Practice ACT - Math - MC5

Poslední aktualizace 4 months ago

45 Dotazy

Poznámka od autora:

Instrukce

IES

Practice ACT - Math - MC5

Poslední aktualizace 4 months ago

45 Dotazy

Poznámka od autora:

MATHEMATICS TEST

50 Minutes—45 Questions

DIRECTIONS: Solve each problem, choose the correct answer, and then fill in the corresponding oval on your answer document.

Do not linger over problems that take too much time. Solve as many as you can; then return to the others in the time you have left for this test.

You are permitted to use a calculator on this test. You may use your calculator for any problems you choose, but some of the problems may best be done without using a calculator.

Note: Unless otherwise stated, all of the following should be assumed.

1. Illustrative figures are not necessarily drawn to scale.

2. Geometric figures lie in a plane.

3. The word “line” indicates a straight line.

4. The word “average” indicates the arithmetic mean.

Instrukce

MATHEMATICS TEST

50 Minutes—45 Questions

DIRECTIONS: Solve each problem, choose the correct answer, and then fill in the corresponding oval on your answer document.

Do not linger over problems that take too much time. Solve as many as you can; then return to the others in the time you have left for this test.

You are permitted to use a calculator on this test. You may use your calculator for any problems you choose, but some of the problems may best be done without using a calculator.

Note: Unless otherwise stated, all of the following should be assumed.

1. Illustrative figures are not necessarily drawn to scale.

2. Geometric figures lie in a plane.

3. The word “line” indicates a straight line.

4. The word “average” indicates the arithmetic mean.

Venn diagram below shows the distribution of the number of athletes competing in each jumping event.

At a college track meet, there are 3 jumping events: high jump, long jump, and triple jump. The Venn diagram below shows the distribution of the number of athletes competing in each jumping event. How many athletes are competing in both high jump and triple jump but not long jump?

A function, $f$, is defined by the equation $f(x) = x^2 + 5$. What is $f(3) + 1$?

Given $b = 40$ and $c = -16$, $b + c$ is equal to the product of $-4$ and what number?

$-14$

$-6$

IES

It takes Collin 24 minutes to walk to school in the morning. What fraction of his 24-hour day is spent walking to school in the morning?

$\dfrac{1}{60}$

$\dfrac{1}{24}$

$\dfrac{1}{12}$

$\dfrac{1}{1{,}440}$

A certain triangle has interior angle measures of $(6x)^\circ$, $(2x)^\circ$, and $x^\circ$. What is the value of $x$?

IES

Which of the following matrices is equal to $6\begin{bmatrix}-5 & 3 \\ 0 & -4\end{bmatrix}$?

$\begin{bmatrix}-30 & -6\end{bmatrix}$

$\begin{bmatrix}1 & 9 \\ 6 & 2\end{bmatrix}$

$\begin{bmatrix} - \frac{5}{6} & \frac{1}{2} \\ 0 & - \frac{2}{3} \end{bmatrix}$

A black line drawing of a circle on a white background. The center of the circle is marked with a solid black dot and labeled with the letter O. Four additional solid black dots are located on the edge (circumference) of the circle: Point A is in the lower-left quadrant. Point B is in the upper-right quadrant. Point D is on the far right edge (3 o'clock position). Point C is in the lower-right quadrant, positioned between point D and the bottom of the circle.

For circle O shown, A, B, C, and D are on circle O; A and B are as far apart as possible; C is halfway between A and B along circle O; and D is halfway between C and B along circle O. What percent of the area enclosed by circle O is enclosed by $\overline{OC}$, $\overline{OD}$, and minor arc $\overgroup{CD}$?

25%

50%

12.5%

100%

An object is launched vertically at 30 meters per second from a 55-meter-tall platform. The height, $h(t)$ meters, of the object $t$ seconds after launch is modeled by $h(t) = -4.9t^2 + 30t + 55$. What will be the height, in meters, of the object 3 seconds after launch?

