Unit 3 4 S2 Final Review - YKPS Online Communitycommunity.ykpaoschool.cn/.../06/Unit-3-4-S2-Final-Review.pdfhollow cone as shown in diagram. The arc AB of the sector becomes the circumference

YK  Pao  Secondary  School    Unit 3/4 Review Name_________________________

1. For the diagram pictured write down

(a) The order of rotational symmetry  

(b) The number of lines of symmetry

2. (a) Shade one square in each diagram so that there is

(i) one line of symmetry (ii) rotational symmetry of order 2

(b) On the diagram below, sketch one of the planes of symmetry of the cuboid.

(c) Write down the order of rotational symmetry of the equilateral triangular prism about the

axis shown.

3. The top of a desk is made from a rectangle and a quarter circle. The rectangle measures 0.8m

by 1.4m. Calculate the surface area of the top of the desk.

4. The semicircle of diameter 6 cm is cut from a rectangle with sides 6 cm and 8 cm. Calculate the

perimeter of the shaded shape, correct to 1 decimal place.

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5. 𝑂𝑃𝑄 is a sector of a circle, radius 125 cm, centre O.

Angle 𝑃𝑂𝑄 = 50°.

𝑂𝑅𝑆 is a sector of a circle, radius 6 cm, also centre

𝑂. Angle 𝑅𝑂𝑆 = 30°.

(a) Calculate the shaded area.

(b) Calculate the perimeter of the shaded area,

𝑃𝑂𝑅𝑆𝑂𝑄𝑃.

6. A cylinder has a height of 14 cm and a volume of 850 𝑐𝑚!. Calculate the radius of the base of

the cylinder.

7. The diagram shows the net of a pyramid. The base 𝐴𝐵𝐶𝐷 is a rectangle 8 cm by 6 cm. All the

sloping edges of the pyramid are of length 7 cm. 𝑀 is the mid-point of 𝐴𝐵 and 𝑁 is the mid-

point of 𝐵𝐶.

(a) Calculate the length of

(i) 𝑄𝑀,

(ii) 𝑅𝑁.

(b) Calculate the surface area of the pyramid.

(c) The net is made into a pyramid, with 𝑃,𝑄,𝑅  and  𝑆 meeting at 𝑃. The mid-point of 𝐶𝐷 is 𝐺

and the mid-point of 𝐷𝐴 is 𝐻. The diagonals of the rectangle 𝐴𝐵𝐶𝐷 meet at 𝑋.

(i) Show that the height, 𝑃𝑋, of the pyramid is 4.90 cm, correct to 2 decimal places.

(ii) Write down the vertices of a triangle which is a plane of symmetry of the pyramid.

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8. A cylindrical glass has a radius of 3 centimeters and a height if 7 centimeters. A large cylindrical

jar full of water is a similar shape to the glass. The glass can be filled with water from the jar

exactly 216 times. Work out the radius and height of the jar.

9. Two similar vases have heights which are in the ratio 3:2.

(a) The volume of the larger vase is 1080 𝑐𝑚!. Calculate the volume of the smaller vase.

(b) The surface area of the smaller vase is 252 𝑐𝑚!. Calculate the surface area of the larger

vase.

10. (a) In the diagram triangles 𝐴𝐵𝐸  and  𝐴𝐶𝐷 are similar.

𝐵𝐸 is parallel to 𝐶𝐷. 𝐴𝐵 = 5  𝑐𝑚,𝐵𝐶 = 4  𝑐𝑚,𝐵𝐸 =

4  𝑐𝑚,𝐴𝐸 = 8  𝑐𝑚,𝐶𝐷 = 𝑝  𝑐𝑚  𝑎𝑛𝑑  𝐷𝐸 = 𝑞  𝑐𝑚. Work

out the values of 𝑝  𝑎𝑛𝑑  𝑞.

(b) A spherical balloon of radius 3 meters has a volume of 36𝜋 cubic meters. It is further

inflated until its radius is 12 m. Calculate its new volume, leaving your answer in terms of 𝜋.

11. (a) A solid metal sphere has a radius of 3.5 cm. One cubic centimeter of the metal has a mass

of 5.6 grams. Calculate

(i) the surface area of the sphere,

(ii) the volume of the sphere,

(iii) the mass of the sphere.

(b) Diagram 1 shows a cylinder with a diameter of 16 cm. It contains water to a depth of 8 cm.

Two spheres identical to the sphere in part (a) are placed in the water. This is shown in

Diagram 2. Calculate ℎ, the new depth of water in the cylinder.

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12. (a) The sector of a circle, centre O, radius 24 cm,

has angle 𝐴𝑂𝐵 = 60°. Calculate

(i) the length of the arc AB,

(ii) the area of the sector OAB 𝑐𝑚!.

(b) The points A and B of the sector are joined together to make a

hollow cone as shown in diagram. The arc AB of the sector becomes

the circumference of the base of the cone. Calculate

(i) the radius of the base of the cone,

(ii) the height of the cone,

(iii) the volume of the cone,