# SAT Math 1

#### A crate of heart-shaped Valentine's candy boxes have a retailÂ price of x dollars. The sales tax is a percentage of retail price. A teacher wants to buy the entire crate for her class. Doing so will require an untaxed flat fee deposit. The total amount paid at purchase time for one crate is shown through the expression 1.08x+18. Find the sales tax expressed as a percentage.Â

The deposit is described as an untaxed flat fee, so that would mean 18 would have to represent it in the equation. If x=100, then 1.08x would equal 108. 108+18=126, but since the 18 is a deposit and the 100 is the retail price, that leaves a remainder of 8, which would have to represent the tax. $8 is eight percent of 100, thus making Answer 4 the only correct choice.

#### Pick the equation with a vertex of (4, -4).

Vertex form of a parabola equation: y=a(x-h)2+k, where (h,k) is the vertex. Plug 4 into the h slot and -4 slot, and Answer 3 will be the only correct choice.

#### Marsha is a power seller on eBay and herÂ gross sales for eachÂ month are represented as x. She must pay the platform 1/3 of this totalÂ along with a flat "storefront" fee of $10Â per month. Which equation below represents her final sales after all fees?

The fraction 1/3 would not be part of any correct answer since the equation represents the final sales of Marsha, so you can eliminate answers 2 and 3 right away. That leaves Answers 1 and 4. Since the parentheses in Answer 4 would mean that you would need to multiply both figures by the fraction, that cannot be correct either. Answer 1 is the only correct answer.

#### What is the equation of a line that has a point (2,-3) and a y-intercept of 4

All the selections utilize slope-intercept y=mx+b where b is y-intercept and x,y are points on line. Answers 2 and 4 produce the wrong results for y when you plug in x. Answer 1 has a y-intercept of -4 instead of 4. This leaves only Answer 3 as the correct choice.

#### The buyers club rewards for a department store card are represented through the function C(r)=4r+12, where r represents the number of purchases made with the store card. If you increase the number of purchases by 4, by how much would you increase the total rewards?Â

For this answer, start by choosing any number. We'll pick 2. 4(2)+12 or 8+12=20. Now increase 2 by 4. 4(6)+12 or 24+12=36. Now subtract 20 from 36 and you're left with 16. Answer 2 is the only correct choice.

#### Cindy finds that adding pearls of identical size into a graduated cylinder will change the total fluid volume each time.Â She has found that the following equation will give her the total fluid inside the cylinder in cubic centimeters regardless of how many pearls are addedÂ (NOTE:Â x represents the number of pearls added.)

V=25pi+x(^{5}/_{4}Ï€r^{3})

If the total volume is 185pi cubic centimeters, what is the maximum number of pearls with a radius of 4 centimeters that can be added so that the fluid does not exceed the cylinder size?

Plug in the answer choices to x and 4 for radius, and you will find that Answer 1 is the only answer that can be plugged into the equation at x where the equation checks out.

#### If a is two more than a third of b, which of the following equations accurately gives the value of b in terms of a?

The easiest thing to do is to first use the word problem to tell you what a is. Doing so, you will see that a=1/3b+2. Multiply both sides of the equation by 3 (the inverse of the fraction) and that will leave you with 3a=b+6. Add -6 to both sides, and you're at 3a-6=b. From the four answers listed, Answer 2 is the only response that equation can be derived from.

#### A blender's rotation rate slows down the more liquid that is added to it. From empty, it goes at around 1,275 rotations per second. The slowdown rate is three rotations per second less than four times the liquid's square height (represented as h). Which of the following equations best represents the appliance's rotation rate B(h)?Â

1,275 represents the starting rotation rate. That will have to be reflected, so you can remove Answer 1. A closer reading of the question will dismiss Answers 2 and 3. Answer 4 is the only one to reflect 1,275 as the starting rotation as well as the reduction in speed -- 3 less (-3) than four times the liquid's square height (4h2), or -3+4h2, which is the same as saying 4h2-3.

#### A condiment company has produced a new 32-ounce bottle mixing their two most famous flavors, SizzlingÂ Sriracha Sauce and Mayo Must Dijon. The sriracha blend contains 0.26% tabasco as the active ingredient while Mayo Must features 0.38% of honey dijon for a total of .083 ounces of active ingredients. Solving which of the following systems of equations will give you the number of ounces of Sizzling Sriracha Sauce, z, and Mayo Must Dijon, m, that are in the new bottle?Â

Start with the simplest equation to figure out. The bottle is a mix of only two products (z and m) and since it's 32 ounces in volume, you have z+m=32. This eliminates Answer 2 straightaway. As for the other two incorrect answers (3 and 4), they give themselves away by the incorrect percent to decimal conversion, leaving Answer 1 as the best choice.