44.1

145

100.9

189.1

Given the function $f(x) = 4x^2 - 14x + 12$, which of the following expressions is equivalent to $f(x)$?

$(2x - 3)(2x + 4)$

$(2x - 4)(2x + 3)$

$(2x - 4)(2x - 3)$

$(-2x + 4)(2x + 3)$

Which of the following is equivalent to $(6x + 3y) - (y - 2x)$?

$5x + y$

$4x + 2y$

$5x + 5y$

$8x + 2y$

Bryce owns an apartment building. He charges $325 per month for each 1-bedroom apartment and $410 per month for each 2-bedroom apartment. Bryce charged a total of $4,905 in rent for 13 apartments this month. How many 1-bedroom apartments did Bryce charge for this month?

A restaurant surveyed its customers to determine whether or not they like hamburgers and whether or not they like turkey burgers. The table shows the results of the survey.
Like hamburgers
Do not like hamburgers
Total
Like turkey burgers
97
39
136
Do not like turkey burgers
98
78
176
Total
195
117
312
To the nearest 1%, what percent of the customers who responded to the survey like hamburgers?

	Like hamburgers	Do not like hamburgers	Total
Like turkey burgers	97	39	136
Do not like turkey burgers	98	78	176
Total	195	117	312

63%

50%

31%

71%

For what value of $n$ does the quadratic equation $x^2 - 4x + n = 0$ have solutions of $x = 7$ and $x = -3$?

$-4$

$-21$

$10$

$4$

The lengths of corresponding sides of 2 similar right triangles are in the ratio $4:5$. The hypotenuse of the smaller triangle is 20 inches long. How many inches long is the hypotenuse of the larger triangle?

A mathematical graph on a Cartesian coordinate system with $x$ and $y$ axes.Axes: The y-axis is labeled with "1" and "-1" tick marks. The origin is labeled "O".Function: A smooth, periodic wave (sinusoidal) is plotted.Key Features: The curve crosses the y-axis at its minimum point ($0, -1$). It reaches a maximum height of $1$ and a minimum of $-1$. The wave repeats consistently across the visible x-axis, showing approximately two and a half full cycles.

What is the amplitude of the graph of function $f(x) = \tfrac{1}{2}\cos(3x + \pi)$, shown in the standard $(x, y)$ coordinate plane?

$2$

$\tfrac{1}{3}$

$3$

$\tfrac{1}{2}$

A circle in the standard $(x, y)$ coordinate plane has its center at $(3, -4)$ and passes through $(0, 0)$. Which of the following is an equation for that circle?

$(x + 3)^{2} + (y - 4)^{2} = 25$

$(x - 3)^{2} + (y + 4)^{2} = 25$

$x^{2} + y^{2} = 5$

$(x + 3)^{2} + (y - 4)^{2} = 7$

$\sqrt{112} + \sqrt{63} + \sqrt{175} = ?$

$7\sqrt{50}$

$60\sqrt{7}$

$12\sqrt{7}$

$7\sqrt{12}$

The sum of 3 positive integers is 180, and the ratio of the integers is $5 : 3 : 2$. What is the value of the smallest of the integers?

$54$

$36$

$18$

$90$

Jeremy reaches into a box in the closet. The box contains 10 gloves that make up 5 matching pairs. He picks 1 glove at random and puts it on. Then he picks another glove at random. What is the probability that he has picked a matching pair?

$\frac{1}{9}$

$\frac{1}{2}$

$\frac{1}{5}$

$\frac{4}{9}$

During an event, a store gave a free T-shirt to every 24th customer that entered the store and a free gift certificate to every 60th customer that entered the store. Given that 500 customers entered the store during the event, how many customers received both a free T-shirt and a free gift certificate?

IES

Cameron’s bookshelf has 3 books with a rating of 10, 5 books with a rating of 100, and 2 books with a rating of 70. There are no other books on the bookshelf. What is the expected value, to the nearest whole number, of the rating of a book randomly selected from Cameron’s bookshelf?

