SAT Practice Test 2 — Questions and Answers
Question 1: 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?</span>
- 0.0925(3p+5)</span></label></li>
- 1.0925(3+5)p</span></label></li>
- 1.0925(3p)+5</span></label></li> (Correct answer)
- 1.0925(3+p)+5</span></label></li>
Correct answer: 1.0925(3p)+5</span></label></li>
First, the cost of 'p' boxes of pencils is 3p dollars. A 9.25% tax is added to this cost, meaning the cost becomes 100% + 9.25% = 109.25% of 3p. This is represented as 1.0925 * (3p). Finally, a flat shipping fee of $5 is added to this taxed amount. Therefore, the total cost is 1.0925(3p) + 5.
Question 2: 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)? </span>
- h(w)=7w</span></label></li>
- h(w)=8w</span></label></li> (Correct answer)
- h(w)=56w</span></label></li>
- h(w)=56+w</span></label></li>
Correct answer: h(w)=8w</span></label></li>
Since the plant grows at a linear rate, the relationship between height (h) and weeks (w) can be modeled by h(w) = mw + b. Assuming the plant starts at 0 height, b=0, so h(w) = mw. We are given that after 7 weeks (w=7), the height is 56 cm (h=56). Plugging these values into the function: 56 = m * 7. Dividing both sides by 7 gives m = 8. Thus, the function that best models the relationship is h(w) = 8w.
Question 3: Which of the following is equivalent to (15x<sup>2</sup>+5x+6y)+(4x<sup>2</sup>-2x+4y)? </span>
- 3x<sup>2</sup>-2x+4y</span></label></li>
- 19x<sup>2</sup>+3x+10y</span></label></li> (Correct answer)
- 19x<sup>2</sup>-3x+10y</span></label></li>
- 19x<sup>2</sup>+3x-10y</span></label></li>
Correct answer: 19x<sup>2</sup>+3x+10y</span></label></li>
To simplify the expression, combine like terms. First, combine the x² terms: 15x² + 4x² = 19x². Next, combine the x terms: 5x - 2x = 3x. Finally, combine the y terms: 6y + 4y = 10y. Putting these together, the simplified expression is 19x² + 3x + 10y.
Question 4: 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?</span>
- Your teeth will be guaranteed stronger if you use PWT.</span></label></li>
- If you do not use PWT, your teeth will eventually fall out.</span></label></li>
- Only one dentist feels PWT is an inferior product.</span></label></li>
- Of the dentists surveyed by PWT, the majority recommended it as a way to improve your dental health.</span></label></li> (Correct answer)
Correct answer: Of the dentists surveyed by PWT, the majority recommended it as a way to improve your dental health.</span></label></li>
The advertisement states that 'Eight out of nine dentists recommend Pearly White Toothpaste.' This is a specific statistic from a likely limited survey. The most valid inference is that among the dentists who were surveyed, the majority (8 out of 9) recommended the toothpaste. The statement does not provide enough information to guarantee stronger teeth, imply negative consequences for not using it, or definitively state the opinions of all other dentists.
Question 5: In the equation below, what is the value of x? <br /><br /><sup>1</sup>/<sub>2</sub>x+8=<sup>3</sup>/<sub>4</sub>x-3</span>
- 5</span></label></li>
- 10</span></label></li>
- 18</span></label></li>
- 44</span></label></li> (Correct answer)
Correct answer: 44</span></label></li>
To solve for x, first gather all x terms on one side and constants on the other. Subtract (1/2)x from both sides: 8 = (3/4)x - (1/2)x - 3. Convert (1/2)x to (2/4)x, so 8 = (3/4)x - (2/4)x - 3, which simplifies to 8 = (1/4)x - 3. Now, add 3 to both sides: 11 = (1/4)x. Finally, multiply both sides by 4 to isolate x: x = 11 * 4 = 44.
