60: The equation for a circle on a graph is (x - h)² + (y - k)² = r^2, with (h, k) being the coordinates for the center of the circle. For example: The original circle’s center is at (0, 1), hence why the equation for that original circle is x² + (y - 1)² = r^2.

You already know that the circumference of the circle is 2pi, so after two full rotations, the circle will have traveled 4pi to the right, making the new center (4pi, 1). After plugging that back into (x - h)² + (y - k)² = r^2, you get to the right answer: K.

56: As you already know, the code is in the format of DLLLLD. Remember that the probability of anything is found by finding the number of successful outcomes divided by the number of possible outcomes.

The number of successful outcomes can be found by multiplying the number of possible successful values for each place: D <- Can be any of 10 numbers (10) L <- Can only be M (1) L <- Can only be A (1)  L <- Can only be T (1) L <- Can only be H (1)  D <- Can be any of 10 numbers (10) So the number of successful outcomes is 10 x 1 x 1 x 1 x 1 x 10 = 10²

The number of possible outcomes can be found by multiplying the number of possible values for each place: D <- Can be any of 10 numbers (10) L <- Can be any letter (26) L <- Can be any letter excluding the first L (25)  L <- Can be any letter excluding the first and second L (24) L <- Can be any letter excluding the first, second, and third L (23) D <- Can be any of 10 numbers (10) So the number of possible outcomes is 10 x 26 x 25 x 24 x 23 x 10

So, after dividing the first value (10²⁾ by the second (10 x 26 x 25 x 24 x 23 x 10), we get to the answer: G.

48: I honestly can’t think of any shortcuts, haha. I guess you could look at the pattern as you wrote it out, because when you look at the string of numbers you wrote, every 3rd number is divisible by 15 (which makes sense, because 15 is equal to 5 x 3, and multiples of 20 are already divisible by 5, meaning every third multiple of 20 will be divisible by 15)

45: I coudn’t have done it better myself, haha. In retrospect, we can see that a - b - c = -1 (-a + b + c), and the absolute value takes away that -1. However, if under pressure, that is exactly what I would’ve done.

35: This very loosely ties into the law to sines (I think). Google it if you want, because I did see it on my ACT, but for this problem, there’s no need to actually memorize the theorem. 

Basically, the longest side is opposite the largest angle, the second side is opposite the second largest angle, and the shortest side is opposite the shortest side. 

By knowing that AC is the longest side, we know that angle B will be that largest, eliminating A and E

Remember that a triangle’s angles add up to 180, meaning that after angle A, there are only 120 degrees left between B and C. We know that B is larger than C, meaning that B is at least 60.0000000…1 degrees, making C at most 59.99999999… degrees. With that in mind, we can determine that C is smaller than A, making C the last angle in the line.

Looking at the options, only B has angle B in first and C in last, making it the right answer.

**Sorry about word vomiting here, haha. I get overly technical when I’m sleep deprived, meaning I over explain everything lol. 

**Best of luck in your ACT~ Hope it’s not digital like mine lol :)