Time Trial 2
1. A
This requires a system of equations. The first equation is generally x+y = a smaller total, and the second equation is the associated values for x and y added together to equal a larger total. Note in this equation that you are solving for y, so eliminate x and solve for y.
2. C
A geometric sequence is a series of numbers that gets multiplied by a constant value. The constant value in this sequence is (-5), so calculate the first 6 terms (the first three are given), and add them up.
3. A
This problem is a trick. Taking an absolute value of a number is another way to state how far away a number is from zero, but it is not possible to have a negative distance from zero. This means that an absolute value equation must always either be equal or greater than zero, so there is “No Solution” to this problem.
4. C
First, to get rid of the negative sign from the exponent outside of the parenthesis, you must flip the numerator and the denominator. Then to eliminate the exponent, square what is inside the parenthesis, and remember that squaring a number/variable with an exponent means multiplying the exponent by two. Lastly, cancel out any common terms between the numerator and denominator. Note, that negative exponents must be moved to the opposite side of a fraction. In doing so, they become positive.
5. E
When given a ratio, create an equation with x’s. Remember that the ratio represents parts. Consequently, 5x + 3x = 48,000. 8x = 48,000. Divide both sides by 8, and x = 6,000. Since the question asked for the winner’s total, multiply 6,000 by 5. The final answer is 30,000 votes.
6. B
When two numbers have exponents and their bases (in this case the bases are 5 and 25) are equal, then you can also set the exponents equal to each other. 25 is another way to say 5 to the second power, so with the term with 25 in it, change 25 to 5 and distribute 2 to the exponent to get 2x – 8. Once the bases are the same, set the exponents equal to each other and solve for x.
7. B
Substitute the quantity (a + b) wherever x is present on the right side of the equation. In this case, you must first square the quantity (a + b), then multiply the result by 5 (distribution).
8. B
Let’s call the first integer n. To get the number after n and then the number after that one, we must add 1 to get the number right after n and then add 1 again to get the number after that one, so we have the terms n, n + 1, and n + 2. Add up these terms to get 3n + 3, then set it equal to 66, then solve for n. 3n + 3 = 66. Subtract 3 from both sides: 3n = 63. Divide both sides by 3: n = 21.
9. C
Simply plug in the values given to the expression given and solve, but remember that any number to the zero power is always equal to 1.
10. C
To take the mean (also known as the average), simply just add up all of the given terms, and then divide by the amount of numbers you added up, in this case, divide the total sum by 8.
11. B
Similar to problem 4, cancel out any common terms between the numerator and the denominator. Remember that 24/36 can be simplified to 2/3.
12. D
Simply plug in the values given into the given equation. Remember that taking a square root generally.yields both a positive and negative square root. Both numbers, once squared, yield the same positive number.
13. A
Simply multiply $85 by 1.08.
The mean, x, is found by adding up 2, 2, 9, 4, 3, 5, 1, 8, and 0, and dividing the sum by 9, which is 3.8. The median, y, is found by finding the middle number of the data set, which is 3. Since the mean is greater than the median, x > y.
14. A
Note that the radical is looking for the fourth root. Square roots can be written as fractional exponents. The number outside of the radical becomes the denominator, and the exponents within the radical become the numerator. In this case, the x is raised to the power of ¾, and the y is raised to the power of 8/4, which simplifies to y2.
15. D
To make this fraction expression undefined, the denominator must equal 0. To find when the denominator equals zero, first set up an equation with x2 – x – 2 on one side and 0 on the other. Factoring x2 – x – 2 is required, and you should get (x + 1)(x + 2) equals 0. Set the two quantities equal to 0 to get x = -1 and x = 2.