SAT Practice Test 1

Question 1

^2c²-c-10/_c²+7c+10= ^c²-4c+5/_c²+2c-9

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

Accepted Answer

4</label></li>

Answer

To find the value of c, the most straightforward method for multiple-choice questions is to substitute each answer choice into the equation. When c = 4, the left side becomes (2(4)² - 4 - 10) / (4² + 7(4) + 10) = (32 - 4 - 10) / (16 + 28 + 10) = 18 / 54 = 1/3. The right side becomes (4² - 4(4) + 5) / (4² + 2(4) - 9) = (16 - 16 + 5) / (16 + 8 - 9) = 5 / 15 = 1/3. Since both sides are equal when c=4, this is the correct value.

Question 2

Which of the following is equivalent to ^2z+6/₄ * ^6z-36/_3z+9?

Accepted Answer

z-6</label></li>

Answer

To simplify the expression, factor out common terms from each part. The expression becomes [2(z+3)/4] * [6(z-6)/3(z+3)]. We can cancel out the (z+3) terms from the numerator and denominator. Then, simplify the numerical coefficients: (2/4) * (6/3) = (1/2) * 2 = 1. This leaves us with 1 * (z-6), which simplifies to z-6.

Question 3

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?

Accepted Answer

$70.00</label></li>

Answer

Cindy charges a base rate of $25 per day. For the hourly rate, she charges $7.50 for every 30 minutes, which means she charges $15 per hour ($7.50 * 2). For three hours of babysitting, her hourly earnings would be $15/hour * 3 hours = $45. Adding this to her daily base rate, her total earnings are $25 + $45 = $70.00.

Question 4

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

20r+10v=100
20v=170-10r

Accepted Answer

9</label></li>

Answer

First, rearrange the second equation to 10r + 20v = 170. Now we have the system: 20r + 10v = 100 and 10r + 20v = 170. Multiply the first equation by 2 to get 40r + 20v = 200. Subtract the second equation from this new one: (40r - 10r) + (20v - 20v) = (200 - 170), which simplifies to 30r = 30, so r = 1. Substitute r=1 into 20r + 10v = 100 to get 20(1) + 10v = 100, leading to 10v = 80, so v = 8. The sum of r and v is 1 + 8 = 9.

Question 5

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.

Accepted Answer

4 feet</label></li>

Answer

The current garden has dimensions 6 feet by 8 feet, giving an area of 48 square feet. If each side is increased by 'x' feet, the new dimensions will be (6+x) feet and (8+x) feet. The new area is 120 square feet, so (6+x)(8+x) = 120. Expanding this gives x² + 14x + 48 = 120, which simplifies to x² + 14x - 72 = 0. Factoring the quadratic equation yields (x+18)(x-4) = 0. Since 'x' must be a positive length, x = 4 feet.