Linear Relations and Polynomials: Core Practice

Harder linear equations, translating a situation into an equation, monomial operations, and pattern rules.

15 questions, free, marked as you go with a worked explanation on every one.

What this covers

Solve for x: 3(2x - 1) = x + 13
Expand: 3x(2x + 5)
A line has slope 3 and y-intercept -2. What is its equation?
Find the slope of the line through (1, 2) and (4, 11).
A relation's table shows: x = 1, y = 5; x = 2, y = 8; x = 3, y = 11; x = 4, y = 14. Which equation matches this relation?
A rental company charges $45 plus $15 per hour. Which equation models the total cost C, in dollars, for h hours?
The first four terms of a pattern are 5, 9, 13, 17. What is the 10th term?
Simplify: (8x² - 12x) / 4x, for x ≠ 0.
A rectangular garden's length is 4 m more than triple its width. If the perimeter is 64 m, what is the width, in metres?
Expand: 4x(3x - 2)
Simplify: (15x³ - 10x²) / 5x, for x ≠ 0.
Expand: -3x(x - 4)
A pattern begins 100, 94, 88, 82, ... decreasing by the same amount each time. What is the 8th term?
A pattern's rule is y = 4x - 3. What is the value of y when x = 6?
A t-chart shows: x = 1, y = 7; x = 2, y = 12; x = 3, y = 17; x = 4, y = 22. Which equation matches this relation?