). |
| None | Last year, Pinwheel Industries introduced a new t… | Translate the given problem into a linear equation. The cost to develop the toy is a fixed cost, wh… |
| None | Suppose that the world's current oil reserves is … | Suppose that the world's current oil reserves is \(R=1890\) billion barrels. If, on average, the to… |
| None | Write an equation for a line parallel to $y=-3 x+… | The slope of a line parallel to another line is the same. So, the slope of the line we are looking … |
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