SUPERVISOR TO ATTACH PROCESSING LABEL HERE Victorian Certificate of Education 2014 Letter STUDENT NUMBER FURTHER MATHEMATICS E L Written examination 2 s n o ti . Monday 3 November 2014 a d c o ate l Reading time: 9.00 am to 9.15 am (15 minutes) l a Writing time: 9.15 am to 10.45 am (1 hour 30 minutes) ic k d r a in m n QUESTION AND ANSWER o d BOOK i t n a ma s Structure of book r n o o f i Core t n s ei e u h t q f4 om 4 15 o r r e yf Module b r m a Nu ay v 6 3 45 m A S M P Number of questions Number of questions to be answered Number of marks Number of modules Number of modules to be answered Number of marks Total 60 • Students are permitted to bring into the examination room: pens, pencils, highlighters, erasers, sharpeners, rulers, one bound reference, one approved graphics calculator or approved CAS calculator or CAS software and, if desired, one scientific calculator. Calculator memory DOES NOT need to be cleared. • Students are NOT permitted to bring into the examination room: blank sheets of paper and/or white out liquid/tape. Materials supplied • Question and answer book of 38 pages, with a detachable sheet of miscellaneous formulas in the centrefold. • Working space is provided throughout the book. Instructions • Detach the formula sheet from the centre of this book during reading time. • Write your student number in the space provided above on this page. • All written responses must be in English. Students are NOT permitted to bring mobile phones and/or any other unauthorised electronic devices into the examination room. © VICTORIAN CURRICULUM AND ASSESSMENT AUTHORITY 2014 2014 FURMATH EXAM 2 Instructions This examination consists of a core and six modules. Students should answer all questions in the core and then select three modules and answer all questions within the modules selected. You need not give numerical answers as decimals unless instructed to do so. Alternative forms may involve, for example, , surds or fractions. Diagrams are not to scale unless specified otherwise. E L s n o ti . a d c o ate l l a ic k d r a in m n d tio n a ma s r n o o f ti in s e e u h t q f om o er y fr b r m a Nu ay v m A S M P FURTHER MATHEMATICS Written examinations 1 and 2 FORMULA SHEET Directions to students Detach this formula sheet during reading time. This formula sheet is provided for your reference. © VICTORIAN CURRICULUM AND ASSESSMENT AUTHORITY 2014 FURMATH EXAM 1 & 2 2 Further Mathematics formulas Core: Data analysis x−x sx standardised score: z= least squares regression line: y = a + bx, where b = r residual value: residual value = actual value – predicted value seasonal index: seasonal index = sy sx and a = y − bx actual figure deseasonalised figure Module 1: Number patterns arithmetic series: a + (a + d ) + … + (a + (n – 1)d ) = geometric series: a + ar + ar2 + … + ar n – 1 = infinite geometric series: a + ar + ar2 + ar3 + … = n n [ 2a + (n − 1)d ] = (a + l ) 2 2 a (1 − r n ) ,r≠1 1− r a , r <1 1− r Module 2: Geometry and trigonometry area of a triangle: 1 bc sin A 2 Heron’s formula: A= circumference of a circle: 2π r area of a circle: π r 2 volume of a sphere: 4 3 π r 3 surface area of a sphere: 4π r 2 volume of a cone: 1 2 π r h 3 volume of a cylinder: π r 2h volume of a prism: area of base × height volume of a pyramid: 1 area of base × height 3 1 s ( s − a )( s − b)( s − c) , where s = (a + b + c) 2 3 Pythagoras’ theorem: c2 = a2 + b2 sine rule: a b c = = sin A sin B sin C cosine rule: c2 = a2 + b2 – 2ab cos C Module 3: Graphs and relations Straight-line graphs y2 − y1 x2 − x1 gradient (slope): m= equation: y = mx + c Module 4: Business-related mathematics PrT 100 simple interest: I= compound interest: A = PRn, where R = 1 + hire-purchase: r 100 2n effective rate of interest ≈ × flat rate n +1 Module 5: Networks and decision mathematics Euler’s formula: v+f=e+2 Module 6: Matrices determinant of a 2 × 2 matrix: a b a b ; det A = A= = ad − bc c d c d inverse of a 2 × 2 matrix: A−1 = 1 d −b where det A ≠ 0 det A −c a END OF FORMULA SHEET FURMATH EXAM 1 & 2

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