MATHEMATIC MATH1722 Yr11 Maths SM Sem2 2019 TA Exam Solution

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Deakin University MATHEMATIC MATH1722 Yr11 Maths SM Sem2 2019 TA Exam Solution Section A – Multiple-choice questions (20 marks) Instructions for Section A i. Answer all questions in pencil ... on the answer sheet provided for multiple-choice questions. ii. iii. iv. v. vi. Choose the response that is correct for the question. A correct answer scores 1; an incorrect answer scores 0. Marks will not be deducted for incorrect answers. No marks will be given if more than one answer is completed for any question. Unless otherwise indicated, the diagrams in this book are not drawn to scale. QUESTION 1 The distance, d , that a car can travel varies directly with the amount of fuel, f , in the fuel tank. If k is the constant of variation, then the equation that represents this situation is A. d=f +k B. d=kf C. d=k f D. k=d-f E. kf =1 d QUESTION 2 If y∝t2 and when t=4 , y=8 then the constant of variation is A. 0.25 y=k t2 ∴8=k (4)2 ∴8=16k ∴k=1 2 B. 0.5 C. 1 D. 2 E. 16 QUESTION 3 The distance, D , that a spring is stretched by a hanging object varies directly as the weight, W , of the object. If a 6 kg object stretches a spring 29cm , then the stretched distance for a 25 kg object is closest to A. 4.8 cm D=kW ∴29=6 k ∴k=29 6 ∴D=29 6 ×25=120.83 B. 19.9 cm C. 60.0 cm D. 120.8 cm E. 187.2 cm VCE Specialist Mathematics – Unit 2 Page 1 of 21 2019 Semester 2 Examination (TA) QUESTION 4 If f (x )=3 x2+8 x+5 , then the graph of y= 1 f (x ) has A. x - intercepts at x=-1 and x=-53 B. vertical asymptotes at x=-1 and x=-5 3 C. Vertical asymptotes at x=-1 and x=-3 5 D. a local minimum at the point (-34 ,-3) E. a local maximum at the point (-34 ,-1 3) QUESTION 5 The equation for the graph shown is A. (x-1)2 9 - y 2 36 =1 B. (x+1)2 9 - y 2 36 =1 C. (x-1)2 9 - y 2 6 =1 D. (x+1)2- y 2 4 =1 E. (x-1)2 9 - y 2 4 =1 VCE Specialist Mathematics – Unit 2 Page 2 of 21 2019 Semester 2 Examination (TA) QUESTION 6 An ellipse has a horizontal semi-axis length of 3 and a vertical semi-axis length of 2 . Given that the centre of the ellipse has coordinates (1,3) , a possible parametric form for the ellipse is A. x=1+9cos (t ) and y=3+4sin (t ) B. x=3+2cos (t ) and y=1+3sin (t ) C. x=1+3cos (t ) and y=3+2cos(t ) D. x=1+3sin (t) and y=3+2 sin (t ) E. x=1+3cos (t ) and y=3+2 sin (t ) QUESTION 7 Which of the following equations, given in polar form, gives the graph of a straight line? A. r=3θ B. r= 4 cos(θ )-2 sin (θ) C. r=-8 sin (θ ) D. r=2+2cos (θ ) E. r2=4 cos(2θ) QUESTION 8 The set of points in the complex plane defined by |z|=|z+2| is A. The point z=-1 √x2+ y2=√(x+2)2+ y2 ∴x2+ y2=x2+4 x+4+ y2 ∴0=4 x+4 ∴x=-1 ∴ℜ(z)=-1 B. The line ℜ(z )=-1 C. The line ℜ(z )=1 D. The circle with centre (2, 0) and radius 2 E. The circle with centre (-2,0) and radius 2 VCE Specialist Mathematics – Unit 2 Page 3 of 21 2019 Semester 2 Examination (TA) QUESTION 9 This velocity-time graph represents the motion of a ball that is thrown vertically upwards from a high balcony and then falls to the ground below. The air resistance is negligible. The height in metres of the balcony above the ground is A. 11.25 125 4 - 45 4 = 80 4 =20metres B. 15 C. 20 D. 25 E. 31.25 QUESTION 10 An object is moving in a northerly direction with constant acceleration of 2m s-2 . When the object is 100m due north of its starting point, its velocity is 30m s-1 . The exact initial velocity of the object could have been A. 10√5m s-1 v2=u2+2as ∴(30 )2=u2+2 (2 )(100) ∴u=± 10√5 B. 5√10m s-1 C. 