The 1st term of a certain sequence is $-10$, and the 2nd term is $1$. Each subsequent term is obtained by adding the 2 immediately preceding terms. What is the 5th term of this sequence?

$-23$

$-17$

$19$

$34$

Which of the following values is the y-value of the solution to the given system of equations?
$\begin{cases} -4y-3=x \\ 2x-22=6y \end{cases}$

$y = -2$

$y = -\tfrac{3}{4}$

$y = 5$

$y = -2\tfrac{1}{2}$

IES

Some values of the function $g$ are given in the table. One of the following equations defines $g$. Which one?
$x$
$-2$
$0$
$1$
$2$
$3$
$g(x)$
$0$
$-8$
$-6$
$0$
$10$

$g(x) = -x - 8$

$g(x) = x^2 + 2$

$g(x) = -2x - 8$

$g(x) = 2x^2 - 8$

The vertex angle of an isosceles triangle is $40^\circ$. What is the measure of a base angle?

$140^\circ$

$100^\circ$

$40^\circ$

$70^\circ$

A black line drawing featuring a circle and a triangle.Circle: The circle has a center marked with a solid dot and labeled with the letter O.Triangle: An inscribed triangle is positioned inside the circle so that all three vertices touch the circle's circumference.Labels: The top vertex is labeled A, the bottom-left vertex is labeled B, and the bottom-right vertex is labeled C. The base of the triangle, segment BC, is a horizontal line.

Equilateral triangle $\triangle ABC$ is inscribed in circle $O$, as shown. What is the degree measure of minor arc $\overgroup{BC}$?

$120^\circ$

$60^\circ$

$90^\circ$

$180^\circ$

A scale model, where 1 coordinate unit represents 1 mile, is drawn in the standard $(x,y)$ coordinate plane. Angelo’s house is at $(4,-3)$, Ella’s house is at $(4,7)$, Troy’s house is at $(-2,7)$, and Yoko’s house is at $(-2,-3)$. Which of the following is closest to the area, in square miles, of the rectangle whose vertices are the real locations of the 4 houses?

100

IES

Let the function $f$ be defined as $f(x) = -9x^2$. In the standard $(x,y)$ coordinate plane, the graph of $y = f(x)$ undergoes a transformation such that the result is the graph of $y = f(x) - 4$. Under this transformation the graph of $y = f(x)$ is:

stretched horizontally by a factor of 4.

shifted downward 4 coordinate units.

shifted left 4 coordinate units.

stretched vertically by a factor of 4.

A diagram representing a real-world trigonometry problem.Geometry: A right-angled triangle is formed by a horizontal ground line, a vertical tree, and a diagonal line of sight (hypotenuse). A square symbol at the base of the tree indicates a $90$-degree angle.Measurements: The horizontal distance from the far vertex to the base of the tree is labeled "18 feet". The angle of elevation at the far vertex is labeled "40°".Objective: The vertical height of the tree is marked with a question mark (?), indicating the value to be solved.

Which of the following expressions equals the height, in feet, of the tree shown?

$\dfrac{\tan 40^\circ}{18}$

$18 \sin 40^\circ$

$18 \tan 40^\circ$

$18 \cos 40^\circ$

A black horizontal line with arrows on both ends, representing a number line.Endpoints: The leftmost marked point is labeled "0" and the rightmost marked point is labeled "8".Points: There are six equal segments between 0 and 8. Five intermediate points are marked with solid dots and labeled consecutively from left to right as "A", "B", "C", "D", and "E".

As shown, the number line between 0 and 8 is divided into 6 segments of equal length by points A through E. Which of the following statements about $\sqrt{8}$ is true?

$\sqrt{8}$ is at C.

$\sqrt{8}$ is between A and B.

$\sqrt{8}$ is between B and C.

