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Linear and Quadratic Algebra

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Linear and Quadratic Algebra

Choose one answer for each multiple-choice question. Show clear working for written questions. Use the drawing spaces to sketch graphs where asked.

Choose and classify

1.Simplify 4(x + 3) − 2x.

2x + 12
6x + 12
2x + 3
4x + 6

2.Factorise x² + 7x + 10.

(x + 5)(x + 2)
(x + 10)(x − 1)
(x + 7)(x + 3)
(x + 5)²

3.At a building site, Talia records a materials delivery fee of $6 plus $1.80 for each kilometre travelled. What is the total fee for a 15 km trip?

$27.00
$33.00
$21.00
$32.80

4.Which equation is written in the form ax² + bx + c = 0, where a, b and c are constants and a ≠ 0?

x² − 6x + 8 = 0
5x − 3 = 12
y = 4x + 2
2x² = 18

5.Which expression is linear in x?

3x − 8
x² + 1
2x² − 5x
x³ + 4

Expand, solve and represent

6.Expand and simplify (3x − 2)(x + 4).

7.Solve 5x − 8 = 2x + 13. Show your working.

8.Solve 4x + 3 > 7x + 15. Give your answer as an inequality.

9.For the linear rule y = 2x + 1, state the gradient and y-intercept. Then find y when x = −1, 0 and 2, and sketch the line through those points.

Plot the points from the previous question and draw the line.

10.For y = x² − 9, give the vertex and both x-intercepts. Then sketch the parabola and label the intercepts.

Draw and label the parabola described in the previous question.

11.A rectangular storage platform at a building site has width x metres and length (x + 3) metres. Write an expression for its area, then calculate the area when x = 4.

12.Explain briefly why it is useful to check an algebraic answer against the original equation or the situation it represents.