1. Of the following, which is greater than ½ ?
2. If an object travels at five feet per second, how many feet does it travel in one hour?
3. What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive?
4. A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long?
5. In a class of 78 students 41 are taking French, 22 are taking German and 9 students are taking both French and German. How many students are not enrolled in either course?
6. If f(x) = │(x² – 50)│, what is the value of f(-5) ?
7. ( √2 - √3 )² =
A. 5 - 2√6
B. 5 - √6
C. 1 - 2√6
D. 1 - √2
8. 230 + 230 + 230 + 230 =
9. Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?
10. In the figure above AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC ?
1.Correct Answer: B
One way to deal with fractions is to convert them all to decimals. (Using your calculator, divide the numerator by the denominator).
In this case all you would need to do is to see which is greater than 0.5.
Otherwise to see which is greater than ?, double the numerator and see if the result is greater than the denominator. In B, the correct answer, doubling the numerator gives us 8, which is bigger than 7.
2.Correct Answer: E
If an object travels at 5 feet per second it covers 5x60 feet in one minute, and 5x60x60 feet in one hour. Answer = 18000 (E)
3.Correct Answer: C
You could add up all the multiples of 10 (10 + 20 + 30 ....+190), and divide by the number of terms (19). Or you could realize that the average of an evenly spaced series of numbers is equal to the value of the middle term (or the average of the two middle terms if there are an even number of terms). The middle term out of 19 is the tenth term in the series = 100.
4.Correct Answer: A
If you double the sides of a cube, the ratio of the surface areas of the old and new cubes will be 1: 4. The ratio of the volumes of the old and new cubes will be 1: 8.
Weight is proportional to volume. So, If the first weighs 6 pounds, the second weighs 6x8 pounds =48.
5.Correct Answer: C
You could solve this by drawing a Venn diagram. A simpler way is to realize that you can subtract the number of students taking both languages from the numbers taking French to find the number taking only French. Likewise find those taking only German. Then we have:Total = only French + only German + both + neither
78 = (41-9) + (22-9) + 9 + neither.
Not enrolled students = 24
6.Correct Answer: B
If x = -5, then (x² – 50) = 25 – 50 = -25
But the sign │x│ means the absolute value of x (the distance between the number and zero on the number line). Absolute values are always positive.
│-25 │ = 25
7.Correct Answer: A
Expand as for (a + b)2.
(√2 - √3)(√2 - √3) = 2 - 2(√2 + √3) + 3 = 5 - 2 √6
8.Correct Answer: C
All four terms are identical therefore we have 4 (230).
But 4 = 22, and so we can write 22. 230
Which is equivalent to 232
9.Correct Answer: B
Amy can travel clockwise or anticlockwise on the diagram.
Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.
Similarly, anticlockwise she has four different routes.
Total routes = 8
10.Correct Answer: D
If we take AE as the base of triangle AEC, then the height is CD.
The height of the triangle is therefore, 9 (given).
To find the base we need to see that triangles AEB and CDE are similar. The ratio AB: CD, is therefore equal to the ratio AE: ED. The given information shows that the ratio is 3:9, or 1:3. Now dividing AD (4) in this ratio gives us AE as 1.
The area of AEC = ½ base x height
=1/2 x 9 = 4.5
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