$\sqrt{8}$ is at D.

IES

Deon often flies his kite. He can only fly his kite on days with wind. He does not fly his kite on every day with wind. For any given day, let Event A be that there is wind and let Event B be that Deon flies his kite. Which of the following values can $P(A \text{ and } B)$ be?

1.5

0.5

Whenever $\dfrac{-3x^{3} + 12x}{x^{3} - x^{2} - 6x}$ is defined, it is equivalent to:

$-2$

$\dfrac{6 - 3x}{x - 3}$

$\dfrac{6 - 3x}{x + 3}$

$\dfrac{1}{x+3}$

The roots of a polynomial equation are 0, 2, and −5. Which of the following is a factored form of the equation?

$x(x + 2)(x - 5) = 0$

$(x - 2)(x + 5) = 0$

$(x - 2)(x + 5) = x$

$x(x - 2)(x + 5) = 0$

If $\dfrac{3x - y}{x + y} = \dfrac{5}{8}$, then $\dfrac{x}{y} = ?$

$\dfrac{2}{19}$

$\dfrac{13}{7}$

$\dfrac{5}{8}$

$\dfrac{13}{19}$

Let the slope of $3x + 2y = 5$ be $m_1$, and the slope of $6x + 4y = 7$ be $m_2$. Which of the following is true?

$m_1 = m_2$

$m_1 = 2m_2$

$7m_1 = 5m_2$

$2m_1 = m_2$

IES

The piecewise functions $f$ and $g$ are given.
$f(x) = \begin{cases} -x^{2} &\text{ for } x<0 \\ 1-x &\text{ for } x \geq 0 \end{cases}$
$g(x) = \begin{cases} |x| + 7 & \text{for } \leq -1 \\ x-3 & \text{for } x >-1 \end{cases}$
What is the value of $f(g(-1))$?

$-16$

$-5$

$-1$

$-7$

Let $f$ be defined by $f(x) = 4x + 7$. Let $g$ be defined by $g(x) = -2x^2 + 11x + 1$. The graphs of $y = f(x)$ and $y = g(x)$ intersect at one of the following $(x, y)$ points. Which one?

$(13,-1)$

$\left(2,\,1\tfrac{1}{2}\right)$

$\left(1\tfrac{1}{2},\,13\right)$

$(-2,-1)$

A tourism organization randomly selected 100 tourists finishing their summer visit to Spain. The organization asked them how many cities they had toured in the country. The table shows the results. Based on these data, for the population of tourists that visited Spain during the summer, what is the best estimate of the mean number of cities toured?
Number of cities
1
2
3
Number of tourists
10
40
50

$3$

$2.4$

$0.8$

$2$

Given that $i$ is the imaginary unit, which of the following numbers is equal to $(7 + 4i)^{2}$?

$33 + 56i$

$14 + 8i$

The product of 2 complex numbers, $x$ and $y$, is a real number that is irrational. Which of the following statements cannot be true?

Both $x$ and $y$ are imaginary.

The product of $x$ and $y$ is negative.

Both $x$ and $y$ are rational.

The product of $x$ and $y$ is $\sqrt{2}$.

The real solution of the equation $3e^{x} = 12$ is:

$3 \ln 12$

$\ln 4$

$\dfrac{\ln 12}{3}$

$4^{e}$

A circle with center O containing an inscribed triangle ABC.Diameter: Segment BC passes through the center point $O$ and is labeled "10 cm", identifying it as the diameter.Triangle: Triangle ABC is inscribed in the circle. Side AB and side AC each have a single tick mark, indicating they are equal in length (isosceles triangle).Arc: The arc between points A and B is highlighted with a thicker black line.

The figure shows $\triangle ABC$, a right isosceles triangle, inscribed in a circle with center $O$ and radius 10 cm. What is the length, in centimeters, of arc $\overset{\frown}{AB}$ shown as the thick curved line?

