Shading regions given by lines.
16 original questions, 59 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.
On the grid, shade the region that satisfies all three of these inequalities.
x ≥ 1
y > 2
x + y < 6
Label the region R.
On the grid, shade the region that satisfies all three of these inequalities.
y ≤ 3
y ≥ x - 1
x > 0
Label the region R.
When a region is shaded on a graph, the boundary line for each inequality is drawn either solid or dashed.
Write "solid" or "dashed" for the boundary line of each inequality.
The region R satisfies all three of these inequalities.
x ≥ 1
y ≥ 2
x + y ≤ 5
Find all the points in R whose coordinates are both integers.
The region R satisfies all three of these inequalities.
y > x
x ≥ 0
y ≤ 4
Amy says the point (2, 2) is in R.
Is Amy correct? You must explain your answer.
A region R is drawn on a coordinate grid.
R is the triangle with vertices (2, 1), (6, 1) and (2, 5), including its boundary.
The three sides of the triangle lie on the lines x = 2, y = 1 and x + y = 7
Find the three inequalities that define R.
On the grid, shade the region that satisfies all four of these inequalities.
x > 0
y > 1
y < 2x
x + y < 6
Label the region R.
The region R satisfies all three of these inequalities.
x > 0
y ≥ 1
x + y < 5
Write down the coordinates of all the points in R with whole number coordinates.
The region R satisfies all three of these inequalities.
x + 2y ≤ 10
x ≥ 0
y > 1
Which of these points are in R?
P(4, 3) Q(6, 2) S(2, 1) T(0, 5)
The region R is bounded by three lines: x = 1, y = 2 and x + y = 8.
R is to the right of x = 1, above y = 2 and below x + y = 8.
The lines x = 1 and x + y = 8 are solid. The line y = 2 is dashed.
Write down the three inequalities that define R.
A region R is drawn on a coordinate grid.
R is the triangle with vertices (0, 1), (4, 1) and (4, 5), including its boundary.
Find the three inequalities that define R.
y ≥ 1
x + y ≤ 8
y ≤ 3x - 1
A straight line passes through (0, 1) and (4, 3).
The region R is on or above this line, on or below the line y = 3, and on or to the right of the y-axis.
Write down the three inequalities that define R.
The region R satisfies all four of these inequalities.
x ≥ 0
y ≥ 0
2x + y ≤ 10
y ≤ x + 2
The point (x, y) is in R and both coordinates are integers.
Find the greatest possible value of x + y
A region R is drawn on a coordinate grid.
R is the triangle with vertices (0, 1), (6, 1) and (2, 5), including its boundary.
Find the three inequalities that define R.
The region R satisfies all three of these inequalities.
x ≥ 1
y > 2
x + y ≤ 8
Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.