SAT Practice Test 2

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?

Accepted Answer

1.0925(3p)+5

Answer

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)?

Accepted Answer

h(w)=8w</span></label></li>

Answer

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 (15x²+5x+6y)+(4x²-2x+4y)?

Accepted Answer

19x²+3x+10y

Answer

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?

Accepted Answer

Of the dentists surveyed by PWT, the majority recommended it as a way to improve your dental health.

Answer

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?

¹/₂x+8=³/₄x-3

Accepted Answer

44</span></label></li>

Answer

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.