Approximation and Error

Transcription

1 Approimation and Error The queue is quite long. We can ride on the roller coaster after 9 rounds. Each round is estimated to last for minutes, correct to the nearest minute. Are we sure that we can ride on it within 0 minutes? The actual time for each round is from.5 to.5 minutes. We ma need to wait for more than 0 minutes! Anthon According to the situation above, the maimum absoluter error in time for each round = 0.5 minute, the greatest possible time for each round =.5 minutes. Therefore, the ma need to wait for (.5 9) minutes =.5 minutes. Benn Hint If the time for ever round is.5 minutes, then the will need to wait for the longest time. Significant figure. The leftmost non-zero digit of a number is the first significant figure. Generall, ever digit, including zeros, at the right of this figure are also significant. st significant figure E.g (cor. to the nearest ten) Number of sig. fig Summer Adventure in Mathematics (S to S)

2 Matching Equation Solution. + 4 = 0 =, = = - = 4, = 0. - = 8 = 4, = - Fill in the Blanks 4. =... ()... () 5. + = = 0... () 6... () Substituting () into (), - Substituting into ( ), = ( ) = The solution is =, =. () - (), - (-) = 0-6 = -6 = Substituting = into (), + ( ) = 0 = The solution is =, =. True or False 6. There are infinitel man solutions for all linear equations in two unknowns. 7. Ever point on the graph of an equation indicates a solution of the equation. 8. (, ) is the solution of + = =. Multiple-choice Questions + = 9. Solve 4 5 graphicall. A. The eact solution is (, 0.5). B. The eact solution is (., 0.5). C. The approimate solution is (, 0.5). D. The approimate solution is (., 0.5) = 0 Linear Equations in Two Unknowns 5

3 0. Which of the following can be the graph of a linear equation in two unknowns and? A. B. C. D.. Complete the following tables and solve For + = 4, 0 + = 4 = graphicall. 4 For - =, Solve the following simultaneous equations ( ) b the method of substitution.. = = 6. = 9 6 Summer Adventure in Mathematics (S to S)

4 Solve the following simultaneous equations (4 5) b the method of elimination. 4. = = 0 6. Solve = 4 = graphicall. 0 Solve the following simultaneous equations (7-9) algebraicall = 0 8. m + n = 9 4m n = 8 Linear Equations in Two Unknowns 7

5 8. In the figure, ABCD is a square. CDE is an equilateral triangle. (a) Find. Scoring Tips (b) Find. B E A C D EYA 9. In the figure, AB, BC and BD are the sides of three different polgons. Is it possible that all of them are regular polgons? Eplain our answer. A Polgon I C Polgon II B Polgon III D Scoring Tips : Find ADE first. 44 Summer Adventure in Mathematics (S to S)

6 In the figure, ABC is an equilateral triangle. P and Q are points on AB and BC respectivel such that AQC = 7 and BPC = 75. Find. A Solution: CBP 0 (propert of equil. ) In BCP, CBP BCP = 80 ( sum of ) In CQR, BCP = 80 BCP = 45 QCR = 80 ( sum of ) Ref: TSA 0 9ME, Q9 B Scoring Tips P R 75 Q 7 Consider a triangle in each step to find the unknown angle. C Follow-up 0. In the figure, ADB, AEC and BCF are straight lines. AC = BC, ADE = 80 and ACF = 0. Find. A D 80 E 0 B C F Let s see the following website to stud the wa of covering a plane using polgons. Angles, Triangles and Polgons 45

7 Revision Test Marks: 7 Section A (6 marks, each answer carries mark). Round off to significant figures. 5. Simplif L : 450 ml. A. 9.6 B A. 0 : B. : 0 C D C. 50 : D. : 50. Which of the following is NT an identit? A. ( + ) = + 6 B. ( - ) = C. ( - )( + ) = - 4 D. ( + 5)( - ) = In the figure, find A. 5 B. 6 C. 75 D. 90. Simplif -. m n A. m - n C. mn B. D. n - m m - n n - m mn 4. Solve the simultaneous equations graphicall. + 5 = = 4 7. Rationalize the denominator of A. C B. D The figure shows a sector. Find the area of the sector in terms of π. = = A. (-, ) B. (, -) C. (-, ) D. (, -) 60 cm A. π cm B. 4π cm C. 60π cm D. 44π cm Revision Test 77

8 Bridging Task Short Questions m. It is given that a = - 6 = m a. Find the value of In a rectangular coordinate plane, for an two points A(, ) and B(, ), the slope of AB is given b - -. A (, ) B (, ) In the figure, find the slope of CD. Slope of CD = C (, ) D (5, 4). It is known that the volume of a sphere is 4 πr, where r is the radius of the sphere. Find the volume of the sphere if r = 5 cm. (Give the answer correct to significant figures.) Volume = 4. For a set of data, the mode is the most frequent value of the set of data. For eample, the mode of a set of data {, 8, 8,, 8, 9} is 8. For the set of data {5, 7, 7, 5, 8, 5, 6}, find the mode. Mode = Revision Test 8