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. 4 0.00.46 450 450 (cor. to the nearest ten) Number of sig. fig. 4 5 6 5 Summer Adventure in Mathematics (S to S)
Matching Equation Solution. + 4 = 0 =, = -. 5 + = - = 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). 4 5 + = 0 Linear Equations in Two Unknowns 5
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 - =, - 0 0 4 Solve the following simultaneous equations ( ) b the method of substitution.. = = 6. = 9 6 Summer Adventure in Mathematics (S to S)
Solve the following simultaneous equations (4 5) b the method of elimination. 4. = 0 5 5. 5 = 0 6. Solve = 4 = graphicall. 0 Solve the following simultaneous equations (7-9) algebraicall. 7. + = 0 8. m + n = 9 4m n = 8 Linear Equations in Two Unknowns 7
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)
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 + 75 + BCP = 80 ( sum of ) In CQR, 60 + 75 + BCP = 80 BCP = 45 QCR + 7 + = 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. http://www.hkep.com/misc/summer/samnd_e/samnd_bk_chapter06e.pdf Angles, Triangles and Polgons 45
Revision Test Marks: 7 Section A (6 marks, each answer carries mark). Round off 9.5974 to significant figures. 5. Simplif L : 450 ml. A. 9.6 B. 9.59 A. 0 : B. : 0 C. 9.594 D. 9.597 C. 50 : D. : 50. Which of the following is NT an identit? A. ( + ) = + 6 B. ( - ) = - 4 + C. ( - )( + ) = - 4 D. ( + 5)( - ) = + - 5 6. In the figure, find. + 75 0 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. 5 6 5 B. D. 5 6 5 6 5. 8. The figure shows a sector. Find the area of the sector in terms of π. = 4 0 + 5 = A. (-, ) B. (, -) C. (-, ) D. (, -) 60 cm A. π cm B. 4π cm C. 60π cm D. 44π cm Revision Test 77
Bridging Task Short Questions m. It is given that a = - 6 = m a. Find the value of - 6.. 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