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The diagram below shows a 1 cm coordinate grid - OCR - GCSE Maths - Question 18 - 2017 - Paper 1
Question 18
The diagram below shows a 1 cm coordinate grid. (a) Find an inequality that defines region A and another inequality that defines region B. (b) Shade the region on ... show full transcript
Worked Solution & Example Answer:The diagram below shows a 1 cm coordinate grid - OCR - GCSE Maths - Question 18 - 2017 - Paper 1
Step 1
Find an inequality that defines region A and another inequality that defines region B.
Answer
To find the inequality that defines region A, we observe that region A is the area above the horizontal line at . Therefore, the inequality defining region A is:
For region B, the area lies below the line with a gradient of -2 and a y-intercept of 6. The equation of this line can be derived as follows: The line passes through the points (0, 6) and (3, 0), leading us to the equation:
Thus, the inequalities are:
- (for region A)
- (for region B)
Step 2
Shade the region on the grid given by the inequality $y > 6$.
Answer
To shade the region for the inequality , we need to identify the area above the horizontal line at . This means shading all points in the region where the y-coordinate is greater than 6. Ensure that a dashed line is used for the line at , as it is not included in the solution.
Step 3
Find the value of k.
Answer
Given that the unshaded region now has an area of 23 cm², we can find k by considering the area change due to the new shaded region added by the line . First, we need to determine the shape of the unshaded region. If we assume this region is a trapezium or a triangle, we can calculate the area accordingly, with the line intersecting the y-axis at and at the x-intercept determined through:
[ k = \frac{28 - 2}{8} = 3.25 ]
So, the final value of k is: