The following chart shows registration for art classes for Fall 2015.
Students Registering For Art Classes | |
---|---|
Course | Number of Students |
Stained Glass | 21 |
Beginning Drawing | 48 |
Sculpture | 13 |
Water colours | 18 |
Total | 10 |
If this is are presentative sampling, how many out of 500 students would be expected to choose Stained Glass for their art course? [2 Mark]
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Solution
Since the sampling is representative, this means that the same trend will be seen when a larger sample is considered.
Thus, multiply by 5 to see how many students out of 500 will choose stained glass 5 × 21 = 105.
If \(p = \frac{\sqrt{3} – 2}{\sqrt{2} + 1}\), then which one of the following equals p – 4 ? [2 Mark]
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Solution
Since none of the answers are fractions, let’s rationalize the given fraction by multiplying top and bottom by the conjugate of the bottom of the fraction:
\(p = \frac{\sqrt{3} - 2}{\sqrt{2} + 1} \times \frac{\sqrt{2} - 1}{\sqrt{2} - 1}\)
\(\frac{\sqrt{3}\sqrt{2} + \sqrt{3}\left ( -1 \right ) + \left (-2 \right )\sqrt{2} + \left ( -2 \right )\left ( -1 \right )}{\left ( \sqrt{2} \right )^{2} - 1^{2}}\)
\(= \frac{\sqrt{6} - \sqrt{3} - 2\sqrt{2} + 2}{2 - 1} = \sqrt{6} - \sqrt{3} - 2\sqrt{2} + 2\)
Now, \(p - 4 = \left (\sqrt{6} - \sqrt{3} - 2\sqrt{2} + 2 \right ) - 4\)
\(\sqrt{6} - \sqrt{3} - 2\sqrt{2} - 2\)
Ten new television shows appeared during the month of September. Five of the shows were sitcoms, three were hour-long dramas, and two were news-magazine shows. By January, only seven of these new shows were still on the air. Five of the shows that remained were sitcoms. Which one of the following statements must be true based on the above? [2 Mark]
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Solution
If there were seven shows left and five were sitcoms, this means that only two of the show could possibly be dramas. Options (a) and (b) may be true, but there is no evidence to indicate this as fact. The fact that all of the sitcoms remained does not necessarily mean that viewers prefer sitcoms (option d).
For too long, school cafeterias, in an effort to provide food they thought would be appetizing to young people, mimicked fast-food restaurants, serving items such as burgers and fries, pizza, hot dogs, and fried chicken. School districts nation wide are now addressing this trend by incorporating some simple and in expensive options that will make cafeteria lunches healthier while still appealing to students. This paragraph best supports the statement that [2 Mark]
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Solution
The final sentence of the paragraph supports choice d. The other choices are not supported by the passage. Choice c may seem correct at first, but the paragraph states that the new initiatives are simple and inexpensive, not major.
In nation wide poll, M people were asked 2 questions. If 3⁄5 answered “yes” to question 1, and of those 1⁄4 also answered “yes” to question 2, which of the following represents the number of people polled who did not answer “yes” to both questions? [2 Mark]
An ant moved for several seconds and covered 3 mm in the first second and 4mm more in each successive second than in its predecessor. If the ant had covered 1 mm in the first second and 8 mm more in each successive second, then the difference between the path it would cover during the same time and the actual path would be more than 6 mm but less than 30 mm. Find the time (in second) for which the ant moved?
A big cube is formed by rearranging the 160 coloured and 56 non-coloured similar cubes in such a way that the exposure of the coloured cubes to the outside is minimum.The percentage of exposed area that is coloured is
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Solution
Total cubes 160 + 56 = 216
Therefore the side of cube is = 6 unit
(vol. = 216 cube unit)
No. of cubes without any exposure = (6 – 2)3 = 64
Thus 64 cubes will be inside of the big cube.
Now rest of the cubes = 160 – 64 = 96
Again the no. of cubes with one face outside = 6 × (4 × 4) = 96
Hence the required percentage = \(\frac{96}{216} \times 100 = 44.44\%\)
Choose the best word to fill the blank.
To ensure that Brenda wouldn’t know where we were going for her birthday, I took the most __________ route I could think of.
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Solution
Circuitous (adj.) means having or taking a round about,lengthy, or indirect course.
Choose the best word to fill the blank. Whenever Tom and I would argue he would _______with his hands and body to accentuate his point.
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Solution
To gesticulate (v.) means to use gestures or make motions; express through motion, especially while speaking.
Choose the best word to fill the blank.
Victor Frankenstein’s creature was a(n) _________, detested by everyone he met.
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Solution
An anathema (n) is one who is detested or shunned; one who is cursed or damned; a curse or vehement denunciation; a formal ban, curse, or excommunication.