$15\pi$

$20\pi$

$5\pi$

$10\pi$

It took Sam $x$ minutes to bike the $d$ miles from home to work. Returning home on the same route, it took Sam $y$ minutes. On the way home his average speed was 2 times his average speed on the way to work. Which of the following equations gives $y$ in terms of $x$?

$y = 2x$

$y = x - 2$

$y = \dfrac{x}{2}$

$y = x + 2$

IES

A graph showing four separate curved branches on x and y axes.Orientation: Two branches open vertically (one up, one down) and two branches open horizontally (one left, one right).Vertices: Each of the four branches has a vertex marked with a solid black dot where it is closest to the origin O.Symmetry: The curves are perfectly symmetrical across both the x-axis and the y-axis.

The hyperbolas $\dfrac{x^2}{9}-\dfrac{y^2}{4}=1$ and $\dfrac{y^2}{36}-\dfrac{x^2}{25}=1$ are graphed in the standard $(x,y)$ coordinate plane. Which of the following equations is an ellipse that intersects all 4 vertices of the hyperbolas?

$\dfrac{x^2}{25}+\dfrac{y^2}{4}=1$

$(x-9)^2+(y-36)^2=1$

$\dfrac{x^2}{25}+\dfrac{y^2}{9}=1$

$\dfrac{x^2}{9}+\dfrac{y^2}{36}=1$

Given that $f(x)=\sqrt[3]{2x-1}$, which of the following expressions is the inverse function, $f^{-1}(x)$?

$\dfrac{x^3+1}{2}$

$(2x-1)^3$

$\dfrac{1}{\sqrt[3]{2x-1}}$

$\sqrt[3]{\dfrac{x+1}{2}}$

Practice ACT - Math - MC5

Practice ACT - Math - MC5

MATHEMATICS TEST

MATHEMATICS TEST

At a college track meet, there are 3 jumping events: high jump, long jump, and triple jump. The Venn diagram below shows the distribution of the number of athletes competing in each jumping event. How many athletes are competing in both high jump and triple jump but not long jump?

A function, $f$, is defined by the equation $f(x) = x^2 + 5$. What is $f(3) + 1$?

Given $b = 40$ and $c = -16$, $b + c$ is equal to the product of $-4$ and what number?

It takes Collin 24 minutes to walk to school in the morning. What fraction of his 24-hour day is spent walking to school in the morning?

A certain triangle has interior angle measures of $(6x)^\circ$, $(2x)^\circ$, and $x^\circ$. What is the value of $x$?

Which of the following matrices is equal to $6\begin{bmatrix}-5 & 3 \\ 0 & -4\end{bmatrix}$?

An object is launched vertically at 30 meters per second from a 55-meter-tall platform. The height, $h(t)$ meters, of the object $t$ seconds after launch is modeled by $h(t) = -4.9t^2 + 30t + 55$. What will be the height, in meters, of the object 3 seconds after launch?

Given the function $f(x) = 4x^2 - 14x + 12$, which of the following expressions is equivalent to $f(x)$?

Which of the following is equivalent to $(6x + 3y) - (y - 2x)$?

Bryce owns an apartment building. He charges $325 per month for each 1-bedroom apartment and $410 per month for each 2-bedroom apartment. Bryce charged a total of $4,905 in rent for 13 apartments this month. How many 1-bedroom apartments did Bryce charge for this month?

For what value of $n$ does the quadratic equation $x^2 - 4x + n = 0$ have solutions of $x = 7$ and $x = -3$?

The lengths of corresponding sides of 2 similar right triangles are in the ratio $4:5$. The hypotenuse of the smaller triangle is 20 inches long. How many inches long is the hypotenuse of the larger triangle?

What is the amplitude of the graph of function $f(x) = \tfrac{1}{2}\cos(3x + \pi)$, shown in the standard $(x, y)$ coordinate plane?

A circle in the standard $(x, y)$ coordinate plane has its center at $(3, -4)$ and passes through $(0, 0)$. Which of the following is an equation for that circle?

