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mensuration flashcards
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Card 1
How does the graph of y against x differ between direct and inverse proportion?
In direct proportion, the graph of y against x is a straight line that passes through the origin. In inverse proportion, the graph of y against x is a hyperbola.
Card 2
DEFINITION: Distinguish between congruent and similar shapes.
Congruent shapes are identical in both shape and size. Similar shapes have the same shape but are scaled up or down, meaning they have the same angles and proportional side lengths but different overall sizes.
Card 3
Explain how the converse of Pythagoras' Theorem can be used to determine if a triangle is right-angled.
The converse of Pythagoras' Theorem states that if the sum of the squares of two sides of a triangle is equal to the square of the third side (a² + b² = c²), then the triangle is a right-angled triangle.
Card 4
How is the total surface area of a closed cone calculated?
The total surface area of a closed cone is calculated by adding its curved surface area and its base area. This is given by the formula πrl + πr², where r is the radius, l is the slant height, and πr² is the base area.
Card 5
DEFINITION: What is the significance of the minimum or maximum point on the graph of a quadratic function?
The minimum point represents the smallest value of y for a quadratic function, while the maximum point represents the largest value of y. These points indicate the vertex of the parabola.
Card 6
Describe the relationship between x and y in an inverse proportion.
In inverse proportion, as x increases, y decreases, and vice versa. Specifically, if x doubles, y is halved. This relationship can be expressed as y = k/x or xy = k, where k is a constant.
Card 7
How is the slant height of a cone calculated?
The slant height (l) of a cone is calculated using the formula √(r² + h²), where r is the radius of the base and h is the perpendicular height of the cone.
Card 8
DEFINITION: What is the volume formula for a hemisphere?
The volume of a hemisphere is half the volume of a full sphere, so it is calculated as 1/2 x 4/3 πr³, which simplifies to 2/3 πr³.
Card 9
How does the 'PRWC' problem-solving method suggest approaching a problem after making a plan and carrying it out?
After making a plan and carrying it out, the 'PRWC' method suggests to convert to the same proper units, and then to check and expand on the solution.
Card 10
If △ ABC is similar to △ DEF, and AB=3cm, DE=6cm, BC=2cm, EF=4cm, CA=4cm, FD=2cm, what can be concluded about the ratios of their corresponding sides?
If △ ABC is similar to △ DEF, then the ratios of their corresponding sides are equal. Specifically, AB/DE = BC/EF = AC/DF, which means 3/6 = 2/4 = 4/2. However, the given values for CA and FD (4cm and 2cm) do not maintain the same ratio as the other sides, indicating an error in the provided example for similar triangles as 4/2 = 2, while 3/6 = 1/2.
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