2008 H I G H E R S C H O O L C E R T I F I C AT E E X A M I N AT I O N Mathematics General Instructions • Reading time – 5 minutes • Working time – 3 hours • Write using black or blue pen • Board-approved calculators may be used • A table of standard integrals is provided at the back of this paper • All necessary working should be shown in every question Total marks – 120 • Attempt Questions 1–10 • All questions are of equal value 212 BLANK PAGE – 2 – Total marks – 120
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– 3 Surface area of sphere = 4 π r 2 1 Volume of cone = – π r2h l 3 h Curved surface area of cone = π rl r In any triangle ABC Area of triangle = 1 – 2 C ab sin C a b b a c Sine rule ––––– = ––––– = ––––– sin A sin B sin C A c B Cosine rule a2 = b2 + c2 – 2bc cos A The Quadratic Equation The solutions of ax2 + bx + c = 0‚ where a ≠ 0‚ are given by – b ± √ (b2 – 4ac) ––––––––––––––– x= 2a (02) WMP/Jun14/4365/1H Do not write outside the box 3 Answer all questions in the spaces
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c++ 1. (10 points) Consider the usual algorithm to convert a fully parenthesized infix expression to a postfix expression. Suppose that you have read 10 input characters during a conversion and that the stack now contains these symbols: | | | + | | ( | bottom |___*___| Now‚ suppose that you read and process the 11th symbol of the input. Draw the stack for the case where the 11th symbol is:
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Watching television 5 Number of hours 4 Playing games 3 2 1 0 Eve Frank Gok Hamza (2 marks) 1 (b) Who watched television for 5 hours? Answer ...................................................................... 1 (c) Who spent more time watching television than playing games? Answer
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Business Decisions Page 475 # 20 A‚ B‚ & C A – Jamie and Alice’s combined housing expense ratio is 20.6% B – Jamie & Alice’s total obligations ratio is 49.6% Total obligations ration (TOR) Total Monthly Financial Obligations (TMFO) Monthly Gross Income (MGI) TMFO = $2811+$2002=$4813 C – Jamie and Alice would not qualify for a conventional nor an FHA mortgage. Page 585 #33 – Replacing the Asset A‚B‚C‚ & D A – The annual depreciation for the original
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Part A Q2-Maths Assignment 2012‚ Mrs Pillai Lvl 1 Irrational numbers are numbers that are neither whole numbers nor ratios of whole numbers. Irrational numbers are real numbers in the sense that they appear in measurements of geometric objects--for example‚ the number pi (II). However‚ irrational numbers cannot be represented as decimals‚ unlike rational numbers‚ which can be expressed either as finite decimals or as infinite decimals that eventually follow a repeating pattern. By contrast‚ irrational
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1. Solve a. e^.05t = 1600 0.05t = ln(1600) 0.05t = 7.378 t = 7.378/.05 t = 147.56 b. ln(4x)=3 4x = e^3 x = e^3/4 x = 5.02 c. log2(8 – 6x) = 5 8-6x = 2^5 8-6x = 32 6x = 8-32 x = -24/6 x = -4 d. 4 + 5e-x = 0 5e^(-x) = -4 e^(-x) = -4/5 no solution‚ e cannot have a negative answer 2. Describe the transformations on the following graph of f (x) log( x) . State the placement of the vertical asymptote and x-intercept after the transformation. For example‚ vertical shift
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save a lot of digging. What is x? So‚ if you walk x paces north‚ then 2x+4 paces east‚ you have moved roughly east northeast to a distance of 2x+6 paces. This is a right angle‚ with 2x+6 on the hypotenuse or line c‚ so we must solve using the Pythagorean Theorem: a² + b² = c² add in the values (x)² + (2x+4)² = (2x+6)² multiply inside the parenthesis x² + 4x² + 16x + 16 = 4x² + 24x + 36 subtract 4x² + 24x + 36 from both sides x² - 8x - 20 = 0 factor the quadratic equation (x -10)(x
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argumentative and analytical writing‚ as well as techniques of basic research paper writing. The course also incorporates debates and other oral activities. An honor section is offered as ENG 137(H). Prerequisite: English 135 Freshman Comp I with a grade of “C” or better. Student Learning Outcomes: By the end of this course‚ you (the student) will be able to do the following: • Generate written assignments using various electronic devices via multimedia and document software. CL1‚ CL2 • Utilize
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Choices: 1. What is the average of A‚ B‚ C? a. ABC/3 c. 3(A+B+C)/.3 b. (A+B+C)/3 d. ABC/A+B+C 2. Which of the following has the LEAST Numerical value? a. 11/12 b. 6/8 c. 5/7 d. ¾ 3. If 2 apples cost P25.00‚ how many apples can be purchased for P100.00? a. 8 aplles c. 2 dozens b. ½ dozen d. 1 ½ dozens 4. If 2 tablespoons= 1 liquid oz.‚ and 5 tablespoons = ¼ cup‚ then‚ how many liquid ounces are there in one cup? a. 4 ounces c. 16 ounces b. 10 ounces d. 24 ounces
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