ACT Mathematics Practice Test

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• The vertex of the parabola y = x^2 - 4x + 5 is at:
• What is the probability of rolling a 5 or a 6 on a fair six-sided die?
• If f(x) = 2x + 3 and g(x) = x^2, what is (g ∘ f)(1)?
• Find the slope of the line through (0,0) and (4,6).
• The area of a triangle with base 12 and height 5 is?
• What is the median of the set {1, 3, 3, 3, 7}?
• A fair coin is flipped twice. What is the probability of at least one heads?
• Using sin^2 θ + cos^2 θ = 1, if cos θ = 1/2 and θ is in the first quadrant, what is sin θ?
• What is (f ∘ g)(3) for f(x) = 2x + 3 and g(x) = x^2?
• What is the radius of the circle defined by x^2 + y^2 = 25?
• From the blood types: O = 62, A = 67, B = 15, AB = 6. What is the probability that a randomly selected person has Type B or AB?
• If tan theta = 3/4 and theta is in the first quadrant, what is sin theta?
• If point D has coordinates (12, 1) and is reflected across the y-axis to D', what are the coordinates of D’?
• If two similar triangles have a linear scale factor of 2:7, what is the ratio of their areas?
• Which expression is equivalent to 1/2 y^2 (6x + 2y + 12x - 2y)?
• If two similar triangles have a linear scale factor of 3:5, what is the ratio of their areas?
• If a quadratic equation ax^2 + bx + c = 0 has two real roots of opposite signs, which statement must be true about a and c?
• In a right triangle with legs 5 and 12, the square of the hypotenuse equals what?
• Factor by grouping: x^3 - 3x^2 + 2x - 6.
• What is the mean of the monthly fees for the five colleges: 370, 310, 380, 340, and 310?
• What is the mean of the numbers 3, 8, 10, and 15?
• The quotient and remainder when dividing x^3 - x^2 + x - 4 by (x - 2) are respectively?
• What is the slope of the line through points (4, -3) and (7, 5)?
• What is cos 60 degrees?
• Which statement describes the domain of y = sqrt(x - 1)?
• If f(x) = 3x + 4, what is f^{-1}(7)?
• If two triangles are similar with scale factor 3:2, what is the ratio of their areas?
• A line perpendicular to y = -2x + 7 has what slope?
• The geometric sequence starts with 1, -3, 9, -27, ... What is the seventh term?
• What is the inverse function of f(x) = 3x - 7?
• Using d = 6t + 14, what is d when t = 7?
• In a circle graph, the central angles of all sectors sum to 360 degrees. If four sectors have central angles 120°, 60°, 90°, and 60°, what is the remaining central angle?
• Gianna will tile the floor portion not covered by cabinets. If the total floor area is 200 square feet and cabinets cover 60 square feet, what area must be tiled?
• A dog eats 7 cans of food in 3 days. At this rate, how many cans are eaten in 3 + d days?
• A silicon chip is 0.32 cm thick. The top and bottom layers are each 0.03 cm thick, and each inner layer is 0.02 cm thick. How many inner layers are in the chip?
• Which equation expresses the Law of Cosines for the angle opposite the largest side 20 in a triangle with sides 14, 18, and 20?
• What is the equation of the line through (2,-3) that is perpendicular to y = x?
• How many ways are there to choose 3 items from 5 when order does not matter?
• Divide (2x^3 - 3x^2 + x - 5) by (x - 2). What is the quotient and remainder?
• Let E(6, 4) and F(14, 12) lie on a segment EF. Point D lies on EF between E and F such that EF is four times as long as DE. Which are the coordinates of D?
• For f(x) = 3x + 4, which is f(2)?
• The slope of the line through (0,2) and (4,6) is?
• The expression (x^2 - 16)/(x^2 - 4x) simplifies to what, for x ≠ 0, 4?
• Find the intersection points of the circle x^2 + y^2 = 16 and the line x + y = 0.