Question 6: 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?</span>
- 38<span style="text-decoration: underline;"><</span>m<span style="text-decoration: underline;"><</span>76</span></label></li> (Correct answer)
- 29<span style="text-decoration: underline;"><</span>m<span style="text-decoration: underline;"><</span>48</span></label></li>
- 380<span style="text-decoration: underline;"><</span>m<span style="text-decoration: underline;"><</span>760</span></label></li>
- 760<span style="text-decoration: underline;"><</span>m<span style="text-decoration: underline;"><</span>1,520</span></label></li>
Correct answer: 38<span style="text-decoration: underline;"><</span>m<span style="text-decoration: underline;"><</span>76</span></label></li>
First, calculate the total weight of the two cats: 15 lbs + 25 lbs = 40 lbs. The milk requirement is 9.5 to 19 ounces per 10 pounds. For 40 pounds, this means multiplying the range by 4 (since 40/10 = 4). The minimum milk needed is 9.5 ounces/10lbs * 40 lbs = 38 ounces. The maximum milk needed is 19 ounces/10lbs * 40 lbs = 76 ounces. Therefore, the total number of ounces of milk (m) needed is in the range 38 < m < 76.
Question 7: 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?<br /><br />(1 ounce=28.3 grams)</span>
- 5,148 grams</span></label></li>
- 4,926 grams</span></label></li>
- 4,522 grams</span></label></li>
- 4,047 grams</span></label></li> (Correct answer)
Correct answer: 4,047 grams</span></label></li>
The ratio of cayenne to paprika is 4:7. If there are 91 ounces of paprika, we can find the amount of cayenne using the proportion 4/7 = cayenne/91, which gives cayenne = (4 * 91) / 7 = 52 ounces. The total ounces of rub is 52 ounces (cayenne) + 91 ounces (paprika) = 143 ounces. To convert this to grams, multiply by the conversion factor: 143 ounces * 28.3 grams/ounce = 4046.9 grams. Rounded to the nearest whole number, this is 4047 grams.
Question 8: It's Presidential election season and a high school is holding a site-wide mock election. Here's how the students voted by grade. <br />10th Grade CLINTON .61 TRUMP .31 OTHER .08 TOTAL 1.00<br />11th Grade CLINTON .49 TRUMP .49 OTHER .02 TOTAL 1.00<br />12th Grade CLINTON .42 TRUMP .53 OTHER .05 TOTAL 1.00<br />Total CLINTON .50 TRUMP .44 OTHER .06 TOTAL 1.00<br /><br />723 students voted for Hillary Clinton. Approximately how many students attend this school?</span>
- 1,346</span></label></li>
- 1,446</span></label></li> (Correct answer)
- 1,546</span></label></li>
- 1,646</span></label></li>
Correct answer: 1,446</span></label></li>
The table shows that Hillary Clinton received 0.50 (or 50%) of the total votes across all grades. If 723 students voted for Hillary Clinton, and this represents 50% of the total student votes, then the total number of students who voted can be found by dividing 723 by 0.50. So, 723 / 0.50 = 1446. This means approximately 1,446 students attend this school, assuming the total percentage refers to the total student population.
Question 9: John is traveling to Ghana, where the Cedi is the monetary unit for purchasing goods and services. He decides to buy travelers checks, which he can then use as cash at any retail location. He pays $29.60 (a 7% fee) for the travelers checks on the total purchase, which equals 600 Cedi. If he is at a trading post and decides to trade a personal possession valued at $4500 USD, how many Cedi is the item worth at the same exchange rate? </span>
- 3,385 Cedi</span></label></li>
- 4,385 Cedi</span></label></li>
- 5,385 Cedi</span></label></li>
- 6,385 Cedi</span></label></li> (Correct answer)
Correct answer: 6,385 Cedi</span></label></li>
First, determine the total USD value of the travelers checks before the fee. If $29.60 is a 7% fee, then $29.60 = 0.07 * Total_Purchase_USD, so Total_Purchase_USD = $29.60 / 0.07 ≈ $422.86. This $422.86 USD is equivalent to 600 Cedi. Now, establish the exchange rate: 600 Cedi / $422.86 USD ≈ 1.4189 Cedi/USD. To find the Cedi value of $4500 USD, multiply $4500 by this exchange rate: $4500 * 1.4189 Cedi/USD ≈ 6385.05 Cedi. Rounded to the nearest whole number, the item is worth 6,385 Cedi.
SAT Practice Test 2
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?