Algebra

Problem
If $\arcsin (3x - 4y) = 1.571$ and $\arccos (x - y) = 1.047$, what is the value of $x$?

A.   0.5 C.   1.5
B.   1.0 D.   2.0

 

Answer Key

Problem
The digits of a three-digit number are in arithmetic progression. If you divide the number by the sum of its digits, the quotient is 26. If the digits are reversed, the resulting number is 198 more than the original number. Find the sum of all the digits.

A.   9 C.   15
B.   12 D.   18

 

Problem
There are 7 arithmetic means between 3 and 35. What is the sum of all the terms?

A.   133 C.   665
B.   608 D.   171

 

Problem
A boat going upstream takes 1.5 times longer than going the same distance downstream. If the water current in the river is 8 kph, calculate the speed of the boat in still water.

A.   30 kph C.   40 kph
B.   50 kph D.   20 kph

 

Problem
When the polynomial $x^4 + bx^3 + 5x^2 + dx + 6$ is divided by $x - 2$ the remainder is 16. When it is divided by $x + 1$ the remainder is 10. Find the value of constant $d$.

A.   7 C.   -5
B.   -7 D.   5

 

Problem
Determine the percentage uncertainty in the area of a square that is 6.08 ± 0.01 m on a side.

A.   0.27% C.   0.26%
B.   0.25% D.   0.29%

 

Problem
In still water, your small boat averages 8 miles per hour. It takes you the same amount of time to travel 15 miles downstream, with the current, as 9 miles upstream, against the current. What is the rate of water's current?

A.   4 miles/hr C.   2 miles/hr
B.   3 miles/hr D.   5 miles/hr

 

Problem
Given the following equations:

$$ab = 1/8 \qquad ac = 3 \qquad bc = 6$$

Find the value of $a + b + c$.

A.   $12$ C.   $\dfrac{4}{51}$
B.   $\dfrac{7}{16}$ D.   $12.75$

 

Problem
In a fund raising show, a group of philanthropists agreed that the first one to arrive would pay 25¢ to enter, and each later would pay twice as much as the preceding person. The total amount collected from all of them was \$262,143.75. How many of them paid?

Problem
How many terms from the progression 3, 5, 7, 9, ... must be taken in order that their sum will be 2600?

A.   80 C.   50
B.   60 D.   70

 

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