SAT Math — Module 2 (harder) practice test

The function $h$ is defined by $h(x)=x^2+x+53$. What is the value of $h(3)$?

What is the positive solution to the given equation?

The variables $h$ and $j$ are positive. Which expression is equivalent to $(h^3{j}^{-2})(h^2{j}^6)$?

The function $f$ is defined by $f(x)=4x-7$, and the function $g$ is defined by $g(x)=f(x)+12$. Which equation defines $g$?

Marcus bikes at a speed of 12 miles per hour and drives at a speed of 40 miles per hour. He bikes for $w$ hours and drives for 1 hour, covering a combined total of 124 miles. What is the value of $w$?

At a music school, the ratio of electric guitars to acoustic guitars is 9 to 7. The school has 208 electric and acoustic guitars in all. How many more electric guitars than acoustic guitars does the school have?

How many solutions does the given system of equations have?

A coach recorded the number of push-ups completed by each of five athletes during a fitness test. The table shows the number of push-ups completed by each athlete.

A sixth athlete joins the group and completes 55 push-ups, and this result is included with the original five. How does the mean number of push-ups for all six athletes now compare with the mean for the original five athletes?

The scatterplot shows the mass, in tens of kilograms, of each of six crates and the delivery cost, in dollars, for each crate.

The line of best fit for the data shown has equation $y=42.1+2.6x$. A crate has a mass of 50 kilograms. Based on the line of best fit, what is the predicted delivery cost, in dollars?

In the figure shown, lines $\mathrm{\ell }$ and $m$ are perpendicular and intersect at point $P=(2,5)$. The slope of line $\mathrm{\ell }$ is $-{\displaystyle \frac{3}{4}}$. Which equation represents line $m$?

A robotics club has $30 to spend on gears and belts. The number of gears $g$ and the number of belts $b$ the club can buy are related by

Which combination of gears and belts could the club buy?

The graph shown could represent which of the following functions?

Two right rectangular prisms are similar. The smaller prism has dimensions 6 centimeters by 9 centimeters by 12 centimeters. The surface area of the larger prism is 1,300 square centimeters. What is the volume, in cubic centimeters, of the larger prism?

Triangles $ABC$ and $DEF$ are similar, where $A$ corresponds to $D$, $B$ corresponds to $E$, and $C$ corresponds to $F$. Angle $C$ is a right angle, and the measure of angle $D$ is $34^{\circ }$. What is the measure of angle $E$?

The quantity $x$ increases by $20\mathrm{\%}$ and then decreases by $10\mathrm{\%}$. The final amount is $k\mathrm{\%}$ of the original amount. What is the value of $k$?

The point $(a,b)$ lies on the circle represented by the given equation and satisfies $a+b=6$. What is the greatest possible value of $a$?

In right triangle $QRS$, angle $S$ is a right angle.

Based on the given equation, which of the following is equal to $(\sin Q)(\sin R)+(\cos Q)(\cos R)$?

In the given equation, $p$ is a constant. The equation has no solution. What is the value of $p$?

In the given system of equations, $c$ is a constant. In the $xy$-plane, the graphs of the given equations have exactly one point in common. What is the $x$-coordinate of that point?

For $x\mathrm{\ne }0$, which expression is equivalent to ${\displaystyle \frac{(x+1{)}^4-(x-1{)}^4}{(x+1{)}^2-(x-1{)}^2}}$?

The table shows two values of $x$ and their corresponding values of $h(x)$, where $h(x)={\displaystyle \frac{p(x)+4}{x-1}}$ and $p$ is a linear function. What is the $y$-intercept of the graph of $y=p(x)$?

The function $f$ is defined by $f(x)=a{x}^2+bx+c$, where $a$, $b$, and $c$ are constants. For every value of $x$, $f(x+1)-f(x)=6x+5$. What is the value of $f(2)-f(0)$?