r6 geometry and symmetry v2020 - math medicine
TRANSCRIPT
1 SEKOLAH BUKIT SION - IGCSE MATH REVISION
MATHEMATICS (EXTENDED) 0580 IGCSE MAY/JUNE 2020
REVISION 6
GEOMETRY AND SYMMETRY
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NOTES:
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1. T R I G O N O M E T R Y From the word above, write down the letters which have
(a) exactly two lines of symmetry.
Answer: ………………………………………… [1]
(b) rotational symmetry of order 2.
Answer: ………………………………………… [1] 2. The volumes of two similar cones are 36𝜋 cm3 and 288𝜋 cm3. The base radius of the smaller cone is 3 cm. Calculate the base radius of the larger cone.
Answer: ………………………………………… [3] 3.
The diagram shows two similar figures. The areas of the figures are 5 cm2 and 7.2 cm2. The lengths of the bases are l cm and 6.9 cm. Calculate l.
Answer: ………………………………………… [3]
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4.
The two containers are mathematically similar in shape. The larger container has a volume of 3456 cm3 and a surface area of 1024 cm2. The smaller container has a volume of 1458 cm3. Calculate the surface area of the smaller container.
Answer: ………………………………………… [4] 5.
These two triangles are congruent. Write down the value of
(a) x Answer: ………………………………………… [1]
(b) y
Answer: ………………………………………… [1]
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6.
Triangle ABC is similar to triangle DEF. Calculate the value of
(a) x
Answer: ………………………………………… [2]
(b) y
Answer: ………………………………………… [2] 7.
The diagram shows two straight lines, AE and BD, intersecting at C. Angle ABC and angle EDC are equal. Triangles ABC and EDC are congruent. Write down two properties of line segments AB and DE.
Answer: AB and DE are …………………………………………
and …………………………………………[2]
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8. (a) (i) Complete quadrilateral ABCD so that the dotted line is the only line of symmetry.
[1] (ii) Write down the special name for quadrilateral ABCD.
Answer: ………………………………………… [1] (b) (i) Complete quadrilateral EFGH so that the dotted line is one of two lines of
symmetry. [1] (ii) Write down the special name for quadrilateral EFGH.
Answer: ………………………………………… [1] 9. (a) Draw a quadrilateral which has rotational symmetry of order 2 and whose diagonals are equal in length. [2]
(c) Write down the special name of this quadrilateral.
Answer: ………………………………………… [1]
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10.
Sarah investigates cylindrical plant pots. The standard pot has base radius r cm and height h cm. Pot A has radius 3r and height h. Pot B has radius r and height 3h. Pot C has radius 3r and height 3h.
(a) Write down the volumes of pots A, B and C in terms of 𝜋, r and h.
Answer: ………………………………………… [3]
Answer: ………………………………………… [4]
Answer: ………………………………………… [3]
(b) Find in its lowest terms the ratio of the volumes of A : B : C.
Answer: ………………………………………… [2]
(c) Which one of the pots A, B or C is mathematically similar to the standard pot? Explain your answer.
Answer: ………………………………………………………………………… [2]
(d) The surface area of the standard pot is S cm2. Write down the surface area of the similar pot in terms of S.
Answer: ………………………………………… [2]
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11.
For the shape above write down
(a) the number of lines of symmetry
Answer: ………………………………………… [1]
(b) the order of rotational symmetry.
Answer: ………………………………………… [1]
12. The area of triangle APQ is 99 cm2 and the area of triangle ABC is 11 cm2. BC is parallel to PQ and the length of PQ is 12 cm. Calculate the length of BC.
Answer: ………………………………………… [3]
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13.
The two cones are similar.
(a) Write down the value of l.
Answer: ………………………………………… [1]
(b) When full, the larger cone contains 172 cm3 of water. How much water does the smaller cone contain when it is full?
Answer: ………………………………………… [2] 14.
(a) Write down the order of rotational symmetry of the diagram.
Answer: ………………………………………… [1]
(b) Draw the lines of symmetry on the diagram. [1]
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15. A model of a car has a scale of 1 : 25.
(a) The length of the car is 3.95 m. Calculate the length of the model. Give your answer in centimetres.
Answer: ………………………………………… [3]
(b) The painted surface area of the model is 128 cm2.
Calculate the painted surface area of the car, giving your answer in square centimetres.
Answer: ………………………………………… [2]
(c) The size of the luggage space of the car is 250 litres. Calculate the size of the luggage space of the model, giving your answer in millilitres.
Answer: ………………………………………… [3] 16. Quadrilaterals P and Q have diagonals which
• are unequal • intersect at right angles.
P has two lines of symmetry. Q has one line of symmetry.
(a) Sketch quadrilateral P. Write down its geometrical name.
Answer: ………………………………………… [2]
(b) Sketch quadrilateral Q.
Write down its geometrical name.
Answer: ………………………………………… [2]
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17.
For the diagram, write down
(a) the order of rotational symmetry
Answer: ………………………………………… [1]
(b) the number of lines of symmetry.
Answer: ………………………………………… [1] 18.
The diagram shows a pyramid on a rectangular base ABCD, with AB = 6 cm and AD = 5cm. The diagonals AC and BD intersect at F. The vertical height FP = 3 cm. How many planes of symmetry does the pyramid have?
Answer: ………………………………………… [1]
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19. A statue two metres high has a volume of five cubic metres. A similar model of the statue has a height of four centimetres.
(a) Calculate the volume of the model statue in cubic centimetres.
Answer: ………………………………………… [2]
(b) Write your answer in part (a) in cubic metres.
Answer: ………………………………………… [1] 20.
For the diagram above, write down
(a) the order of rotational symmetry
Answer: ………………………………………… [1]
(b) the number of lines of symmetry.
Answer: ………………………………………… [1]
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21. (a) Shade one square in each diagram so that there is
(i) one line of symmetry [2]
(ii) rotational symmetry of order 2. [2
(b) On the diagram below, sketch one of the planes of symmetry of the cuboid. [1] (c) Write down the order of rotational symmetry of the equilateral triangular prism about the axis shown.
Answer: ………………………………………… [1]
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22.
Diagram 1 Diagram 2 Diagram 3
(a) Write down the order of rotational symmetry of each diagram.
Answer (Diagram 1): …………………………… [1]
Answer (Diagram 2): …………………………… [1]
Answer (Diagram 3): …………………………… [1]
(b) Draw all the lines of symmetry on each diagram. [3] 23. The pyramid below has a rectangular base. The vertex of the pyramid is vertically above the centre of the base. Write down the number of planes of symmetry for the pyramid.
Answer: ………………………………………… [1]
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24.
The diagrams show some polygons and their diagonals.
(a) Complete the table. [3]
(b) Write down the total number of diagonals in
(i) a decagon
Answer: ………………………………………… [1] (ii) a 12-sided polygon
Answer: ………………………………………… [1]