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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!

The document you uploaded appears to be a Grade 12 Mathematics test with three main questions, totaling 50 marks.

This Grade 12 Mathematics test covers functions, trigonometric identities, and geometric proofs, with detailed questions about inverse functions, angle transformations, and triangle similarity.

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