Term 1 review
Answers are for parents and teachers.
1
Solve 2^(3x) = 64 and 9^x = 1/3.
3x = 6, x = 2; 9ˣ = 3⁻¹ gives 2x = −1, x = −1/2.
2
For f(x) = −x² + 6x − 5 find the vertex, the zeros and the maximum value.
Vertex (3, 4); zeros 1 and 5; maximum 4.
3
Simplify (x² − 25) ÷ (x² − 3x − 10) and state the domain of the original.
(x − 5)(x + 5) ÷ ((x − 5)(x + 2)) = (x + 5) ÷ (x + 2); domain R − {−2, 5}.
4
A model car is 12 cm long and the real car is 4.2 m long. Find the ratio and the real height if the model is 3.5 cm high.
4.2 m = 420 cm; ratio 420 ÷ 12 = 35; real height 3.5 × 35 = 122.5 cm.
5
Data 2, 3, 5, 7, 8: find σ. Then find the equation of the line through (0, 2) and (3, 8) in standard form.
σ = √5.2 ≈ 2.28. Slope 2, y = 2x + 2, so 2x − y = −2.