AQA · Mathematics · 8300
GCSE Maths: Inequalities: regions
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Inequalities: regions (Corbettmaths Video 182), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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When graphing a linear inequality with ≥ or ≤, what type of line should be drawn?
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A solid line. The solid line indicates that points on the line are included in the solution region.
When graphing a linear inequality with > or <, what type of line should be drawn?
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A dashed (or dotted) line. The dashed line indicates that points on the line are not included in the solution region.
For the inequality y > 2x + 3, which side of the line y = 2x + 3 should be shaded?
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Above the line. For y > (expression), shade the region above the boundary line.
For the inequality y ≤ 3x - 1, which side of the line y = 3x - 1 should be shaded?
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Below the line. For y ≤ (expression), shade the region below the boundary line.
When graphing multiple inequalities on the same grid, what does the solution region represent?
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The area where all the inequalities are satisfied simultaneously (the overlap of all individual regions).
How do you convert the inequality x + y < 4 into the form y < mx + c for graphing?
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Rearrange to get y < -x + 4. Subtract x from both sides to isolate y.
The inequality x ≥ 3 is represented graphically by a ? line through x = 3.
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vertical
In a fitness class problem where y = men and x = women, what does the inequality y > x represent?
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There are more men than women at the fitness class.
A greengrocer sells up to 50 apples (x) and up to 60 oranges (y), with no more than 90 total. What inequality represents the total constraint?
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x + y ≤ 90. The total number of apples and oranges cannot exceed 90.
To test which side of a boundary line to shade for an inequality, what method can be used?
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Test a point (often the origin (0,0) if not on the line). If the point satisfies the inequality, shade the side containing that point; otherwise shade the opposite side.
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