Hi, Please find the attached math assignment due on Thursday please
Purpose: To apply the proficiencies of understanding and fluency and reasoning and problem solving across the topics of Geometric Reasoning, Pythagoras’ Theorem and Trigonometry. Students will apply mathematical processes, solve problems and communicate their understanding. This exam contributes 50% to the final grade for the semester. A B C D E The folio of a student’s work has the following characteristics: Un de rs ta nd in g an d flu en cy Co nc ep tu al un de rs ta nd in g connection and description of mathematical concepts and relationships in unfamiliar situations connection and description of mathematical concepts and relationships in complex familiar situations recognition and identification of mathematical concepts and relationships in simple familiar situations some identification of simple mathematical concepts statements about obvious mathematical concepts Pr oc ed ur al flu en cy recall and use of facts, definitions, technologies and procedures to find solutions in unfamiliar situations recall and use of facts, definitions, technologies and procedures to find solutions in complex familiar situations recall and use of facts, definitions, technologies and procedures to find solutions in simple familiar situations some recall and use of facts, definitions, technologies and simple procedures partial recall of facts, definitions or simple procedures Ma th em at ica l lan gu ag e a nd sy m bo ls effective and clear use of appropriate mathematical terminology, diagrams, conventions and symbols consistent use of appropriate mathematical terminology, diagrams, conventions and symbols use of appropriate mathematical terminology, diagrams, conventions and symbols use of aspects of mathematical terminology, diagrams and symbols use of everyday language Pr ob lem -s ol vin g an d re as on in g P ro bl em so lvi ng ap pr oa ch es systematic application of relevant problem-solving approaches to investigate unfamiliar situations application of relevant problem-solving approaches to investigate complex familiar situations application of problem-solving approaches to investigate simple familiar situations some selection and application of problem-solving approaches in simple familiar situations partial selection of problem-solving approaches Ma th em at ica l m od ell in g development of mathematical models and representations in unfamiliar situations development of mathematical models and representations in complex familiar situations development of mathematical models and representations in simple familiar situations statements about simple mathematical models and representations isolated statements about given mathematical models and representations Re as on in g an d ju st ifi ca tio n clear explanation of mathematical thinking and reasoning, including logical justification of choices made, evaluation of strategies used, proofs formulated and conclusions reached explanation of mathematical thinking and reasoning, including reasons for choices made, strategies used, proofs formulated and conclusions reached description of mathematical thinking and reasoning, including discussion of choices made, strategies used, proofs formulated and conclusions reached statements about choices made, strategies used and conclusions reached isolated statements about given strategies or conclusions Key shading emphasises the qualities that discriminate between the A–E descriptors Formula sheet (10 Mathematics – Standard) Mensuration circumference of a circle C = 2π r area of a circle A = π r² area of a parallelogram A = b h area of a trapezium A = ½(a + b)h area of a triangle A = ½ b h volume of a prism V = A h total surface area of a cylinder S = 2π r h + 2π r² volume of a cylinder V = π r² h Finance simple interest ?? = ?????? compound interest ?? = ??(1 + ??)?? Trigonometry trigonometric ratios ?????? ??= ????????????????ℎ?????????????????? ?????? ??= ???????????????? ℎ?????????????????? ?????? ??= ???????????????? ???????????????? Pythagoras’ theorem ??2 + ??2 = ??2 Statistics mean ?? = ?????? ???? ?????? ???????? ???????????? ???????????? ???? ???????? ???????????? ?? = ∑???? ?? median �??+1 2 � ??ℎ data value Probability probability of an event occurring ??(??????????) = ???????????? ???? ???????????????????? ???????????????? ?????????? ???????????? ???? ???????????????? probability of independent events ??(?? ?????? ??) = ??(??) × ??(??) conditional probability ??(??|??) = ??(?? ∩ ??) ??(??) WORKING is to be completed on this paper. If you need extra room or to redo a question, note this on this paper and attach the extra pages used. Be sure to label your work clearly. Question 1 SF UF 1 mark State the bearing of the point P in each of the following diagrams: a) b) Question 2 SF PSR 3 marks A helicopter hovers 152m directly above an ocean swimmer. A boat is 300m from the swimmer. Draw and label a diagram and determine the angle of depression from the helicopter to the boat, correct to the nearest degree. Question 3 SF UF 1½ marks Use techniques of deduction to determine the following a) If ?? = 12 and ?? = ?? then determine ?? b) If ?? + ?? = 31 and ?? = ?? then determine ?? + ?? c) If ?? + ?? = 18 and ?? + ?? = 18 then what is the relationship between ?? and ??. Question 4 SF PSR 3 marks A square field has a diagonal of 18m. The owner would like to install a fence on all four sides of the field. Determine the length of fencing required. (Give your answer correct to 2 decimal places) Question 5 SF UF 2 marks Calculate the value of t in the triangle below, correct to two decimal places. Question 6 SF UF 2½ marks In the diagram given, ???? = ???? and ???? ∥ ???? Prove ∆?????? is congruent to ∆?????? by completing the table. Statement Reason 1 ???? = ???? Given 2 3 4 ∆?????? ≅ ∆?????? Question 7 SF UF 2½ marks The two triangles in the diagram are similar. Determine the width of the river, to the nearest metre. Question 8 SF PSR 3½ marks An observer who is standing 32m from a building measures the angle of elevation of the top of the building as 25°. If the observer’s eye is 170cm from the ground, determine the height of the building, correct to 2 decimal places. Question 9