$\sqrt{112} + \sqrt{63} + \sqrt{175} = ?$

The sum of 3 positive integers is 180, and the ratio of the integers is $5 : 3 : 2$. What is the value of the smallest of the integers?

Jeremy reaches into a box in the closet. The box contains 10 gloves that make up 5 matching pairs. He picks 1 glove at random and puts it on. Then he picks another glove at random. What is the probability that he has picked a matching pair?

Cameron’s bookshelf has 3 books with a rating of 10, 5 books with a rating of 100, and 2 books with a rating of 70. There are no other books on the bookshelf. What is the expected value, to the nearest whole number, of the rating of a book randomly selected from Cameron’s bookshelf?

The 1st term of a certain sequence is $-10$, and the 2nd term is $1$. Each subsequent term is obtained by adding the 2 immediately preceding terms. What is the 5th term of this sequence?

Which of the following values is the y-value of the solution to the given system of equations? $\begin{cases} -4y-3=x \\ 2x-22=6y \end{cases}$

Some values of the function $g$ are given in the table. One of the following equations defines $g$. Which one?$x$$-2$$0$$1$$2$$3$$g(x)$$0$$-8$$-6$$0$$10$

The vertex angle of an isosceles triangle is $40^\circ$. What is the measure of a base angle?

Equilateral triangle $\triangle ABC$ is inscribed in circle $O$, as shown. What is the degree measure of minor arc $\overgroup{BC}$?

Let the function $f$ be defined as $f(x) = -9x^2$. In the standard $(x,y)$ coordinate plane, the graph of $y = f(x)$ undergoes a transformation such that the result is the graph of $y = f(x) - 4$. Under this transformation the graph of $y = f(x)$ is:

Which of the following expressions equals the height, in feet, of the tree shown?

As shown, the number line between 0 and 8 is divided into 6 segments of equal length by points A through E. Which of the following statements about $\sqrt{8}$ is true?

Deon often flies his kite. He can only fly his kite on days with wind. He does not fly his kite on every day with wind. For any given day, let Event A be that there is wind and let Event B be that Deon flies his kite. Which of the following values can $P(A \text{ and } B)$ be?

Whenever $\dfrac{-3x^{3} + 12x}{x^{3} - x^{2} - 6x}$ is defined, it is equivalent to:

The roots of a polynomial equation are 0, 2, and −5. Which of the following is a factored form of the equation?

If $\dfrac{3x - y}{x + y} = \dfrac{5}{8}$, then $\dfrac{x}{y} = ?$

Let the slope of $3x + 2y = 5$ be $m_1$, and the slope of $6x + 4y = 7$ be $m_2$. Which of the following is true?

The piecewise functions $f$ and $g$ are given.$f(x) = \begin{cases} -x^{2} &\text{ for } x<0 \\ 1-x &\text{ for } x \geq 0 \end{cases}$$g(x) = \begin{cases} |x| + 7 & \text{for } \leq -1 \\ x-3 & \text{for } x >-1 \end{cases}$What is the value of $f(g(-1))$?

Let $f$ be defined by $f(x) = 4x + 7$. Let $g$ be defined by $g(x) = -2x^2 + 11x + 1$. The graphs of $y = f(x)$ and $y = g(x)$ intersect at one of the following $(x, y)$ points. Which one?

Given that $i$ is the imaginary unit, which of the following numbers is equal to $(7 + 4i)^{2}$?

The product of 2 complex numbers, $x$ and $y$, is a real number that is irrational. Which of the following statements cannot be true?

The real solution of the equation $3e^{x} = 12$ is:

The figure shows $\triangle ABC$, a right isosceles triangle, inscribed in a circle with center $O$ and radius 10 cm. What is the length, in centimeters, of arc $\overset{\frown}{AB}$ shown as the thick curved line?

