| Topic | Problem | Solution |
|---|---|---|
| None | 10 (b) Use calculus to find the value of $x$ for … | Let the wire be bent into a rectangle with sides of length a and b. The perimeter of the rectangle … |
| None | 6. The point $Q(-3,6)$ is on the terminal arm of … | \(Q(-3,6)\) is on the terminal arm of angle \(\theta\) in standard position. |
| None | A game is played by first placing a token on the … | Calculate the probability of winning the game on a $4 \times 4$ board using dynamic programming. |
| None | Question 4 of 10 A survey asked 40 students if th… | Given data: \(40\) students in total, \(25\) students play an instrument, \(20\) students are in ba… |
| None | $\sqrt{x+11} \sqrt{x-4}=3$ | Square both sides of the equation: \((\sqrt{x+11} \sqrt{x-4})^2 = 3^2\) |
| None | 1. Isabelle is flying a kite on a windy day. When… | Let the length of the string be L, the height of the kite be H, and the angle of elevation be A. We… |
| None | convert $2 x^{2}-3 x-2$ to vertex form | Factor out the coefficient of the x^2 term: \(y = 2(x^2 - \frac{3}{2}x) - 2\) |
| None | Determine the equation of a quadratic relation in… | Given the vertex form of a quadratic relation: \(y = a(x - h)^2 + k\), where \((h, k)\) is the vert… |
| None | 1. Use the given information to determine the equ… | Use the given information to determine the equation of each quadratic relation in vertex form, $y=a… |
| None | $f(x)=-(x+6)^{2}+4$ | Given the function: \(f(x) = -(x+6)^{2} + 4\) |
| None | EXAM REVISION 2 1. The diagram shows a sketch of … | \(f(x) = 3|x-4| - 5\) |
| None | $-5 \cdot$ (3 marks) A lock has 5 dials, each wit… | Find the total number of possible sequences: \(10^5 = 100000\) |
| None | Now consider a larger group of students: Alice, B… | Break the problem into two cases: (1) Lisa and Claire are in the same group, but Frank is not. (2) … |
| None | Find the expected value of a random variable $x$ … | \(E(x) = \sum xP(x)\) |
| None | A principal of $\$ 2100$ is invested at $6.75 \%$… | Given: Principal (P) = $2100, Annual Interest Rate (r) = 6.75% = 0.0675, Compounded Annually (n = 1… |
| None | (b) Let $A(x)=(x-2)^{2}(3 x-4)^{2}$ Find $A^{\pri… | Let \(A(x) = (x-2)^{2}(3x-4)^{2}\) |
| None | Assume that 500,000 people take the GED exam (hig… | Assume that 500,000 people take the GED exam each year and their scores form a normal distribution.… |
| None | (c) (i) Show that $P(x)=x^{4}-3 x^{3}-15 x^{2}-17… | Let $x$ be a triple zero of $P(x) = x^4 - 3x^3 - 15x^2 - 17x - 6$. Then $P(x) = (x - a)^3(x - b)$ f… |
| None | $\left\{\begin{array}{l}3 x+2 y=5 \\ -3 x+4 y=1\e… | \(\begin{cases} 3x + 2y = 5 \\ -3x + 4y = 1 \end{cases}\) |
| None | b Describe the limiting behaviour of the polynomi… | Using Vieta's formulas, we have \(\alpha + \beta + \gamma = 2\), \(\alpha\beta + \alpha\gamma + \be… |
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