• Using the Law of Cosines, with a = 5, b = 7, and included angle C = 60 degrees, what is c?
• Factor and solve: x^2 - 5x + 6 = 0. Which of the following expresses the solutions?
• Simplify sqrt(50).
• What is f(2) if f(x) = x − 1/x?
• If f(x) = x^2, what is f(5)?
• Solve 2x + 3 = 7. What is x?
• Using f(x) = (3x + 7)^2, what is f(-1)?
• In trapezoid ABCD, AB is parallel to DC. If angle D measures x degrees, what is the measure of angle A in terms of x?
• The slope of CD is sought for points C(9,4) and D(12,1). What is the slope of CD?
• If a, b, and c are positive integers such that a^b = x and c^b = y, then xy = ?
• Compute 3^4 * 3^(-2).
• If x:y = 5:2 and y:z = 3:2, what is the ratio x:z?
• Factor the polynomial 6x^2 - 9x.
• A tank is initially 3/10 full. After adding 5 cups, it becomes 1/2 full. What is the tank's total capacity in cups?
• If a point at (3, -7) is reflected across the y-axis, which are its coordinates after the reflection?
• In a line segment EF with E at (-10, 0) and F at (2, 8), D lies on EF such that the line segment DE is exactly 1/2 of EF. What are the coordinates of D?
• In a 30-60-90 right triangle, with hypotenuse length 2, what are the lengths of the legs?
• The graphs of f(x) = (x - 3)^2 + 2 and g(x) = (1/2)x + 1 intersect at exactly how many x-values?
• If a dog eats 7 cans in 3 days, how many cans are eaten in 9 days?
• Which description matches the graph of the region defined by 1 < x + y < 2?
• Evaluate sin 60°.
• A school has tenth graders comprising 86/225 of the student population and eleventh graders comprising 18/51 of the population. If a student is selected at random, which grade is most likely?
• A rectangle has area 54 square centimeters and length 9 cm. What is its perimeter?
• In a box containing 750 regular pieces and 5 extras, what is the probability of selecting a normal piece?
• If f(x) = x^2 and g(x) = 2x + 1, what is f(g(2))?
• A rectangular floor measures 18 feet by 12 feet. Cabinets cover 36 square feet. What area must be tiled?
• A rectangle has width 6 and area 60. What is its length?
• Isosceles right triangle has a hypotenuse of 8√2 inches. What is its perimeter?
• Compute (3 + 4)^2.
• The minimum value of f(x) = (x - 2)^2 is which value?
• If f(x) = (3x + 7)^2, what is f(1)?
• In a right triangle with legs 5 and 12, the hypotenuse is 13. Which value is the hypotenuse?
• Which system of inequalities corresponds to the standard region inside a circle centered at (1,2) with radius 3 and below the line y = -x + 2?
• If f(x) = 2x + 3 and g(x) = x^2, what is (f ∘ g)(2)?
• The mode of the data set {5, 5, 7, 9, 9, 9, 11} is?
• In a triangle with side lengths 14 cm, 18 cm, and 20 cm, which angle is smallest?
• What is the area of a circle with radius 6?
• Find the equation of the line through points (0,-1) and (2,3).
• Which inequality describes the interior of a circle with center (1, 2) and radius 3?
• How many ways to arrange 4 distinct letters A, B, C, D?
• The circumference of a circle with radius 6 is 12π. What is the circumference for a circle with radius 3?
• What is f(2) for f(x) = (3x + 7)^2?
• What is the inverse function of f(x) = 2x + 3?
• If a = 3 and b = 4, what is (a + b)^2?
• Solve for x: (x - 2)/(x + 4) = 3/5, with x ≠ -4.
• Find the area of a semicircle with radius 7.
• Simplify the rational expression (x^2 - 9)/(x^2 - 3x) for x ≠ 0, 3. Which expression is equivalent?
• In a right triangle with legs 9 and 12, what is the hypotenuse?
• If y = 2x + 5 and x = -3, what is y?