It took Sam $x$ minutes to bike the $d$ miles from home to work. Returning home on the same route, it took Sam $y$ minutes. On the way home his average speed was 2 times his average speed on the way to work. Which of the following equations gives $y$ in terms of $x$?

The hyperbolas $\dfrac{x^2}{9}-\dfrac{y^2}{4}=1$ and $\dfrac{y^2}{36}-\dfrac{x^2}{25}=1$ are graphed in the standard $(x,y)$ coordinate plane. Which of the following equations is an ellipse that intersects all 4 vertices of the hyperbolas?

Given that $f(x)=\sqrt[3]{2x-1}$, which of the following expressions is the inverse function, $f^{-1}(x)$?

MATHEMATICS TEST

MATHEMATICS TEST

At a college track meet, there are 3 jumping events: high jump, long jump, and triple jump. The Venn diagram below shows the distribution of the number of athletes competing in each jumping event. How many athletes are competing in both high jump and triple jump but not long jump?

A function, $f$, is defined by the equation $f(x) = x^2 + 5$. What is $f(3) + 1$?

Given $b = 40$ and $c = -16$, $b + c$ is equal to the product of $-4$ and what number?

It takes Collin 24 minutes to walk to school in the morning. What fraction of his 24-hour day is spent walking to school in the morning?

A certain triangle has interior angle measures of $(6x)^\circ$, $(2x)^\circ$, and $x^\circ$. What is the value of $x$?

Which of the following matrices is equal to $6\begin{bmatrix}-5 & 3 \\ 0 & -4\end{bmatrix}$?

An object is launched vertically at 30 meters per second from a 55-meter-tall platform. The height, $h(t)$ meters, of the object $t$ seconds after launch is modeled by $h(t) = -4.9t^2 + 30t + 55$. What will be the height, in meters, of the object 3 seconds after launch?

Given the function $f(x) = 4x^2 - 14x + 12$, which of the following expressions is equivalent to $f(x)$?

Which of the following is equivalent to $(6x + 3y) - (y - 2x)$?

Bryce owns an apartment building. He charges $325 per month for each 1-bedroom apartment and $410 per month for each 2-bedroom apartment. Bryce charged a total of $4,905 in rent for 13 apartments this month. How many 1-bedroom apartments did Bryce charge for this month?

For what value of $n$ does the quadratic equation $x^2 - 4x + n = 0$ have solutions of $x = 7$ and $x = -3$?

The lengths of corresponding sides of 2 similar right triangles are in the ratio $4:5$. The hypotenuse of the smaller triangle is 20 inches long. How many inches long is the hypotenuse of the larger triangle?

What is the amplitude of the graph of function $f(x) = \tfrac{1}{2}\cos(3x + \pi)$, shown in the standard $(x, y)$ coordinate plane?

A circle in the standard $(x, y)$ coordinate plane has its center at $(3, -4)$ and passes through $(0, 0)$. Which of the following is an equation for that circle?

$\sqrt{112} + \sqrt{63} + \sqrt{175} = ?$

The sum of 3 positive integers is 180, and the ratio of the integers is $5 : 3 : 2$. What is the value of the smallest of the integers?

Jeremy reaches into a box in the closet. The box contains 10 gloves that make up 5 matching pairs. He picks 1 glove at random and puts it on. Then he picks another glove at random. What is the probability that he has picked a matching pair?

Cameron’s bookshelf has 3 books with a rating of 10, 5 books with a rating of 100, and 2 books with a rating of 70. There are no other books on the bookshelf. What is the expected value, to the nearest whole number, of the rating of a book randomly selected from Cameron’s bookshelf?

The 1st term of a certain sequence is $-10$, and the 2nd term is $1$. Each subsequent term is obtained by adding the 2 immediately preceding terms. What is the 5th term of this sequence?

