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Algebra Practice Mixed Problems
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Algebra Practice Mixed Problems
Simplify expressions fully and solve equations. Show your working where needed. Give exact answers unless a question asks otherwise.
Simplifying Expressions
Collect like terms, expand brackets or use index laws as needed.
1.Simplify 9x − 4x + 2x.
2.Expand and simplify 3(2y − 5) + 4y.
3.Expand and simplify (x + 6)(x − 3).
4.Simplify 4p²q × 3pq⁴.
5.Match each expression to its simplified form.
- 5a + 2a − 3a
- 2(3b + 1)
- (m + 2)(m + 5)
- 6r² × 2r³
- m² + 7m + 10
- 4a
- 12r⁵
- 6b + 2
Solving Linear Equations
Find the value of the variable. Include enough working to make your method clear.
6.Solve 4x + 9 = 29.
7.Solve 6(y − 1) = 2y + 14.
8.Solve (3x − 2) ÷ 4 = 4.
9.Which value of t solves 7t − 5 = 30?
- 3
- 5
- 7
- 25
Quadratic Equations
Solve each equation. Check that your solutions satisfy the original equation.
10.Solve by factorising: x² + 7x + 12 = 0.
11.Solve 3x² − 10x + 3 = 0 using the quadratic formula.
12.Solve x² − 9 = 0. Give both solutions.
13.A rectangular flower bed has a length of (x + 4) metres and a width of (x − 2) metres. Its area is 32 m². Find the positive value of x.
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