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1. What is the value of log_{2}(8) + log_{2}(16)?
8
16
7
6
9
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Correct answer is option  3 Explanation: log_{2}(8) can also be written as log_{2}(2^{3}).
Similarly log_{2}(16) can be also written as log_{2}(2^{4}).
According to the logarithm rule we have: log(a^{m}) = m * log(a).
Therefore we get: log_{2}(8) + log_{2}(16) = log_{2}(2^{3}) + log_{2}(2^{4}) ==> 3log_{2}(2) + 4log_{2}(2)
According to the rule: log_{a}(a) = 1.
Hence we get: 3log_{2}(2) + 4log_{2}(2) = 3(1) + 4(1) = 7.
2. In a bookstore, price of a pencil set is onethird the price of a pen set and the price of the pen set is onefifth the price of a book. If the total cost of all the three items is $76, then what is the cost of the pen set?
$3
$76
$4
$12
$60
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Correct answer is option  4 Explanation: Let the price of the book be = $x.
Then the price of a pen set = 1/5 * x = $ (x/5)
Then price of a pencil set = 1/3 * (x/5) = $ (x/15).
Given the total cost of the items = $76.
This gives: x + (x/5) + (x/15) = $76 ==> Now we take ‘15’ as the common denominator.
Hence we get: (15x + 3x + x)/ 15 = $76.
This implies: 19x/ 15 = 76 ==> x = (76 * 15)/ 19 ==> x = $60 = cost of the book!
Therefore the price of the pen set = $ (x/5) = $(60/5) ==> $12.
3. Which of the following is equivalent to the expression, 9x^{4} – y^{8}?
Correct answer is option  3 Explanation: 9x^{4} – y^{8} can also be written as: (3x^{2})^{2} – (y^{4})^{2}.
The reason why we split it in the above way is because we want it to be in the form of (a^{2} – b^{2}) as the expression can be factored as: (a^{2} – b^{2}) = (a + b) (a – b).
Therefore we get: (3x^{2})^{2} – (y^{4})^{2} = (3x^{2} – y^{4}) (3x^{2} + y^{4}).
4. Which of the following is equivalent to the expression, (cotx)/ (csc x)?
sinx/ cosx
1/ sinx
1/ cosx
(cscx) / (cot x)
cos x
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Correct answer is option  5 Explanation: cot(x) is the reciprocal of tan(x) and hence cotx = cosx/ sinx.
Simlarlycscx is the reciprocal of also written as: 1/sinx.
Hence the expression can also be written as: (cotx)/ (csc x) = (cosx/sinx)/ (1/sinx).
Taking the reciprocal of the denominator we get: (cosx) * (sinx)/ sinx.
Cancelling ‘sinx’ we get: (cotx)/ (csc x) = cosx.
5. Marc bought an item of cost $20.00, but the final bill at the billing counter for the item is given as $22.50. What is the sales tax rate on the item?
9%
12%
3%
12.5%
15.5%
Show me the answers!
Correct answer is option  4 Explanation: Original price of the item = $20.00
Final cost of the item = $22.50.
The tax added on the item = $22.50  $20.00 = $2.50
Here the above sales tax is a certain percentage of the original price. Let that certain percentage be = x%.
Then we have: (x/100) * $20.00 = $2.50.
Now solving for ‘x’ we get: x = ($2.50 * 100)/ $20.00 ==> x = 12.5%.
6. If the function f(x) = x^{2} – 9x + 20, then what are the xintercepts for this function?
(0, 4) and (0, 5)
(4, 0) and (5, 0)
(0, 2) and (10, 0)
(2, 0) and (10, 0)
(0, 4) and (0, 5)
Show me the answers!
Correct answer is option  2 Explanation: In order to find the xintercepts of any function, we should set the ‘y’ value or the f(x) = 0 since they are the points where the function cuts the Xaxis.
Hence the function f(x) = 0 which implies ==>x^{2} – 9x + 20 = 0.
We can factor the above quadratic function as: (x – 4) (x – 5) = 0.
This gives: (x – 4) = 0 ==> x = 4 and (x – 5) = 0 ==> x = 5.
Hence the xintercept points are: (4, 0) and (5, 0).
7. What is the simplified form of the expression: 8 – 4[3 – 2(8 – 6)] ÷ 2?
6
7
8
9
10
Show me the answers!
Correct answer is option  5 Explanation: Here in the given numerical expression, we have to consider the order of operations and calculate the value accordingly.First we start with parenthesis and the priority goes with multiplication or division, and then goes to addition or subtraction. This gives: 8 – 4[3 – 2(2)] ÷ 2 ==> 8 – 4[3 – 4] ÷ 2
This implies: 8 – 4[1] ÷ 2 ==> 8 + 4 ÷ 2 ==> Here we first divide 4 by 2 and then proceed further to addition due to its priority ==> 8 + 2 = 10.
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