PWN Test Prep SAT Q&A

difference between x6 and x3, in terms of y ?

If x^3 = y, then square both sides to get x^6 = y^2.

From there, we find the difference between x^6 and x^3 by subtracting: x^6 - x^3. Then we just substitute:

When a line passes through the origin, all of the points on the line (other than the origin) tell you the slope. So the answer here is 3/8. 

Think of it this way. You can calculate the slope using the two points you know: (0, 0) and (8, 3). Use the slope formula: 

(3 – 0)/(8 – 0) = 3/8

That same slope must apply for any other point on the line, like (a, b):

You can’t solve this to precisely one number, but you can identify a number of integer solution sets. If this were a real test question it would be worded to say something like “which of the following could be the number of students this year?” 

Let’s say the class had b boys and g girls last year. 

This year, there’s one more kid in the class, so the total should be b + g + 1. 

We also know, however, that the numbers of boys and girls changed: this year there are (1 + 0.2)b boys and (1 – 0.2)g girls.

We can set those two expressions equal and simplify.

b + g + 1 = (1 + 0.2)b + (1 – 0.2)g b + g + 1 = 1.2b + 0.8g 1 = 0.2b – 0.2g 5 = b – g

That’s as far as you can get, so now you’re just left with possible sets that can work. For example, there could have been 15 boys and 10 girls last year, which would mean there are b + g + 1 = 26 students this year.

It’s easier to figure out the probability of the sum being 5 or less, and then you can subtract that from 1 to find the answer you actually want. 

To get 5 or less, you can only have these two pulls:

1, 1 1, 2 1, 3 1, 4 2, 1 2, 2 2, 3 3, 1 3, 2 4, 1

That’s 10 possible outcomes of 5 or less. Out of how many total outcomes? 

Well, you have 10 possible numbers to select, and you’re selecting with replacement, so there are 10*10 = 100 outcomes. 

Just do trial and error here. 

2^2 = 4, there’s only one integer between 2 and 4.

I think you mean in a CUBIC foot--you can’t compare cubic inches to feet diresctly.

If three bags cost m cents, then each bag costs one third of that: m/3. 

This is a right triangle question. The hypotenuse is 15 and the leg on the ground is 4.75. What’s the other leg? 

The x-intercepts tell you the factors, and because the leading term (x^3) has a coefficient of 1 you know there are no constants being multiplied through the whole thing. So you know the factored version of the equation is:

y = (x + 4)(x + 5)(x + 7)

Multiply that out.

y = (x^2 + 9x + 20)(x + 7) y = x^3 + 9x^2 + 20x + 7x^2 + 63x + 140 y = x^3 + 16x^2 + 83x + 140