Which of the following values is the y-value of the solution to the given system of equations? $\begin{cases} -4y-3=x \\ 2x-22=6y \end{cases}$

Some values of the function $g$ are given in the table. One of the following equations defines $g$. Which one?$x$$-2$$0$$1$$2$$3$$g(x)$$0$$-8$$-6$$0$$10$

The vertex angle of an isosceles triangle is $40^\circ$. What is the measure of a base angle?

Equilateral triangle $\triangle ABC$ is inscribed in circle $O$, as shown. What is the degree measure of minor arc $\overgroup{BC}$?

Let the function $f$ be defined as $f(x) = -9x^2$. In the standard $(x,y)$ coordinate plane, the graph of $y = f(x)$ undergoes a transformation such that the result is the graph of $y = f(x) - 4$. Under this transformation the graph of $y = f(x)$ is:

Which of the following expressions equals the height, in feet, of the tree shown?

As shown, the number line between 0 and 8 is divided into 6 segments of equal length by points A through E. Which of the following statements about $\sqrt{8}$ is true?

Deon often flies his kite. He can only fly his kite on days with wind. He does not fly his kite on every day with wind. For any given day, let Event A be that there is wind and let Event B be that Deon flies his kite. Which of the following values can $P(A \text{ and } B)$ be?

Whenever $\dfrac{-3x^{3} + 12x}{x^{3} - x^{2} - 6x}$ is defined, it is equivalent to:

The roots of a polynomial equation are 0, 2, and −5. Which of the following is a factored form of the equation?

If $\dfrac{3x - y}{x + y} = \dfrac{5}{8}$, then $\dfrac{x}{y} = ?$

Let the slope of $3x + 2y = 5$ be $m_1$, and the slope of $6x + 4y = 7$ be $m_2$. Which of the following is true?

The piecewise functions $f$ and $g$ are given.$f(x) = \begin{cases} -x^{2} &\text{ for } x<0 \\ 1-x &\text{ for } x \geq 0 \end{cases}$$g(x) = \begin{cases} |x| + 7 & \text{for } \leq -1 \\ x-3 & \text{for } x >-1 \end{cases}$What is the value of $f(g(-1))$?

Let $f$ be defined by $f(x) = 4x + 7$. Let $g$ be defined by $g(x) = -2x^2 + 11x + 1$. The graphs of $y = f(x)$ and $y = g(x)$ intersect at one of the following $(x, y)$ points. Which one?

Given that $i$ is the imaginary unit, which of the following numbers is equal to $(7 + 4i)^{2}$?

Which of the following values is the y-value of the solution to the given system of equations?
$\begin{cases} -4y-3=x \\ 2x-22=6y \end{cases}$

Some values of the function $g$ are given in the table. One of the following equations defines $g$. Which one?
$x$
$-2$
$0$
$1$
$2$
$3$
$g(x)$
$0$
$-8$
$-6$
$0$
$10$

The piecewise functions $f$ and $g$ are given.
$f(x) = \begin{cases} -x^{2} &\text{ for } x<0 \\ 1-x &\text{ for } x \geq 0 \end{cases}$
$g(x) = \begin{cases} |x| + 7 & \text{for } \leq -1 \\ x-3 & \text{for } x >-1 \end{cases}$
What is the value of $f(g(-1))$?

Which of the following values is the y-value of the solution to the given system of equations?
$\begin{cases} -4y-3=x \\ 2x-22=6y \end{cases}$

Some values of the function $g$ are given in the table. One of the following equations defines $g$. Which one?
$x$
$-2$
$0$
$1$
$2$
$3$
$g(x)$
$0$
$-8$
$-6$
$0$
$10$

The piecewise functions $f$ and $g$ are given.
$f(x) = \begin{cases} -x^{2} &\text{ for } x<0 \\ 1-x &\text{ for } x \geq 0 \end{cases}$
$g(x) = \begin{cases} |x| + 7 & \text{for } \leq -1 \\ x-3 & \text{for } x >-1 \end{cases}$
What is the value of $f(g(-1))$?