Lesson D15-D16
D15-D16 Curve sketching and transformations of curves Quiz: AQA Further Maths, Unit 2
20 questions
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Lesson D15-D16, Curve sketching and transformations of curves: 20 multiple choice questions for the AQA Further Maths (7367), Unit 2: Compulsory content, written with Revision Ninja.
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The 20 questions
-
What type of curve is given by the equation y^2 = 4ax for a > 0?
- Ellipse
- Hyperbola
- Parabola
- Circle
-
What are the asymptotes of the rectangular hyperbola xy = c^2?
- Directrices
- Lines y = ±x
- Lines y = ±c
- Coordinate axes
-
What are the asymptotes of x^2/a^2 - y^2/b^2 = 1?
- x = plus or minus a
- y = plus or minus (a/b)x
- y = plus or minus (b/a)x
- y = plus or minus x
-
Where does the ellipse x^2/9 + y^2/4 = 1 meet the x-axis?
- x = plus or minus 3
- x = plus or minus 2
- x = plus or minus 4
- x = plus or minus 9
-
What are the asymptotes of y = 1/(x - 2) + 3?
- x = 2 and y = 3
- x = -2 and y = 3
- x = 2 and y = -3
- x = 3 and y = 2
-
What transformation maps y = f(x) to y = f(x - 2) + 3?
- Translation by vector (-2, 3)
- Translation by vector (2, -3)
- Translation by vector (2, 3)
- Translation by vector (3, 2)
-
Which transformation maps the curve y = f(x) to y = f(2x)?
- Horizontal stretch factor 1/2
- Vertical stretch factor 2
- Vertical stretch factor 1/2
- Horizontal stretch factor 2
-
Which transformation maps the curve y = f(x) to y = f(-x)?
- Translation by -x
- Reflection in x-axis
- Reflection in y-axis
- Rotation of 180°
-
Which point lies on xy = 4?
- (4, 4)
- (2, 4)
- (1, 3)
- (2, 2)
-
What is the centre of the ellipse (x - 1)^2/4 + (y + 2)^2/9 = 1?
- (1, -2)
- (1, 2)
- (-1, -2)
- (-1, 2)
-
What is the y-intercept of y = (x - 1)(x + 2)^2?
- -2
- 2
- 4
- -4
-
What are the vertex and direction of y = 1 - (x - 3)^2?
- Vertex (1, 3), opening downwards
- Vertex (-3, 1), opening downwards
- Vertex (3, 1), opening downwards
- Vertex (3, 1), opening upwards
-
What are the asymptotes of x^2/16 - y^2/9 = 1?
- x = plus or minus 4
- y = plus or minus (4/3)x
- y = plus or minus (9/16)x
- y = plus or minus (3/4)x
-
Describe the horizontal transformation that maps y = f(x) to y = 2f(x/3).
- Stretch scale factor 1/3
- Stretch scale factor 3
- Translation of 3 units
- Reflection in y-axis
-
What are the vertices of x^2/9 - y^2/4 = 1?
- (0, 3) and (0, -3)
- (2, 0) and (-2, 0)
- (9, 0) and (-9, 0)
- (3, 0) and (-3, 0)
-
Under reflection of y = f(x) in the line y = -x, where does the point (a, b) go?
- (-a, -b)
- (b, a)
- (a, -b)
- (-b, -a)
-
Which transformation maps the curve y = f(x) to y = -f(x)?
- Translation down 1
- Rotation of 180°
- Reflection in y-axis
- Reflection in x-axis
-
Which equation is the rectangular hyperbola with the coordinate axes as asymptotes that passes through (2, 3)?
- x^2 + y^2 = 13
- xy = 6
- x + y = 6
- xy = 5
-
What is the focus of the parabola y^2 = 8x?
- (4, 0)
- (8, 0)
- (0, 2)
- (2, 0)
-
What are the coordinates of the vertex of y = x^2 - 6x + 10?
- (6, 10)
- (-3, 1)
- (3, 10)
- (3, 1)
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