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Linear and Quadratic Algebra
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Linear and Quadratic Algebra
📚 Part 1: Multiple Choice & Classification
1. Simplify: 3(x + 4) − 2x
x + 12
5x + 12
3x + 8
x + 4
2. Factorise: x² + 5x + 6
(x + 2)(x + 3)
(x + 6)(x − 1)
(x + 3)²
Prime — cannot be factorised
3. A taxi charges a $4 flag fall plus $2.50 per kilometre. What is the fare for a 10 km trip?
$25.00
$29.00
$30.00
$24.00
4. Check all that apply: Which of the following are quadratic equations?
x² − 4x + 4 = 0
3x + 2 = 7
y = 2x + 1
x² = 9
✏️ Part 2: Short Answers & Working
5. Expand and simplify: (2x − 3)(x + 5)
6. Solve. Show your working: 4x − 7 = 2x + 9
7. Solve the inequality and write the solution clearly: 3x + 6 > 6x + 12
8. For y = 3x − 2: state the gradient and the y-intercept, then sketch a quick graph for x = −1, 0, 1.
Gradient: _______________ Y-intercept: _______________
9. For y = x² − 4: give the vertex and the x-intercepts, then sketch the parabola (label intercepts).
Vertex: _______________ x-intercepts: _______________
10. In one or two sentences, explain why checking your algebraic solution in the context of a problem is important. (Give a New Zealand example if you can.)
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