The document you uploaded appears to be a Grade 12 Mathematics test with three main questions, totaling 50 marks. Here's a summary of the questions:

Question 1 (11 marks)

Involves functions: 1.1: Find the values of constants $a$ and $b$ for functions $y = f(x) = bx^2$ and $y = g(x) = ax$. 1.2: Suggest a restriction for $f(x)$ so its inverse is a function. 1.3: Determine the equation of the inverse of $f(x)$. 1.4: Write the inverse function of $g(x)$ as $g^{-1}(x) = ...$. 1.5: Given $h(x) = g(x - 2) + 3$, describe the transformation from $g(x)$ to $h(x)$.

Question 2 (29 marks)

Focuses on trigonometric identities: 2.1: Complete trigonometric expressions involving angles. 2.2: Express trigonometric functions in terms of $t = \cos 48^\circ$. 2.3: Prove a trigonometric identity. 2.4: Calculate a trigonometric ratio without using a calculator. 2.5: Solve a trigonometric equation. 2.6: Use a diagram to find $\cos(2A)$ given $\sin(A)$.

Question 3 (10 marks)

Geometric proof: 3.1: Prove similarity between triangles. 3.2: Prove a geometric ratio involving segments. 3.3: Prove another ratio involving tangent and chord properties.

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Let me know which specific question you'd like to explore, or if you need help solving any of the problems!

Here are 5 follow-up questions to expand on this material:

1. How do you find the inverse of a quadratic function like $f(x) = bx^2$?
2. What is the role of angle identities in simplifying trigonometric equations?
3. How can you use transformations to shift and stretch the graph of a function like $g(x)$?
4. What geometric principles are used to prove the similarity between triangles?
5. How do you approach solving trigonometric equations with multiple angles like $\cos(2x)$?

Tip: When proving trigonometric identities, try expressing all terms in terms of sine and cosine—it often simplifies the process!