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Section Number: Question No. Multiple Choice Questions Essay Question 1 Earned Points Essay Question 2 Essay Question 3 Essay Question 4 Essay Question5 Total I. MULTIPLE CHOICE QUESTIONS (Worth 12 points). You may solve all questions. Each question is worth 3 points. Your grade in this part is that of the best 4 questions. ……………………………………………………………………………... Q–1 Choose the option which gives 40: (a) 20 (40 10) (b) (20 40) 10 (c) (20 5) 10 (d) 20 (5 10) (e) none ………………………………………………………………………………... Q–2: The mean of x-3,x,2x,2x-11 is equal to 4.What is x? (a) 9 (b) 5 (c) 1/3 (d)49 (e) none .……………………………………………………………………………………. Q–3: The gradient of the line y=0.5x is: 1 (a) 2 (b) 50 (c) 0 (d)1/2 (e) none …………………………………………………………………………….. Q–4: Which of the following expression that is not equal to 9 6 : (a) 95 9 (b) 912 1 9 (c) ( ) 6 (d) 9 2 9 4 (e) none ........................................................................................................................... 3 5 Q-5: The y- intercept of the line y= x 2 is: (a) 2 (b) 3 5 (c) -2 (d) 1 2 (e) none ………………………………………………………………………………... II. ESSAY QUESTIONS (Worth 48 points). >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You may solve all questions in this part. Each question is worth 12points. Your grade in this part is that of the best 4 questions. Please show the details of your work and not just the final answer. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Q–1: (2 points each) Answer the following questions. a. Round 8.75 to the nearest tenth. Answer: 8.8 3 5 b. Change 8 to an improper fraction. Answer: 43/5 c. Change 39 to mixed number. 24 2 Answer: 1 15 24 d. Express 0.375 as a common fraction. Answer: 0.375= e. Express 375 3 1000 8 5 as a decimal. 8 Answer: 5/8 = 0.625 7 as a percent. 8 7 Answer: 100% 87.5% 8 f. Express ………………………………………………………………………………... Q–2 (4 points each) a. Modern furnishings spent 3.4% of its sales on advertising. If sales amounted to $146,280 what amount was spent on advertising? Answer: 3,4 146,280 $ 4973.52 100 b. A hospital charges a patient $7.80 for capsules. How much should it charge for 18 capsules? Answer: No where in the question it mentions that capsules contain a dozen number of pills… so the question should be solved as x = 7.80 and 18 x = $140.4 c. Simplify the expression -3x (-2x) – (-2x)x + 9x² answer: 6x² + 2x² +9x² = 17x² d. Without using calculator, write the following in scientific notation (1.5 10 2 ) (7.5 10 3 ) Answer: Here it should be7.5 x 10^-3 not 7.3 x 10^-3 so the answer should be 7.5 x 10^-3 (15 10 3 ) (7.3 10 3) (15 7.3) 10 3 7.7 10 3 (answer is in scientific notation) ………………………………………………………………………………... 3 Q–3: (4 points each) a. What annual rate of return needed to receive $960 in one year on an investment of $12,000? Answer: 960 100% 8% 12000 So the annual rate is 8% b. At a business meeting there were 25 more women than men. The total number of people at the meeting was 139.Find the number of men. Answer: Let x represent the number of men. the Number of men + the number of women= total x + (x+25) 2x +25 = 139 = 139 x 57 2x=114 c. Without using calculator, write the following in scientific notation (6 10 9 ) (510 6 ) Answer: (6 5)(10 9 10 6 ) 30 10 3 = 3.0 10 4 (answer in scientific notation ) d. Simplify the expression 4x +0 .5yxt – 2(-0.5x) answer: 4x+x+ 1 1 yxt = 5x+ xyt 2 2 ………………………………………………………………………………... Q–4: (12 points) a. (2 points) Solve the equation 6x-2=4x+10 Answer: 6x-2=4x+10 6x – 4x =10 +2 2x = 12 x=6 b.(2 points) Make y the subject of the equation z Answer: 4 x y 1 x z(y+1) = x zy + z = x y 1 xz Zy = x-z y = z z c. (2 points each)Write down the equation of the following lines. i. The line that has slope 2 and y-intercept 3 Answer: y = 2x +3 ii. The line that passes through the points (-2,5) and (4,8) Answer: 85 3 1 4 (2) 6 2 1 1 y = mx +c y x c 8 (4) c c 6 2 2 1 y = x 6 2 m= iii. The line that is parallel to the x-axis and passes through the point (3,2) Answer: m=0, so the equation is y=2 iv. The line that is parallel to the y-axis and passes through the point (-3,4) Answer: m is not defined, so the equation is x=-3 ………………………………………………………………………………... Q–5 (4points each) Given the gross weekly earnings of ten school teachers(in pounds) as shown below 165 188 233 275 147 350 249 200 a. Calculate the mean and the median. Answer: Mean = 130 147 ............. 350 226.7 10 130 147 165 188 200 233 249 275 330 350 Median = 200 233 216.5 2 b. Calculate the lower quartile and the upper quartile. Answer: 5 130 330 Lower quartile = 165 upper quartile = 275 c. Find the range and inter quartile range. Answer: Range = 350 – 130 = 220 Inter quartile range = 275 – 165 = 110 d. Find the standard deviation. Answer: From part a the mean=226.7 Data value 130 147 165 188 200 233 249 275 330 350 Deviations(d) 130-226.7= -96.7 147-226.7= -79.7 165-226.7= - 61.7 188-226.7= -38.7 200-226.7= -26.7 233-226.7= 6.3 249-226.7= 22.3 275-226.7=48.3 330-226.7= 103.3 350-226.7= 123.3 d 2 50464.1 5046.41 10 10 So, the standard deviation is 5046.42 =71.038 The variance= 6 d² 9350.89 6352.09 3806.89 1497.69 712.89 39.69 497.29 2332.89 10670.89 15202.89