SAT数学Problem Solving练习题(5)-智课教育出国考试.pdf

智 课 网 S A T 备 考 资 料 SAT数学Problem Solving练习题 5 智课教育出国考试 SAT数学Problem Solving练习题 Question 1 If a b and c are consecutive integers a b c and a b c 96 what is the value of b a 30 b 31 c 32 d 33 e 34 Solution If a b and c are consecutive numbers b a 1 and c a 2 Then a a 1 a 2 96 so 3 a 3 96 a 96 3 3 31 b a 1 32 Question 2 The price of wheat was 5 bushel on January 2007 and 9 bushel on January 2008 By what percentage did the price change a 10 b 40 c 60 d 80 e 90 Answer The price change is Price2008 Price2007 Price2007 100 9 5 5 100 4 5 100 80 Question 3 In the figure below angle AMB is 100o angle BMD is 40o and angle CME is 60o What is the value of angle CMD Figure not drawn to scale a 20o b 30o c 40o d 50o e 80o Answer If angle AMB is 100o then angle BME is 180o 100o 80o BMC CMD 40o BMC CMD DME 80o If we subtract the 2 equations DME 40o CMD DME 60o BMC CMD DME 80o If we subtract the 2 equations BMC 20o CMD BME BMC DME 80o 40o 20o 20o Question 4 A vehicle runs from town A to town B at a speed of 20 miles hour while another vehicle runs from town B to town A at a speed of 60 miles hour Both vehicles start their trips at the same time and the distance between towns is 100 miles How long does it take from the time they start running to the moment they are at the same point on the road a 1 hour b 1 hour and 15 minutes c 1 hour and 30 minutes d 1 hour and 45 minutes e 2 hours and 15 minutes 100 miles d1 d2 This is equation 1 It take the same time for the 2 cars to meet t d1 20 miles hour d2 60miles hour This is equation 2 We solve the system of 2 equations to find d1 and d2 From equation 2 3 d1 d2 Then 100 miles d1 d2 4 d1 so d1 25 miles and d2 75 miles The answer is t d1 20miles hour 25 20 5 4 1 hour and 15 minutes Question 5 Given the list of integers 2 2 0 6 8 0 5 9 10 4 which of the following statements is true a mode median average b median mode average c median average mode d mode median average e average median mode Answer We need to rearrange the list of integers in order 5 2 0 0 2 4 6 8 9 10 The average will be the sum of all integers divided by the number of integers 32 10 3 2 The median will be the mean of the 2 middle numbers 2 and 4 so the median is 3 The mode is 0 as 0 occurs the most in the list The correct answer is mode median 0 b a b c c a c 2 b d b c a e a b b c a c Answer The first answer is true since the product of 2 positive reals will be positive The second and the fourth answers are also true since the sum of 2 sides of a triangle is always higher than the third side The fifth answer is also true because it is just a multiplication of the second and fourth inequalities Answer three should be the one that is not true and we can verify this result with an example an isosceles triangle with a 3 b 3 c 10 will not satisfy the inequality Question 9 If x 4y 6 and x 2y 3 which of the following statements is not true a y 1 2 b x 4 c y 2 d xy 2 e x y 9 2 Answer In order to find the values of x and y we multiply the second equation by 2 and add the 2 equations x 4y 6 2x 4y 3 3x 12 and x 4 y 6 3 4 1 2 y 2 is the only equality that is false Question 10 Prizes totaling 60 000 were awarded unequally between 3 contestants Which of the following choices could be the highest prize a 5 000 b 10 000 c