Practice SAC. Unit 4 Further Mathematics: Geometry and Trigonometry Module

Transcription

1 Practice SAC Unit 4 Further Mathematics: Geometry and Trigonometry Module Student Name: Subject Teacher s Name: Equipment Permitted: Writing materials, 1 bound reference, CAS- Calculator Structure of book Section No. of questions No. of marks Total: 41 1

2 2 Point Cook Senior

3 SECTION 1 (Multiple Choice): Instructions for Section 1 Answer all questions in this section by marking your answer on the paper. Choose only one response that is correct for the questions. A correct answers scores 1, an incorrect answer scores 0. No marks will be given if more than one response has been marked per question. Question 1 Examine the triangle in the following figure. The value of x is: A 33 B 59 C 68 D 90 E 57 Question 2 A monster slice of pizza is made in the shape below. Find the length of the side a (to the nearest m). A 14 m D 17 m B 15 m E 18 m C 16 m 3

4 Question 3 Given AB = 12 cm, BC = 16 cm and sin C = 0.75, then sin (A) equals: A B 1 C 16 9 D 4 3 E 9 16 Question 4 A boat travels on a bearing of 045 T for 141 km. How far north of its starting point is the boat to the nearest km? A 100 km B 110 km C 71 km D 191 km E 45 km Question 5 The bearing shown in the figure above is: A 059 T D 201 T B 291 T E none of the above C 301 T 4

5 Question 6 The circumference of the base of the larger cone is closest to: A B C D E 113 mm 151 mm 190 mm 302 mm 459 mm Question 7 The straight line distance from A to B in the figure above is closest to: A 5 m D 55 m B 10 m E 60 m C 50 m Question 8 The height difference between A and B in Qn. 7 is: A 0 m B 10 m C 20 m D 40 m E 30 m 5

6 Question 9 A large cone is filled to half its height with water as shown. The ratio of the volume of water to air is: A 1 : 7 D 1 : 9 B 1 : 8 E 1 : 2 C 8 : 1 Question 10 A rectangular box has a rod positioned as shown in the diagram below. The expression that describes the angle the rod makes with the base of the box is: 5 12 A tan ( θ ) = C tan ( ) 4 13 B sin( θ ) = D tan ( ) E cos( ) 4 θ = 12 4 θ = 13 5 θ = 12 Question 11 The total surface area of a closed cylinder with a radius of 40 cm and height 20 cm to the nearest cm 2 is: A 5027 cm 2 D cm 2 B cm 2 E 7540 cm 2 C cm 6

7 Question 12 A group of hikers walk from A to B and then make a left turn and travel to C. The distances and angles are as shown in the figure below: Determine the distance east and north of point C from point B. A B C D E 1 km east, 1 km north 1 km east, 1.7 km north 1.7 km east, 1 km north 1.7 km east, 1.7km north 1 km east, 0.87 km north Question 13 Examine the following figure The area of the shape is: A ( π) mm² D ( π) mm² B ( π) mm² E mm 2 C ( π) mm² 7

8 Question 14 The volume of a sphere with a diameter of 15 cm is closest to: A 560 π cm 3 B 900 π cm 3 C 4500 π cm 3 D π cm 3 E π cm 3 Question 15 A regular hexagon is inscribed in a circle of radius 2cm, as shown. The perimeter of the hexagon in cm is: A 4π D 18 B 16 E 12 C 17 8

9 SECTION 2 (Short Answer): Instructions for Section 2 Answer all questions in the space provided. You need not provide numerical answers as decimals unless otherwise stated. Alternative forms may include for example surds, fractions or π. Unless otherwise stated, the diagrams in this book are not drawn to scale. Answer all questions to 1 decimal place unless otherwise stated. Question 1 Find the distance from B to C in the figure below. 1 mark Question 2 Find the area of a triangle with side lengths equal to 5 cm, 7 cm and 3 cm. 1 mark 9

10 Question 3 A surveyor wishes to know the distance between two towns (A and B) but cannot measure them because of an intervening forest. She drives 10 km south of B to point C and constructs a similar triangle CDE as shown in the figure. Determine the distance from A to B, given that CE = 100 m and CD = 147 m. Give the answer in km. 2 marks Question 4 Consider a block of butter 10 cm long, square in cross- section with side length 5 cm. A chef cuts it in half along the diagonal of the square. What is the surface area of one of the cut surfaces? 2 marks 10

11 Question 5 Find the unknown angles of the standard triangle shown below, A, B, C, when a=10, b=12 and c=3. Question 6 4marks Hiker A is walking on a bearing of N19 46 W, while Hiker B is walking on a bearing of S73 08 E. What bearing should Hiker C walk so that the angles she makes with A and B are equal? 4 marks 11

12 Question 7 Find the perimeter and area of the following figure. 4 marks 12

13 Question 8 Examine the diagram below. For the object shown: (a) what is the volume contained by the solid and framed sections to 1 decimal place? 2marks (b) what is the volume of the solid (shaded) part only? 2marks 13

14 20 Point Cook Senior Question 9 a. From the contour map below, give an appropriate profile along the cross- sectional line A B. END OF PAPER 4marks 14