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Year 10 Algebra Booklet
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Year 10 Algebra Booklet
📐 Part 1: Quadratic Equations & Inequalities
1. Which of the following is the correct factorised form of x² + 7x + 12?
(x + 3)(x + 4)
(x + 2)(x + 6)
(x + 1)(x + 12)
(x - 3)(x - 4)
2. Solve the quadratic equation: x² - 5x + 6 = 0
3. A football is kicked upward. Its height h (in metres) after t seconds is given by h = -5t² + 20t + 1. After how many seconds does the ball reach its maximum height?
4. Solve the inequality: 2x + 3 ≤ 11
Answer: x ≤ _______
🔢 Part 2: Simultaneous Equations & Polynomials
5. Solve this system of equations using substitution or elimination:
3x + 2y = 16
x - y = 2
Solution: x = _______, y = _______
6. Expand and simplify: (2x + 3)(x - 4)
7. A movie theatre charges $15 for adults and $8 for children. If 120 tickets were sold for a total of $1410, how many adult tickets and how many child tickets were sold?
Adult tickets: _______ Child tickets: _______
📈 Part 3: Exponential Functions & Applications
8. Which graph represents an exponential growth function?
y = 2x + 3
y = 2ˣ
y = x²
y = -3x
9. A bacteria culture doubles every 3 hours. If there are initially 500 bacteria, write an equation for the number of bacteria N after t hours.
10. A car worth $25,000 depreciates by 15% each year. What will the car be worth after 4 years? (Round to the nearest dollar)
Value after 4 years: $__________
11. Solve for x: 3ˣ = 27
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