1. If a2 = 12, then a4 =

　　A. 144

　　B. 72

　　C. 36

　　D. 24

　　E. 16

　　2. If n is even, which of the following cannot be odd?

　　I n + 3

　　II 3n

　　III n2 - 1

　　A. I only

　　B. II only

　　C. III only

　　D. I and II only

　　E. I, II and III

　　3. One side of a triangle has length 8 and a second side has length 5. Which of the following could be the area of the triangle?

　　I 24

　　II 20

　　III 5

　　A. I only

　　B. II only

　　C. III only

　　D. II and III only

　　E. I, II and III

　　4. A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 91 pounds?

　　A. 12

　　B. 11

　　C. 10

　　D. 9

　　E. 8

　　5. A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?

　　A. 8p

　　B. pq

　　C. pq + 27

　　D. -p

　　E. (p - q)6

　　6. What is the length of the line segment in the x-y plane with end points at (-2,-2) and (2,3)?

　　A. 3

　　B. √31

　　C. √41

　　D. 7

　　E. 9

　　7. n is an integer chosen at random from the set

　　{5, 7, 9, 11 }

　　p is chosen at random from the set

　　{2, 6, 10, 14, 18}

　　What is the probability that n + p = 23 ?

　　A. 0.1

　　B. 0.2

　　C. 0.25

　　D. 0.3

　　E. 0.4

　　8. A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?

　　A. 0.75D

　　B. 0.76D

　　C. 0.765D

　　D. 0.775D

　　E. 0.805D

　　9. All the dots in the array are 2 units apart vertically and horizontally. What is the length of the longest line segment that can be drawn joining any two points in the array without passing through any other point ?

　　A. 2

　　B. 2√2

　　C. 3

　　D. √10

　　E. √20

　　10. If the radius of the circle with centre O is 7 and the measure of angle AOB is 100, what is the best approximation to the length of arc AB ?

　　A. 9

　　B. 10

　　C. 11

　　D. 12

　　E. 13

　　1.Correct Answer: A

　　Explanation:

　　a4 = a2 x a2 = 12 x 12 = 144

　　2.Correct Answer: B

　　Explanation:

　　In case I , even plus odd will give odd

　　In case II, odd times even will give even

　　In case III even squared is even, and even minus odd is odd.

　　(You can check this by using an easy even number like 2 in place of n)

　　Only case II cannot be odd.

　　3.Correct Answer: D

　　Explanation:

　　The maximum area of the triangle will come when the given sides are placed at right angles. If we take 8 as the base and 5 as the height the area = x 8 x 5 = 20

　　We can alter the angle between the sides to make it less or more than 90, but this will only reduce the area. (Draw it out for yourself). Hence the area can be anything less than or equal to 20.

　　4.Correct Answer: E

　　Explanation:

　　Food consumed per day = 39/6.

　　In the remaining days it will consume 91 - 39 pounds = 52 pounds

　　Now divide the food by the daily consumption to find the number of days

　　52 / (39/6) = 52 x (6 / 39) = 8

　　5.Correct Answer: C

　　Explanation:

　　A perfect cube will have prime factors that are in groups of 3; for example 125 has the prime factors 5 x 5 x 5 , and 64 x 125 will also be a cube because its factors will be 4 x 4 x 4 x 5 x 5 x 5

　　Consider the answer choices in turn.

　　8 is the cube of 2, and p is a cube, and so the product will also be a cube.

　　pq will also be a cube as shown above.

　　pq is a cube and so is 27, but their sum need not be a cube. Consider the case where p =1 and q = 8, the sum of pq and 27 will be 35 which has factors 5 x 7 and is not a cube.

　　-p will be a cube.

　　Since the difference between p and q is raised to the power of 6, this expression will be a cube (with cube root = difference squared).

　　6.Correct Answer: C

　　Explanation:

　　Sketch a diagram and calculate the distance (hypotenuse of a right triangle) using Pythagoras theorem.

　　Vertical height of triangle = 5 ; horizontal side = 4 ; hypotenuse = √(25 + 16) = √41

　　7.Correct Answer: A

　　Explanation:

　　Each of the integers in the first set could be combined with any from the second set, giving a total of 4 x 5 = 20 possible pairs.

　　Of these the combinations that could give a sum of 23 are (5 + 18), and (9 + 14)

　　This means that the probability of getting a sum of 23 is 2/20 = 1/10

　　8.Correct Answer: C

　　Explanation:

　　If the price is reduced by 15 %, then the new price will be 0.85D

　　If this new price is further reduced by 10%, the discounted price will be 0.9 x 0.85D = 0.765D

　　9.Correct Answer: E

　　Explanation:

　　The longest line segment that can be drawn without passing through any dots other than those at the beginning and end of the segment, such a line could go from the middle dot in the top row to either the bottom left or right dot. In any case the segment will be the hypotenuse of a right triangle with sides 2 and 4. Using Pythagoras theorem the hypotenuse will be √(2 2 + 4 2 ) = √20

　　10.Correct Answer: D

　　Explanation:

　　If the radius is 7, the circumference = 14π

　　The length of the arc is 100/360 of the circumference

　　Taking π as 22/7 we get

　　(100 x 14 x 22) / (360 x 7) which reduces to 440/ 36 = 12.22 (i.e. approx. 12)

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