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Year 10 Algebra Booklet
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Year 10 Algebra Booklet
Show your working where needed. Give money answers in Australian dollars and round as directed.
Quadratics and Inequalities
1.Which expression is the factorised form of x² + 9x + 20?
- (x + 4)(x + 5)
- (x + 2)(x + 10)
- (x - 4)(x - 5)
- (x + 1)(x + 20)
2.Find both solutions of x² − 7x + 10 = 0.
3.A model rocket’s height after t seconds is h = −4t² + 24t + 2, where h is measured in metres. At what time does it reach its maximum height?
4.Solve 3x − 5 ≤ 16. Write your answer as an inequality.
Simultaneous Equations and Polynomials
5.Solve the simultaneous equations 2x + 3y = 17 and x − y = 1. Find the values of x and y.
6.Expand and simplify (3x − 2)(x + 5).
7.A concert sells adult tickets for $18 and concession tickets for $10. A total of 90 tickets are sold, bringing in $1,340. How many adult tickets and how many concession tickets were sold?
Exponential Functions and Applications
8.Which rule describes exponential growth?
- y = 4x + 1
- y = 3ˣ
- y = x² + 1
- y = −2x
9.A yeast culture starts with 240 cells and triples every 2 hours. Write a rule for the number of cells, N, after t hours.
10.A laptop worth $2,400 loses 12% of its value each year. Calculate its value after 3 years, rounded to the nearest dollar.
11.Solve 2ˣ = 32.
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