IB Mathematical Studies Revision Questions

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Martha Scott
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1 I Mathematical Studies Revision Questions 1. rectangular block of wood with face D leans against a vertical wall, as shown in the diagram below. = 8 cm, = 5 cm and angle ÂE = 8. Wall F D E 8º Find the vertical height of above the ground. Ground. In the diagram, triangle is isosceles. =, = 15 cm and angle is 3. 3º 15 cm. Find the size of angle ; the length of 3. The diagram shows a water tower standing on horizontal ground. The height of the tower is 6.5 m. x m From a point on the ground the angle of elevation to the top of the tower is 8. On the diagram, show and label the angle of elevation, 8. alculate, correct to the neatest metre, the distance x m. 1

2 4. The following diagram shows a triangle. = 8 m, = 14 m, = 18 m, and Â = m 110º Diagram not to scale 14 m 18 m alculate the area of triangle ; the size of angle Ĉ. 5. For y = 0.5 cos 0.5 x, find (i) the amplitude; the period. Let y = 3 sin x +, where 90 x 70. y drawing the graph of y or otherwise, complete the table below for the given values of y. x y 1 6. gardener pegs out a rope, 19 metres long, to form a triangular flower bed as shown in this diagram. 5 m 6 m alculate the size of the angle ; the area of the flower bed.

3 7. In the diagram below, PQRS is the square base of a solid right pyramid with vertex V. The sides of the square are 8 cm, and the height VG is 1 cm. M is the midpoint of [QR]. V VG = 1 cm P G 8 cm M Q S 8 cm R (i) Write down the length of [GM]. Find (i) alculate the length of [VM]. the total surface area of the pyramid; the angle between the face VQR and the base of the pyramid. 8. elow is a graph of the function y = a + b sin(cx) where a, b and c are positive integers and x is measured in degrees. y Find the values of a, b and c x 3

4 9. The diagram below shows a crane PQR that carries a flat box W. (PQ) is vertical, and the floor (PM) is horizontal. R 7.8 m 6.5 m Q 10º W 11.1 m h P M Given that PQ = 11.1m, QR = 7.8m, PR; angle P Rˆ Q ; P Qˆ R =10 and RW = 6.5 m, calculate the height, h, of W above (PM). 10. The diagram shows the graph of y = sin ax + b. y x Using the graph, write down the following values (i) the period; the amplitude; (iii) b. alculate the value of a. 4

5 11. ndrew is at point in a park. deer is 3 km directly north of ndrew, at point D. rian is 1.8 km due west of ndrew, at point. Draw a diagram to represent this information. alculate the distance between rian and the deer. rian looks at ndrew, and then turns through an angle θ to look at the deer. alculate the value of θ. 1. The following diagram shows the rectangular prism DEFGH. The length is 5 cm, the width is 1 cm, and the height is 4 cm. H G D E F Find the length of [DF]. Find the length of [F]. 13. The figure shows two adjacent triangular fields and D where D = 30 m, D = 80 m, = 50m. Dˆ = 60 and Â = m 60 D 50 m 30 m 30 Note: Diagram not drawn to scale Using triangle D calculate the length. alculate the size of ˆ. 5

6 14. The following diagram shows the side view of a tent. The side of the tent is 6 m high. The ground slopes upwards from the bottom of the tent at point, at an angle of 5 from the horizontal. The tent is attached to the ground by a rope at point, a distance of 8 m from its base. 5 rope 8 m 6 m alculate the angle. alculate the length of the rope,. alculate the angle that the rope makes with the sloping ground. 15. D is a trapezium with = D and [] parallel to [D]. D = cm, = 1 cm, = 13 cm. E D Show that E = 5 cm. alculate the height E of the trapezium. alculate (i) ÂE ; ĈD. (d) alculate the length of the diagonal []. 6

I.B. Geometry. 3d- Figures min 218 marks

I.B. Geometry. 3d- Figures min 218 marks I.. Geometry 3d- Figures 20-04-07 200 min 218 marks 1. In the diagram below, PQRS is the square base of a solid right pyramid with vertex V. The sides of the square are 8 cm, and the height VG is 12 cm.