student-produced response questions參考答案

　　1.Correct Answer: 3240

　　Explanation:

　　A 20 per cent increase on 45 words per minute = 1.2 x 45 = 54 words per minute.

　　To get words per hour, multiply by 60 = 3240

　　2.Correct Answer: 2

　　Explanation:

　　This is a pair of simultaneous equations. Rearrange :

　　2y - x = 8; -y +3x = 1; multiply the second by 2

　　-2y + 6x = 2; then add to the first to give

　　5x = 10; x = 2

　　3.Correct Answer: 101

　　Explanation:

　　Four consecutive integers can be written n + (n + 1) + (n + 2) + (n + 3)

　　Their sum = 4n + 6 = 410

　　4n = 404; n = 101

　　4.Correct Answer: 2

　　Explanation:

　　Draw a diagram.

　　A and D can be the same color because they do not share a border. Also B and C can be one color, but B and C must differ from A and D. So two colors are needed.

　　5.Correct Answer: 5

　　Explanation:

　　The diagonal and two sides form an isosceles right triangle.

　　Using Pythagoras s² + s² = d²; 2s² = d²

　　Since these terms are equal we can replace d² in the given equation

　　Hence 2s² + 2s² = 100; 4s² = 100; s² = 25; s = 5

　　6.Correct Answer: 12

　　Explanation:

　　First imagine C in second position. This gives a choice of 1 out of three for first place, and one out of two for third place. This is equivalent to 6 possible combinations.

　　Now putting B in second place and using the same logic there are 6 more combinations.

　　Total = 12

　　7.Correct Answer: 1.35

　　Explanation:

　　This is a weighted average problem.

　　The average weight = (40 x 1 + 50 x 1.5 + 10 x 2) 100

　　(40 + 75 + 20)/100 = 1.35

　　8.Correct Answer: 60

　　Explanation:

　　Let the smallest angle = x

　　The sum of two vertically opposite angles = 2x

　　The sum of the other pair of vertically opposite angles = 360 - 2x

　　But since they are double the measure of angle x their sum also = 4x

　　Equating gives 360 - 2x = 4x; 360 = 6x; 60 = x

　　[Or even simpler: the sum of one angle and its neighbor =180. The angles are x and 2x, so 3x = 180 ; x = 60]

　　9.Correct Answer: 7

　　Explanation:

　　The area of the shaded region is the area of the large triangle enclosed between the axes minus the area of the small un-shaded triangle.

　　8 - 1 = 7

　　10.Correct Answer: 2/7

　　Explanation:

　　The probability is the ratio of the area of the beds to the total area. The sides of the square beds = 4y – 2y = 2y. Area of one bed = 4y². Area of two beds = 8y². Total area is 4y x 7y = 28y². Probability = 8/28 = 2/7