SAT Math 1 — Questions and Answers
Question 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. </span>
- 0.08%</span></label></li>
- 18%</span></label></li>
- 1.08%</span></label></li>
- 8%</span></label></li> (Correct answer)
Correct answer: 8%</span></label></li>
The total amount paid is given by the expression 1.08x + 18. In this expression, 'x' represents the retail price, and the sales tax is applied to this price. The '1.08x' component indicates that the original price (1x) is increased by 0.08x for the tax. Converting 0.08 to a percentage, we multiply by 100, which gives 8%.
Question 2: Pick the equation with a vertex of (4, -4).</span>
- y=5(x+4)<sup>2</sup>-4</span></label></li>
- y=5(x-4)<sup>2</sup>+4</span></label></li>
- y=5(x-4)<sup>2</sup>-4</span></label></li> (Correct answer)
- y=5(x+4)<sup>2</sup>+4</span></label></li>
Correct answer: y=5(x-4)<sup>2</sup>-4</span></label></li>
The standard vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex. Given that the vertex is (4, -4), we substitute h=4 and k=-4 into the formula. This yields y = a(x - 4)^2 - 4. Among the provided options, y=5(x-4)^2-4 is the only equation that correctly matches this vertex form with the specified coordinates.
Question 3: 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?</span>
- 2</sup>/<sub>3</sub>x-10</span></label></li> (Correct answer)
- 1</sup>/<sub>3</sub>(x-10)</span></label></li>
- 1</sup>/<sub>3</sub>x-10</span></label></li>
- 2</sup>/<sub>3</sub>(x-10)</span></label></li>
Correct answer: 2</sup>/<sub>3</sub>x-10</span></label></li>
Marsha's gross sales are 'x'. She must pay the platform 1/3 of this total, which is (1/3)x. Additionally, she pays a flat storefront fee of $10. To find her final sales, we subtract these fees from her gross sales: x - (1/3)x - 10. Combining the 'x' terms, x - (1/3)x simplifies to (2/3)x, resulting in the final sales equation (2/3)x - 10.
Question 4: What is the equation of a line that has a point (2,-3) and a y-intercept of 4</span>
- y=-3.5x-4</span></label></li>
- y=-2x+4</span></label></li>
- y=-3.5x+4</span></label></li> (Correct answer)
- y=x+4</span></label></li>
Correct answer: y=-3.5x+4</span></label></li>
A y-intercept of 4 means the line crosses the y-axis at (0, 4). We are also given the point (2, -3). To find the equation of the line (y = mx + b), first calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1) = (4 - (-3)) / (0 - 2) = 7 / -2 = -3.5. Since the y-intercept (b) is 4, the equation of the line is y = -3.5x + 4.
Question 5: 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? </span>
- 12</span></label></li>
- 16</span></label></li> (Correct answer)
- 19</span></label></li>
- 23</span></label></li>
Correct answer: 16</span></label></li>
The function C(r) = 4r + 12 indicates that the total rewards (C) increase by 4 for every unit increase in the number of purchases (r). If the number of purchases increases by 4, the total rewards will increase by 4 times that increment. Therefore, the increase in total rewards is 4 * 4 = 16.
Question 6: 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.)<br /><br />V=25pi+x(<sup>5</sup>/<sub>4</sub><span style="font-family: symbol;">π</span>r<sup>3</sup>)<br /><br />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?</span>
- 2</span></label></li> (Correct answer)
- 3</span></label></li>
- 4</span></label></li>
- 5</span></label></li>
Correct answer: 2</span></label></li>
First, substitute the given values into the equation: 185π = 25π + x(5/4 * π * 4^3). Simplify the pearl volume term: 4^3 is 64, so (5/4 * π * 64) becomes (5 * π * 16), which is 80π. The equation is now 185π = 25π + x(80π). Subtract 25π from both sides: 160π = x(80π). Finally, divide by 80π to solve for x: x = 160π / 80π = 2. Thus, a maximum of 2 pearls can be added.
Question 7: 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?</span>
- b=a-<sup>2</sup>/<sub>3</sub></span></label></li>
- b=3(a-2)</span></label></li> (Correct answer)
- b=a+<sup>2</sup>/<sub>3</sub></span></label></li>
- b=3(a+6)</span></label></li>
Correct answer: b=3(a-2)</span></label></li>
First, translate the statement into an algebraic equation: "a is" means a =; "two more than" means + 2; "a third of b" means (1/3)b. So, the equation is a = (1/3)b + 2. To solve for b, subtract 2 from both sides: a - 2 = (1/3)b. Then, multiply both sides by 3: 3(a - 2) = b.
Question 8: 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)? </span>
- 3-4h<sup>2</sup></span></label></li>
- 1,275-(4-12h)</span></label></li>
- 1,275-(12h-3)</span></label></li>
- 1,275-(4h<sup>2</sup>-3)</span></label></li> (Correct answer)
Correct answer: 1,275-(4h<sup>2</sup>-3)</span></label></li>
The base rotation rate of the blender is 1,275 rotations per second. The slowdown rate needs to be subtracted from this base rate. The slowdown is described as "three rotations per second less than four times the liquid's square height (h)." Four times the liquid's square height is 4h^2. "Three less than" this amount is expressed as 4h^2 - 3. Therefore, the appliance's rotation rate B(h) is the base rate minus the slowdown: 1,275 - (4h^2 - 3).
Question 9: 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? </span>
- z+m=32<br />0.0026z+0.0038m=0.083</span></label></li> (Correct answer)
- z+m=0.083<br />0.0026z+0.0038m=32</span></label></li>
- z+m=32<br />0.26z+0.38m=0.083</span></label></li>
- z+m=32<br />0.026z+0.38m=0.083</span></label></li>
Correct answer: z+m=32<br />0.0026z+0.0038m=0.083</span></label></li>
The first equation represents the total volume of the mixture: the sum of the ounces of Sizzling Sriracha Sauce (z) and Mayo Must Dijon (m) must equal the total bottle size of 32 ounces, so z + m = 32. The second equation represents the total active ingredients: 0.26% of z is 0.0026z, and 0.38% of m is 0.0038m. Their sum must equal the total active ingredients, 0.083 ounces, leading to 0.0026z + 0.0038m = 0.083.
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.Â