SAT Practice Test 1 — Questions and Answers
Question 1: <sup>2c<sup>2</sup>-c-10</sup>/<sub>c<sup>2</sup>+7c+10 </sub>= <sup>c<sup>2</sup>-4c+5</sup>/<sub>c<sup>2</sup>+2c-9</sub><br /><br />In the equation above, what is the value of c?</span>
- -3</span></label></li>
- 3</span></label></li>
- -2</span></label></li>
- 4</span></label></li> (Correct answer)
Correct answer: 4</span></label></li>
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 <sup>2z+6</sup>/<sub>4</sub> * <sup>6z-36</sup>/<sub>3z+9</sub>?</span>
- z-<sup>6</sup>/<sub>4</sub></span></label></li>
- <sup>8z-32</sup>/<sub>3z+15</sub></span></label></li>
- z-6</span></label></li> (Correct answer)
- <sup>12z<sup>2</sup>-216</sup>/<sub>12z+36</sub></span></label></li>
Correct answer: z-6</span></label></li>
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? </span>
- $32.50</span></label></li>
- $40.00</span></label></li>
- $55.00</span></label></li>
- $70.00</span></label></li> (Correct answer)
Correct answer: $70.00</span></label></li>
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. <br /><br />20r+10v=100<br />20v=170-10r</span>
- <sup>1</sup>/<sub>9</sub></span></label></li>
- 9</span></label></li> (Correct answer)
- 3.67</span></label></li>
- 12</span></label></li>
Correct answer: 9</span></label></li>
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. </span>
- 4 feet</span></label></li> (Correct answer)
- 5 feet</span></label></li>
- 6 feet </span></label></li>
- 7 feet</span></label></li>
Correct answer: 4 feet</span></label></li>
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.
Question 6: 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<span style="text-decoration: underline;"><</span>x<span style="text-decoration: underline;"><</span>20. In the context of this equation, what does the number 1.0735 most likely represent? </span>
- The estimated complaints received in 1995. </span></label></li>
- The estimated complaints received in 2015. </span></label></li>
- The factor by which complaints increase each year for business B. </span></label></li> (Correct answer)
- The factor by which complaints decrease each year for business B. </span></label></li>
Correct answer: The factor by which complaints increase each year for business B. </span></label></li>
The equation C = 1.0735x + 325 is a linear equation in the form y = mx + b, where 'm' is the slope. In this context, 'C' represents the number of complaints and 'x' represents the number of years since 1995. The coefficient 1.0735 is the slope, which indicates the rate of change of complaints per year. Since it's a positive value, it represents the estimated increase in complaints each year.
Question 7: If x<sup>2</sup>+16x=225 and x>0, what is the value of x? </span>
- 3</span></label></li>
- 5</span></label></li>
- 7</span></label></li>
- 9</span></label></li> (Correct answer)
Correct answer: 9</span></label></li>
To solve the quadratic equation x² + 16x = 225, first set it to zero: x² + 16x - 225 = 0. We can factor this equation by finding two numbers that multiply to -225 and add to 16, which are 25 and -9. So, (x + 25)(x - 9) = 0. This gives two possible solutions: x = -25 or x = 9. Since the problem states that x > 0, the correct value for x is 9.
Question 8: 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?</span>
- d<span style="text-decoration: underline;"><</span>120-<sup>23</sup>/<sub>8</sub></span></label></li> (Correct answer)
- d<span style="text-decoration: underline;">></span>120+<sup>23</sup>/<sub>8</sub></span></label></li>
- d<span style="text-decoration: underline;"><</span>120-23+8d</span></label></li>
- d<span style="text-decoration: underline;"><</span>120+23-8d</span></label></li>
Correct answer: d<span style="text-decoration: underline;"><</span>120-<sup>23</sup>/<sub>8</sub></span></label></li>
The total usable wall space for display cases is the total wall space minus the window space: 120 feet - 23 feet = 97 feet. Each display case is 8 feet long. To find the maximum number of display cases (d) that can fit, divide the usable wall space by the length of one case: d ≤ 97 / 8. This simplifies to d ≤ 12.125. The inequality d < (120 - 23) / 8 correctly represents that the number of cases must be less than or equal to the total available length divided by the length per case.
Question 9: If c<sup>3</sup>+12c=-112 and c<0, what is the value of c?</span>
- -2</span></label></li>
- 0</span></label></li>
- 2</span></label></li>
- -4</span></label></li> (Correct answer)
Correct answer: -4</span></label></li>
To solve the equation c³ + 12c = -112, rearrange it to c³ + 12c + 112 = 0. Since the problem states c < 0, we can test negative integer values. By substituting c = -4, we get (-4)³ + 12(-4) + 112 = -64 - 48 + 112 = -112 + 112 = 0. Since c = -4 satisfies the equation and the condition c < 0, it is the correct value.
SAT Practice Test 1
2c2-c-10/c2+7c+10 = c2-4c+5/c2+2c-9
In the equation above, what is the value of c?