Mathematics for IGCSE & O level - Coordinate Geometry (Section 1)

1
Which of the following equations represents a line with a negative gradient?
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B
D
2
What is the gradient of the line joining the points (2,1) and (5,7)?
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(B)
2
3
If the equation of a line is 2x + y = 4, what is the y-intercept?
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(B)
4
4
Which of the following equations represents a line parallel to y = 3x - 1?
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(C)
y = 3x + 2
5
Which statements are true for the equation of a straight line in the form Ax + By = C?
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A
B
C
D
6
Determine the equation of the line that passes through the point (1, 3) and has a slope of -1.
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(D)
y = x + 2
7
The midpoint of a line segment with endpoints (0, 0) and (6, 4) is:
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(A)
(3, 2)
8
Find the midpoint of the line segment with endpoints (0, 0) and (4, 6).
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(A)
(2, 3)
9
What is the gradient of the line that passes through the points (1,5) and (3,9)?
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(B)
2
10
The line segment AB has endpoints A(2, 1) and B(6, 3). Which statements are true?
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A
B
C
D
11
Which of the following equations represents a line parallel to the line y = 2x + 5?
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(C)
y = 2x - 3
12
What is the x-intercept of the line 3x + 4y = 12?
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(B)
4
13
Given the points A(1, 5) and B(4, 2), select the correct statements.
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A
C
D
14
What is the gradient of a line perpendicular to a line with a gradient of 1/2?
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(A)
-2
15
Which of the following is the general form of the equation of a straight line?
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A
B
C
16
The gradient of a line is calculated using which formula given two points (x1, y1) and (x2, y2)?
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(B)
(y2 - y1) / (x2 - x1)
17
Which of the following describes a line with a gradient of zero?
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(B)
A horizontal line.
18
If two lines are perpendicular, and one has the equation y = (1/3)x + 2, what is a possible equation for the other line?
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(C)
y = -3x + 4
19
Which equations represent a line perpendicular to y = (1/2)x + 3?
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A
C
20
The equation of a line is y = 3x - 4. At what point does this line intersect the y-axis?
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(B)
(0, -4)
21
If the gradient of a line is positive, which direction does the line slope?
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(B)
Up to the right.
22
If a line passes through (2, -1) and has a gradient of 3, what is the equation of the line?
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(B)
y = 3x - 7
23
The line passes through the points (1, 1) and (3, 5). What is its gradient?
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(B)
2
24
The equation of a line is given as y = 2x + 3. What is the y-intercept of this line?
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(B)
3
25
Consider a line with the equation 2x + 3y = 6. Which of the following statements are true?
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A
B
C
26
A line has a gradient of 2/3. What is the gradient of a line perpendicular to it?
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(A)
-3/2
27
If a line has a gradient of 3, what is the gradient of a line perpendicular to it?
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(C)
-1/3
28
What is the gradient of a line that passes through the points (0, 3) and (2, 7)?
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(B)
3
29
Which of the following equations is parallel to the line y = 2x - 1?
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(C)
y = 2x + 3
30
If two lines are parallel, what can you say about their gradients?
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(B)
Their gradients are equal.
31
The equation of a line is y = -4x + 3. What can you say about a line parallel to it?
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(C)
It has a gradient of -4.
32
Which statements are true for the line defined by the equation 4x + y = 2?
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B
C
D
33
What is the gradient of the line that passes through the points (1, -2) and (3, 2)?
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(B)
2
34
Which describes the gradient of a vertical line?
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(C)
Undefined
35
What is the gradient of the line passing through points (1, 2) and (3, 6)?
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(B)
2
36
If a line has a gradient of -1/3, what is the gradient of a line perpendicular to it?
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(C)
3
37
If the gradient of one line is 2, what is the gradient of a line perpendicular to it?
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(C)
-1/2
38
Which of the following is true for two perpendicular lines?
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A
C
D
39
Which of the following is the formula for calculating the length of a line segment with endpoints (x1, y1) and (x2, y2)?
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(B)
√(x2 - x1)^2 + (y2 - y1)^2
40
What is the distance between the points (2, 1) and (5, 5)?
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(C)
5
41
Regarding a straight line, what is the relationship between the gradient and the y-intercept?
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A
C
D
42
What is the midpoint of the line segment joining the points (-3, 2) and (5, 6)?
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(A)
(1, 4)
43
What is the slope of the line represented by the equation 3x + y = 5?
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(C)
-3
44
The equation of a line is y = -x + 5. At what point does this line intersect the y-axis?
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(C)
(0, 5)
45
In the equation y = -x + 5, what is the gradient of the line?
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(B)
-1
46
Determine the x-intercept of the line defined by 2x - y = 4.
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(B)
-2
47
If the line segment AB has coordinates A(1,3) and B(4,7), what is true?
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A
C
D
48
What is the slope of the line represented by the equation x + 2y = 4?
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(B)
-1/2
49
If the gradient of a line is 0, then the line is:
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(B)
Horizontal
50
A line has a y-intercept of 4 and a gradient of -2. What is the equation of the line?
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(B)
y = -2x + 4