SAT Math 1

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.

Accepted Answer

8%</label></li>

Answer

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).

Accepted Answer

y=5(x-4)²-4

Answer

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?

Accepted Answer

2/3x-10</label></li>

Answer

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

Accepted Answer

y=-3.5x+4</label></li>

Answer

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?

Accepted Answer

16</label></li>

Answer

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.

SAT Practice Test

SAT Practice Test

SAT Math 1