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A good overall review of basic ACT Math questions!
Questions and Answers
1.
Given the following sentence:
What is the value of x when 2x + 3 = 3x – 4 ?
A.
B.
C.
D.
E.
Describe how you would solve this problem:
2.
How do you find the slope of a line?
3.
Read the question below, and (1) describe what basic shapes are included in this problem, and (2) which equations are needd to solve it:
The geometric figure shown below consists of a square and 4 semicircles. The diameters of the semicircles are the sides of the square, and each diameter is 10 centimeters long. Which of the following is the closest approximation of the total area, in square centimeters, of this geometric figure?
4.
Describe how you would find the slope of the line parallel to another line:
5.
Given the following sentence:
What is the slope of any line parallel to the line 9x + 4y = 7 ?
Describe how you would solve this problem:
6.
Given the following sentence:
What is the slope of any line perpendicular to the line 9x + 4y = 7 ?
Describe how you would solve this problem:
7.
What four basic shapes are most often tested on the ACT Math section?
A.
Square, Trapezoid, Parallelogram, and Circle
B.
Square, Trapezoid, Triangle, and Circle
C.
Square, Parallelagram, Triangle, and Circle
D.
Square, Rectangle, Triangle, and Circle
Correct Answer D. Square, Rectangle, Triangle, and Circle
Explanation Most every shape presented in various ACT math questions can be broken down into squares, rectangles, triangles, and circles. This is helpful when finding areas and/or perimeters; for example, shapes such as trapezoids and parallelograms can be broken into basic parts like rectangles and triangles, and areas can be found individually, then added together.
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8.
Which of the following is the equation for the Area of a Rectangle?
A.
B.
C.
D.
Correct Answer D.
Explanation The equation for the area of a rectangle is length multiplied by width.
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9.
Consider the following sentence problem:
A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would cost for this car to travel 2,727 typical miles?
Which of the following are key words to help you set-up and solve this problem?
A.
Per
B.
Average...
C.
Miles..
D.
Gas costs...
Correct Answer A. Per
Explanation The word per is one of four keywords that tells us to set up a fraction with proportions. The other words include: for, to, and in. Such words are used to describe ratios or rates. This includes 6 apples for $1. These keywords act as the fraction bar so that you can set-up an equation. In this case our equation would look like the following:
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10.
Consider the following sentence problem:
A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would cost for this car to travel 2,727 typical miles?
What are you being asked to solve for?
A.
The total number of miles traveled
B.
The amount of gas used when driving 2,727 miles
C.
The amount of time it takes to travel 2,727 miles
D.
The cost of gas when driving 2,727 miles
Correct Answer D. The cost of gas when driving 2,727 miles
Explanation The last sentence of all ACT problems contains the actual question that you are trying to solve for. Math presented as sentence problems can become confusing with all the information given. Be sure to focus on that last sentence to make sure you know what you are solving for.
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11.
Which of the following general equations can be used to find the slope of a line?
A.
X + y = mb
B.
Y = mx + b
C.
2x + b = y +m
D.
B = my + x
Correct Answer B. Y = mx + b
Explanation The equation y = mx + b is the standard form of a linear equation, where m represents the slope of the line and b represents the y-intercept. Therefore, this equation can be used to find the slope of a line.
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12.
Given the equation:
y = mx + b
Which of the following represents the slope?
A.
Y
B.
M
C.
X
D.
B
Correct Answer B. M
Explanation The variable "m" in the equation represents the slope. The slope is a measure of how steep a line is. In the equation y = mx + b, "m" is the coefficient of the x variable, which determines the rate at which y changes with respect to x. Therefore, "m" represents the slope in the equation.
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13.
Given the equation:
y = mx + b
Which of the following represents the y - intercept?
A.
Y
B.
M
C.
X
D.
B
Correct Answer D. B
Explanation The letter "b" in the equation represents the y-intercept. In the equation y = mx + b, the y-intercept is the value of y when x is equal to 0. It is the point where the line intersects the y-axis. Changing the value of b will shift the entire line up or down along the y-axis.
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14.
Which of the following is the equation for the Area of a Triangle?
A.
B.
C.
D.
Correct Answer C.
Explanation The equation for the area of a triangle is 1/2 times the base of the triangle multiplied by the height of the triangle.
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15.
Which of the following is the equation for the Area of a Circle?
A.
B.
C.
D.
Correct Answer B.
Explanation The equation for the area of a circle is A = πr^2, where A represents the area and r represents the radius of the circle.
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16.
Which of the following is the equation for the Volume of a Rectangle (or a rectangular prism)?
A.
B.
C.
D.
Correct Answer A.
Explanation The equation for the volume of a rectangular prism is given by multiplying the length, width, and height of the prism.
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17.
Which of the following is the equation for the Perimeter of a Rectangle?
A.
B.
C.
D.
Correct Answer D.
Explanation The equation for the perimeter of a rectangle is P = 2l + 2w, where P represents the perimeter, l represents the length, and w represents the width.
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18.
Which of the following is the equation for the Perimeter of a Circle?
(Hint - the perimeter is the distance around the outside of an object...so this is another way of asking for the Circumference)
A.
B.
C.
D.
Correct Answer C.
Explanation The equation for the perimeter of a circle is 2πr, where r is the radius of the circle. The perimeter or circumference of a circle is the distance around the outside of the circle, and it is calculated by multiplying the radius of the circle by 2π (approximately 3.14159).
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19.
What is the sum of the angles in a Triangle?
A.
90
B.
180
C.
270
D.
360
Correct Answer B. 180
Explanation The sum of the angles in a triangle is always 180 degrees. This is a fundamental property of triangles in Euclidean geometry.
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20.
What is the sum of the angles in a Quadrilateral?
A.
90
B.
180
C.
270
D.
360
Correct Answer D. 360
Explanation A quadrilateral is a polygon with four sides. The sum of the angles in any polygon can be found using the formula (n-2) * 180, where n is the number of sides. In this case, since a quadrilateral has 4 sides, the sum of the angles is (4-2) * 180 = 360.
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21.
What is the degree measure of a Circle?
A.
90
B.
180
C.
270
D.
360
Correct Answer D. 360
Explanation A circle is a closed curve with all points equidistant from a fixed center point. It consists of 360 degrees. This means that if you were to travel around the circumference of a circle, you would have traveled 360 degrees. Therefore, the degree measure of a circle is 360.
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22.
Which of the following equations can be used to find the mid-point?
A.
B.
C.
D.
Correct Answer C.
Explanation The equation for finding the midpoint of a line segment is (x₁ + x₂)/2, (y₁ + y₂)/2. This equation takes the average of the x-coordinates and the average of the y-coordinates of the two endpoints of the line segment. By finding the average, we can determine the point that lies exactly in the middle of the line segment.
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23.
Which of the following represents the standard equation of a circle?
A.
B.
C.
D.
Correct Answer D.
Explanation The standard equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the coordinates of the center of the circle and r represents the radius. This equation represents a circle because it states that the sum of the squares of the differences between the x-coordinate and the center's x-coordinate, and the y-coordinate and the center's y-coordinate, is equal to the square of the radius. This equation can be used to graph a circle on a coordinate plane.
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24.
Which of the following equations would be used to solve the following problem? A circle has a circumference of feet. What is the radius of the circle in feet?
A.
B.
C.
D.
Correct Answer C.
Explanation The formula used to solve this problem is C = 2πr, where C represents the circumference of the circle and r represents the radius. By rearranging the formula, we can solve for the radius by dividing both sides of the equation by 2π. This will give us the equation r = C / (2π), which can be used to find the radius of the circle in feet.