SAT Math Practice Test 0 (module 2)

Elaine and Jayden each have some complete apples in their backpacks. The ratio of their quantities is [math]4:3[/math]. After Elaine gives Jayden [math]k[/math] apples, the ratio of their apples becomes [math]2:7[/math]. Which of the following values could be the initial number of apples Elaine had?

If the equation [math]|x – a| + |x – b| < 12[/math] has no solutions, where [math]a[/math] and [math]b[/math] are integers and [math]a < b[/math], which of the following values cannot be the value of [math]b – a[/math]?

$$f(n)−f(n−2)=f(n+2)−f(n)$$

If the function [math]f[/math] satisfies the property above for all real numbers [math]n[/math], which of the following statements is true?

$$\dfrac{x}{a}+\dfrac{y}{b}=1$$

If [math]a[/math] and [math]b[/math] are nonzero numbers, what is the slope of [math]\ell[/math]?

$$4x+3y=24$$

If [math](x,y)=(2r, 3r)[/math] is a solution to the equation, which of the following is also a solution to the equation?

A gaming company released a new game priced at [math]x[/math] dollars. To increase revenue, the company also launched four DLC side missions, each priced at [math]y[/math] dollars. Usho bought the game along with one DLC, spending 51.6 dollars. Kyle purchased the same game along with four DLCs, spending 59.4 dollars. Since both of them kept recommending the game to Franky, he decided to buy the game along with two DLCs. How much did Franky spend?

A polynomial function [math]f(x)[/math] has three factors: [math](x + 1)[/math], [math](x – 4)[/math], and [math](x + 3)[/math]. If [math]g(x) = f(x + a)[/math], and the y-intercept of [math]g(x)[/math] is 0, where [math]a[/math] is an integer, which of the following could not be the value of [math]a[/math]?

Franky has a 400-gram bag of flour. He took out 50 grams to make a honey cake but discovered 13 flour beetles in it. If the flour beetles are evenly distributed throughout the flour, how many beetles are approximately left in the bag?

Two trucks depart from the same point at the same time to deliver goods. The first truck moves north at a speed of 50 km/h. The second truck moves east at a speed of 20 km/h. After how many hours (integer) will the straight-line distance between the two trucks exceed 120 km?

Figure not drawn to scale

In the figure above, [math]\angle AOB = 60^\circ[/math], and [math]OAB[/math] is a sector with radius 10. Circle [math]C[/math] touches the boundary of sector [math]OAB[/math]. What is the radius of circle [math]C[/math]?

If [math]\dfrac{3x-2}{x^2+x}=\dfrac{a}{x}+\dfrac{b}{x+1}[/math] where [math]a[/math] and [math]b[/math] are constants, what is the value of [math]a + b[/math]?

$$ax^2-2abx+5a=0$$

In the equation above, [math]a[/math] and [math]b[/math] are positive numbers. If the equation has only one solution, what is the value of [math]b[/math]?

In Happy City, 5% of people believe that the mayor takes bribes. A journalist who dislikes the mayor tries to randomly survey people until he finds someone who believes that the mayor takes bribes. He can then use this to hype up the news. What is the probability that this “unbiased” journalist surveys a total of 8 people?

$$f(x)=\sqrt{x}-k$$

In the function above, [math]k[/math] is a positive integer. If the minimum integer solution to the inequality [math]f(n)>0[/math] is [math]n=1776[/math], what is the maximum value of [math]k[/math]?

A geologist measured the pH levels of a lake. The calculated statistics from the original data set were as follows: the mean was [math]-5.7[/math], the median was [math]-5.2[/math], the range was [math]4.2[/math], and the standard deviation was [math]2.3[/math]. Later, the geologist discovered that the measuring device had malfunctioned, causing every recorded value to be multiplied by [math]-1[/math]. After correcting the data, the question is: how many of these four statistics (mean, median, range, and standard deviation) became positive numbers?

Consider a line [math]\ell: 4x+3y=12[/math] and two points [math]P(a,b)[/math] and [math]Q(4,5)[/math]. If [math]P[/math] is on [math]\ell[/math], what is the value of minimum value of [math]a[/math] such that [math]PQ[/math] is minimum?

$$f(x)=x^2-bx-c$$

In the function above, [math]b[/math] and [math]c[/math] are constants. If [math]f(x)[/math] passes through [math](3,0)[/math] and [math](0,\pi)[/math], what is the [math]x[/math]-coordinate of the vertex of [math]f(x)[/math]?

Let [math]a[/math] and [math]b[/math] be two positive number satisfying [math]a^7=b^{11}[/math]. If [math]b\sqrt{a}=a^{m}[/math] where [math]m[/math] is a constant, what is the value of [math]m[/math]?

Consider a rectangle [math]ABCD[/math]. If [math]m\angle CAB=0.4[/math] and [math]AC=2[/math], what is the area of [math]ABCD[/math]?

A product costs [math]p[/math] dollars, and it is originally sold for a profit of 20 dollars. In 2025, however, the product becomes subject to a 20% tariff. To maintain the same profit of 20 dollars, by how much should the selling price increase?

The scatterplot above shows the IQ and corresponding SAT Math scores of 15 students from Happy High School. The line of best fit (dashed line) is given by the equation [math]y = mx + b[/math]. Which of the following statements is correct?

Consider a circle and a square. The radius of the circle is [math]r[/math]. If the circumference of the circle and the perimeter of the square are the same, what is the ratio of the area of the circle to the area of the square?