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Advanced Algebra Practice

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Advanced Algebra Practice

Show your working for written problems. Give exact answers and include units where needed.

Algebra Skills

1.Which expression is equivalent to 4a + 12?

4(a + 3)
4a + 3
a + 12
16a

2.Factorise y² − 16.

(y − 4)(y + 4)
(y − 8)(y + 2)
y(y − 16)
It cannot be factorised

3.Find the value of m if 5m − 6 = 19.

m = 3
m = 5
m = 6
m = 25

4.Which inequality means that t is no more than 7?

t < 7
t ≤ 7
t > 7
t ≥ 7

5.Match each expression to its simplified or factorised form.

3(x + 5)
x² − 25
2x + 4x − 7
x² + 8x + 16
5(x − 2) + 3

6x − 7
(x + 4)²
5x − 7
3x + 15
(x − 5)(x + 5)

Solve and Expand

6.Solve the quadratic equation x² − 7x + 12 = 0.

7.Factorise 3x² + 15x + 18 completely.

8.Solve 4p + 3 ≤ 23 and show the solution on the number line.

9.A rectangle has side lengths (x + 6) cm and (x − 1) cm. Write its area as an expanded expression.

Challenge Problems

10.A square courtyard has an area of x² + 14x + 49 square metres. Factorise the area expression to find a simplified expression for one side length.

11.Ari is x years old and their cousin is 5 years younger. Together their ages total more than 31 years. Write an inequality and solve it to find the possible values of x.