• If a rectangle has left edge x = -10 and right edge x = 2, which vertical line x = k bisects the width, i.e., area, of the rectangle?
• What is the area of a circle with radius 6?
• If an isosceles right triangle has leg length 6, what is its perimeter?
• Evaluate f(-2) for f(x) = 2x^2 - 3x + 1.
• Kami sold 70 figurines in two sizes; large at $12 each, small at $8 each. The amount of money from the large figurines equals the amount from the small ones. How many large figurines were sold?
• Evaluate f(0) for f(x) = 2x^2 - 3x + 1.
• Which of the following expresses the solution set for the compound inequality -5 < 1 - 3x < 10?
• The range of the data set {2, 4, 9, 9, 15} is?
• A cart moves along a straight line such that its distance from a reference point at times t = 0, 1, 2, 3, 4, 5 seconds are 14, 20, 26, 32, 38, 44 feet respectively. Which equation best represents d in terms of t?
• What is the probability of drawing a red card from a standard deck?
• In a circle graph representing a school day, the Core subjects sector accounts for 4 hours out of a 9-hour day. What is the central angle for the Core subjects sector?
• Compute 2^3 * 2^4.
• The area of a circle with radius 3 is 9π. Which option equals the area?
• Solve 3y - 4 = 2y + 9.
• What is the mean of the set 2, 4, 6, 8?
• If f(x) = sqrt(x) and g(x) = x - 1, the domain of f(g(x)) is:
• A rectangular solid has surface area A = 2lw + 2lh + 2wh. If each dimension is doubled, by what factor is the surface area multiplied?
• Solve for x: 2^x = 32.
• How many ways to choose 3 items from 6 without regard to order?
• Past records show 80% of applicants pass the written test and 60% of those who pass the written test pass the driving test. In a random group of 1,000 applicants, how many would you expect to get driver's licenses?
• A 15-foot wall is drawn on a scale where 1 inch represents 8 feet. How many inches long is the wall on the drawing?
• In a survey of 120 students about skiing, 65 said they had skied either cross-country or downhill. Among these 65, 28 said they had skied downhill, 45 said they had skied cross-country. If 8 students skied both, how many students skied exactly one of the two?
• What is sin 0 degrees?
• If the radius of a circle is doubled, by what factor does its area increase?
• Solve 3x - 5 = 16.
• Solve by quadratic formula: 2x^2 - 4x - 6 = 0. Which are the solutions?
• From the system x + y = 7 and 2x - y = 1, what is the value of x?
• On the same map, how many miles are 3 inches apart?
• Solve the system 2x + y = 5 and x - y = 1. What are the values of x and y?
• In the formula p = (1/2 a r y + a) / (12 y) for the monthly payment, when a is doubled, what is the effect on p?
• An artist’s profit from selling p paintings is P(p) = 500p - p^2. What is the smallest integer p for which P(p) ≥ 60,000?
• The median of the data set {3, 7, 8, 12, 14} is?
• A solid object is submerged in a rectangular tank with base 40 cm by 30 cm and is submerged from the surface, raising the water level by 0.25 cm. If the tank was filled to depth 20 cm initially, what is the volume of the object in cubic centimeters?
• Find the area of a trapezoid with bases 5 and 9 and height 4.
• Which statement about h(x) = |x - 3| is true?
• If log base 10 of x equals 2, what is x?
• A circle has diameter 6. What is its area?
• Write the equation of the circle with center at (2, -1) and radius 5.
• Flip a fair coin twice. What is the probability of getting exactly one head?
• In a square partitioned into three horizontal rows of equal area, the top row contains regions A and B such that A has the same area as B. The middle row is divided into three regions of equal area. What fraction of the square's area is in region A?
• In a right triangle with legs 6 and 8, what is the length of the hypotenuse?
• For f(x) = (x - 2)^2, what is the x-coordinate of the vertex?
• Find the area of a trapezoid with bases 3 and 9 and height 5.
• The area of a triangle with base 8 and height 5 is 20 square units. What is the area?