10√7m s-1 D. -10√7 ms-1 VCE Specialist Mathematics – Unit 2 Page 4 of 21 2019 Semester 2 Examination (TA) E. QUESTION 11 7√10m s-1 The diagram shows a body, B , attached to the end of a light string. The string is fixed at its other end to a point, A , on a vertical wall. The force on B due to the tension in the string is T´ and the weight force is W´ . When a horizontal force P´ (directed away from the wall) is applied, B is held in equilibrium with the string inclined at 45° to the vertical as shown. Which one of the following vector equations is true? A. P´ =W´ B. 2T´ =P´ +W´ C. P´ +W´ -T´ =O´ D. P´ +W´ +T´ =O´ E. √2T´ =P´ +W´ QUESTION 12 If cos ( x )=-1 10 and π 2 <x<π , then cosec (x ) equals A. 10√11 33 sin2 (x)+cos2 (x )=1 ∴sin2(x )+(-101)2=1 ∴sin2(x )+ 1 100 =1 ∴sin2(x )= 99 100 Sine is positive for given domain ∴sin ( x )= 3√11 10 ∴cosec(x )= 1 sin ( x ) = 10 3√11 ∴cosec(x )= 10 3√11 × √ √11 11 B. 10 √101 C. √101 10 D. -10 3√11 E. -10 VCE Specialist Mathematics – Unit 2 Page 5 of 21 2019 Semester 2 Examination (TA) ∴sin (x )=±√100 99 =± 310 √11 ∴cosec(x )=1033 √11 QUESTION 13 The value of cosec(π 6)is A. √3 2 cosec(π 6)= 1 sin(π 6) ∴cosec(π 6 )= 1 1 2 =2 B. 2√3 3 C. √2 D. 2 E. 12 QUESTION 14 Which of the following is not equal to tan(π 5)? A. sin(π5) cos(π 5) B. 1 cot(π 5 ) C. cot(310π) D. 2tan(10 π ) 1-tan2(10 π ) E. 2tan(25π ) 1-tan2(25π) VCE Specialist Mathematics – Unit 2 Page 6 of 21 2019 Semester 2 Examination (TA) VCE Specialist Mathematics – Unit 2 Page 7 of 21 2019 Semester 2 Examination (TA) QUESTION 15 The graph shown above could be A. y=arctan (x) B. y=arccos (x ) C. y=arcsin (x ) D. y=cot (x) E. y=sec (x ) QUESTION 16 The points A , B and C lie on a circle with centre O , as shown in the diagram below. The size of ∠ ACB is 40 ° . The value of ∠ AOB is A. 20 ° ∴∠ AOB=2 ×∠ ACB ∴∠ AOB=80 ° B. 40 ° C. 70 ° D. 80 ° E. 90 ° VCE Specialist Mathematics – Unit 2 Page 8 of 21 2019 Semester 2 Examination (TA) QUESTION 17 The points A , B and P lie on a circle centred at O . The tangents to the circle at A and B meet at the point T , and ∠ ATB=θ . What is ∠ APB in terms of θ ? A. θ2 ∠ APB=∠ AOB 2 ∴∠ APB=180-θ 2 ∴∠ APB=90-θ 2 B. 2θ C. 90°-θ 2 D. θ E. 180°-θ QUESTION 18 Consider the linear transformation T : R2→R2 , where T([x y])=[0 2 -02][xy] . The correct geometric interpretation of the linear transformation, T , is A. Rotates counter-clockwise through 180° . B. Rotates counter-clockwise through 90° and doubles the length. C. Rotates counter-clockwise through 90° and halves the length. D. Rotates counter-clockwise through 90° and quadruples the length. E. Rotates clockwise through 90° and doubles the length. VCE Specialist Mathematics – Unit 2 Page 9 of 21 2019 Semester 2 Examination (TA) QUESTION 19 The transformation given by the matrix T([x y])=[-01 0 2][xy] is applied to the straight line x+2 y=3 . The equation of the image graph is A. 4 x-y=6 x ' =-x y ' =2 y ∴x=-x' ∴ y= y ' 2 ∴-x'+2(y2')=3 ∴ y-x=3 B. y-x=3 C. x-4 y=3 D. 2x+2 y=3 E. 2 y-2x=3 QUESTION 20 Consider the graphs of y=f (x ) and y=g (x ) shown below. Which of the following equations are true? A. g (x)=f (-x ) B. g (x)=f -1(x ) C. g (x)=-f (x ) D. g (x)= 1 f (x) E. g (x)=(f (x ))2 END OF SECTION A VCE Specialist Mathematics – Unit 2 Page 10 of 21 2019 Semester 2 Examination (TA) THIS PAGE HAS BEEN INTENTIONALLY LEFT BLANK. VCE Specialist Mathematics – Unit 2 Page 11 of 21 2019 Semester 2 Examination (TA) Section B – Extended response (60 marks) Instructions for Section B [Show More]

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