Algebra Practice Test

✏️ Algebra Practice Test
Section A: Simplifying Expressions

1. Simplify:
3x+5x−73x + 5x - 73x+5x−7
2. Expand and simplify:
(x+4)(x−2)(x + 4)(x - 2)(x+4)(x−2)
3. Simplify:
5(2x−3)+4x5(2x - 3) + 4x5(2x−3)+4x

Section B: Solving Equations

1. Solve for xxx:
2x+7=192x + 7 = 192x+7=19
2. Solve for xxx:
3x−5=2x+93x - 5 = 2x + 93x−5=2x+9
3. Solve for xxx:
x4+3=7\frac{x}{4} + 3 = 74x​+3=7
4. Solve for yyy:
2y+5=3(y−1)2y + 5 = 3(y - 1)2y+5=3(y−1)

Section C: Inequalities

1. Solve and graph on a number line:
4x−3<94x - 3 < 94x−3<9
2. Solve:
2x+7≥132x + 7 \geq 132x+7≥13

Section D: Word Problems

1. Sarah is twice as old as Ben. The sum of their ages is 36. How old is each?
2. A rectangle has a length that is 3 more than its width. If the perimeter is 30, find the
dimensions of the rectangle.
3. A taxi company charges a base fare of $5 plus $2 per km. Write an equation for the total
cost CCC after kkk kilometres, and find the cost of a 12 km trip.

Section E: Graphing / Functions

1. For the equation:
y=2x+1y = 2x + 1y=2x+1
State the gradient and y-intercept.
Find yyy when x=3x = 3x=3.
2. For the quadratic function:
y=x2−4x+3y = x^2 - 4x + 3y=x2−4x+3
Factorise it.
Find the x-intercepts.