• The slope of the line through (0,2) and (4,-2) is what?
• The functions y = sin x and y = sin(x + a) + b have the same maximum value. Which statement about a and b must be true?
• How many real solutions does the quadratic x^2 + 3x - 4 = 0 have?
• The volume of a rectangular prism with length 3, width 4, height 5 is 60. Which value is the volume?
• Elliott is answering four multiple-choice questions, each with 3 possible answers, only 1 correct. What is the probability that all four answers are correct by random guessing?
• For f(x) = (x - 2)^2, what is the y-coordinate of the vertex?
• Convert 0.75 to a fraction.
• In a rectangle whose left edge is at x = 0 and right edge at x = 13, which vertical line x = k divides the rectangle into two regions of equal area?
• Evaluate the product (-2i + 5)(2i + 5).
• Simplify ((2^3)^4).
• A line passes through the points (0, 2) and (3, 8). What is its slope?
• Solve for x: 3x - 7 = 2x + 5.
• Which of the following is the correct ascending order of the numbers 1/2, 5/6, and 5/8?
• In a 45-45-90 triangle, if a leg length is 6, what is the length of the hypotenuse?
• Given f = c d^3, with f = 450 and d = 10, what is c?
• The quotient and remainder when dividing x^3 - 6x^2 + 11x - 6 by (x - 1) are?
• If sin θ = 3/5 and θ is in the first quadrant, what is cos θ?
• If the average of 4, 7, x, and 11 is 9, what is x?
• What is the sum of the first 20 positive integers?
• The circumference of a circle with radius 6 is 12π. Which expression gives the circumference?
• The data set {1,1,2,2,2,3} has which mode?
• How many days would it take the dog to eat 28 cans at that rate?
• What is the distance between the points (1,2) and (4,6)?
• A rope of length 30 units is cut into two pieces such that the longer piece is twice the shorter. What are the lengths?
• Which equation represents the line through (0, 2) with slope 2?
• If a car travels at 60 mph for 2 hours and 40 minutes, how far does it travel?
• Evaluate cos 30°.
• What is tan 45 degrees?
• A line parallel to the line y = -2x + 7 has which slope?
• The 5th term of the geometric sequence 1, -3, 9, -27, ... is what?
• Using the same distance-time relation, what is d when t = 7?
• These are the monthly car sales for last year: 25, 15, 22, 19, 16, 13, 19, 25, 25, 27, 28, 29. What is the median value of this data set?
• If f(x) = x − 1/x and g(x) = 1/x, what is f(g(1/2))?
• For f(x) = (x - 2)^2, what is the minimum value?
• If tan theta = 5/12 and theta is in the first quadrant, what is sin theta?
• Which statement describes the solution set for the inequality |x - 5| < -1?
• Compute (2/3) ÷ (4/5). Which fraction is the result?
• If ∠BAC = 60° in the same configuration as the previous angle-question, what is ∠BAD?
• What is the rate, in cans per day, at which the dog eats?
• Which of the following is the y-intercept of the line y = -x + 1?
• A sector of a circle has radius 8 and central angle 120 degrees. What is its area?
• The quotient and remainder when dividing x^3 - 6x^2 + 11x - 6 by (x - 2) are?
• What fraction lies exactly halfway between 2/3 and 3/4?
• On a map where 1/2 inch represents 18 miles, about how many miles apart are two towns that are 2.5 inches apart?
• A container is initially 1/8 full of liquid. After adding 10 cups, the container becomes 3/4 full. What is the container’s total capacity in cups?
• What is the distance between the points (0,0) and (3,4)?
• What is the slope of a line perpendicular to y = x?
• On a map with scale 1 inch represents 2 feet, an object 18 feet long would be how many inches long on the map?
• How many ways to choose 2 items from 5 without regard to order?
• Factor the quadratic expression x^2 - 4x - 5.
• A fair six-sided die is rolled. What is the probability of getting an even number?
