# SAT Math 1

#### A crate of heart-shaped Valentine's candy boxes have a retail 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.

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 her gross sales for each month are represented as x. She must pay the platform 1/3 of this total along with a flat "storefront" fee of $10 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?

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. 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 added (NOTE: x represents the number of pearls added.)

V=25pi+x(^{5}/_{4}πr^{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)?

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, Sizzling 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?

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.

^{2c2-c-10}/_{c2+7c+10 }= ^{c2-4c+5}/_{c2+2c-9}

In the equation above, what is the value of c?

Easiest option: plug in the numbers. Doing so, you will see that Answer 4 is the only choice that ends with the true statement that 1/3=1/3.

#### Which of the following is equivalent to ^{2z+6}/_{4} * ^{6z-36}/_{3z+9}?

Substitute 2 for the variable and solve.

#### Cindy's babysitting services are charged at $25 per day, plus $7.50 for every 30 minutes. How much has Cindy earned after three hours of babysitting?

Remember $7.50 is every 30 minutes, so that's the equivalent of $45 for the three hours plus the $25 flat fee.

#### Find the sum of r and v in the system of equations below.

20r+10v=100

20v=170-10r

20r+10v=100 20v=170-10r A10r 10r+20v=170 20r+10v=100 + 10r+20v=170 30r+30v=270 D30 r+v=9

#### Karen is building a garden. She started the year cultivating a plot of land with an area of 48 feet. Next year she wants to bump it to an area of 120 feet. This year l and w are 6 and 8 feet, respectively. Next year she will have to increase each side by x feet.

A=lw A=6*8=48 feet A=10*12=120 feet 10-6=4 12-8=4 She will have to increase each side by four feet, answer 1.

#### The number of complaints (C) of business (B) since 1995 can be estimated by the equation C=1.0735x+325, where x is the number of years since 1995 and 0<x<20. In the context of this equation, what does the number 1.0735 most likely represent?

C is the number of complaints. x represents the number of years since 1995, so it can't be Answers 1 and 2. Since the complaints are growing, it can't be Answer 4 either. Process of elimination.

#### If x^{2}+16x=225 and x>0, what is the value of x?

Simply plug in the options. Start with Answer 4 since the sum is a larger number. It will get you to the right answer more quickly.

#### Steve is ordering new display cases for his store. Each case is 8 feet in length and extends from floor to ceiling. His store has 120 feet of wall space that includes 23 feet of windows along the walls. If the display cases cannot be moved in front of the windows, which of these inequalities includes all possible values of d, the number of display cases that could be used?

Answers 2 and 4 can be eliminated right away because they add instead of take away window space. From there, Answer 3 can also be eliminated because you're trying to isolate the value of d.

#### If c^{3}+12c=-112 and c<0, what is the value of c?

Plug in the options. Start with your negatives since the end result is negative. That should help you arrive at Answer 4 on your first or second try.

#### Jack orders a box of pencils for $3 per box. A tax of 9.25% is added to the cost of the pencils before a flat shipping fee of $5 closes out the transaction. Which of the following represents total cost of pencils in dollars?

3p represents the cost of each box times the number of boxes purchased. Multiplying this number times 1.0925 will increase the value by the 9.25%. Then you add the $5 shipping fee for the total.

#### A plant grows at a linear rate. After seven weeks, the plant is 56 centimeters tall. Which function best models the relationship between height (h) and weeks of growth (w)?

7*8 is 56, so we know that 8 will have to be a part of the function. Plug in 7 for w and Answer 2 is your correct answer.

#### Which of the following is equivalent to (15x^{2}+5x+6y)+(4x^{2}-2x+4y)?

Simple addition: add all parts with like signs and you get Answer 2.

#### An advertisement for a toothpaste reads: "Eight out of nine dentists recommend Pearly White Toothpaste for your dental health." No other information is given. Based on what is here, which of the following inferences is most valid?

Answers 1 and 2 are not implied in any way. Just because there is one dentist who didn't recommend (Answer 3), that doesn't mean he feels PWT is inferior. Process of elimination points to Answer 4.

#### In the equation below, what is the value of x?

^{1}/_{2}x+8=^{3}/_{4}x-3

1/2x+8=3/4x-3 A-8 1/2x=3/4x-11 A-2/4, 11 1/4x=11 CROSS-MULTIPLY, and you get 44=x. Check your work by plugging in 44 for x and the two sides will equal one another. Answer 4 is the correct choice.

#### A happy cat enjoys 9.5 to 19 ounces of milk for every 10 pounds of his weight. John has 15- and a 25-pound cats. Which of the following ranges represents the approximate total number of ounces of milk (m) that the two cats need to be happy?

You have about 40 pounds of cat in the word problem. For every 10 of those pounds, you have anywhere from 9.5 to 19 ounces. Multiply both times 4 and you get 38 and 76 ounces on the low and high ends, respectively. Therefore, Answer 1 is correct.

#### Jean is making a dry rub based on a recipe his friend from the United States sent to him, but he needs to convert ounces to grams to understand the recipe. If the rub requires 4 ounces of cayenne for every 7 ounces of paprika and there is 91 total ounces of paprika in the rub, how many total grams of cayenne and paprika are required?

(1 ounce=28.3 grams)

4/7=x/91 CROSS-MULTIPLY 7x=364 D7 x=52 4/7=52/91 These two fractions are equivalent to one another, so we know 52 equals x. Since we're looking for the total grams of both ingredients, it's necessary to add 52 and 91, then multiply the product times 28.3 grams. This gets you to Answer 4 as the correct response.

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