• In a circle graph representing hours, if a sector has a central angle of 160°, what percent of the circle does it represent?
• In a triangle with sides 14 cm, 18 cm, and 20 cm, which equation expresses the Law of Cosines for the angle opposite the smallest side 14?
• What is the larger root of x^2 - 5x + 6 = 0?
• The line through (0,-1) and (2,3) has slope 2. Which equation represents that line?
• The range of the data set {6, 10, 14, 14, 20} is?
• How many permutations exist for five distinct items?
• Which equation represents the line perpendicular to y = x that passes through (0,1)?
• A car accelerates from 88 feet per second to 220 feet per second in 3 seconds (constant acceleration). What is the acceleration in ft/s^2?
• What is the distance between the two intersection points of the circle x^2 + y^2 = 16 and the line x + y = 0?
• If the average of the numbers 4, 7, x, and 13 is 9, what is x?
• If sin θ = 3/5 and θ is in Quadrant II, what is cos θ?
• In a right circular cone with base radius 5 inches and height 7 inches, the angle θ is formed between the slant height and the radius. Which equation expresses tan θ?
• Compute (a + b)^2 when a = 3 and b = 4.
• A puzzle box contains 750 regular pieces and 5 extra pieces that do not fit. If you randomly select one piece, what is the probability that it is an extra piece?
• Last month, Lucie had total expenditures of $900. The category with the greatest expenditure was Clothes at $254. What percent of the total expenditures does this represent, to the nearest 1%?
• In a diagram, ∠BAC = x + 20°, ∠BAD = 90°. What is ∠CAD?
• Domain of f(x) = sqrt(x - 1) is which of the following?
• How many permutations exist for four distinct items?
• What is the equation of the parabola with vertex at (0, -4) that passes through (3, 5)?
• If two triangles are similar with scale factor 2:1, what is the ratio of their areas?
• A fair die is rolled. What is the probability of rolling an even number?
• Which of the following describes the solution set of the inequality x^2 - 4x - 5 > 0?
• The quadratic y = ax^2 + bx + c is graphed in the coordinate plane. When y = 0, which statement best describes the real solutions for x if a > 0 and c < 0?
• Simplify sqrt(50).
• What is the measure of each interior angle of a regular octagon?
• A shipping rate for a 15-pound box is calculated as a fixed fee plus a per-pound charge. If the fee and rate yield a total of $19.75 for 15 pounds, which is the total shipping cost?
• Solve 2(x - 3) = 4x + 1 for x.
• Solve the system: 2x + 3y = 12 and x - y = 1. What are the values of x and y?
• For the system x + y = 7 and 2x - y = 1, what is y?
• Using the relation d = 6t + 14, what is d when t = 5?
• Evaluate 4/√2 + 2/√3 and select its equivalent expression from the options.
• In a plane, lines AB and CD intersect at A with A between C and D. If ∠BAC = 47°, what is ∠BAD?
• Compute the product (-3i + 4)(3i + 4).
• Write the equation of the circle with center at (0,0) and radius 5.
• Solve the system 3x - y = 5 and x + y = 3.
• What is the value of g(2) if g(x) = 1/x?
• From the system 2x + 3y = 12 and x - y = 1, what is y?
• Solve |2x - 5| = 7 for x.
• In a study of 150 people, what is the probability that a randomly selected person has Type A or Type AB blood?
• Jorge's current hourly wage is $12.00. At the start of next month, his wage increases by 6%. What is the new hourly wage?
• A parabola with vertex at (0, -4) passes through (1, -3). What is its equation?
• If two events A and B are independent with P(A)=0.5 and P(B)=0.6, what is P(A ∩ B)?
• The mean of numbers 3, 7, 7, 7, 9 is what?
• If the radius is tripled, by what factor does the circle's area increase?
• A rectangle extends from x = -5 to x = 7. The vertical line that cuts the rectangle into two regions of equal area is x = k. What is k?
• In scientific notation, 670,000,000 + 700,000,000 equals which of the following?