ACT Mathematics Practice Test

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• What is f(2) if f(x) = x − 1/x?
• How many real solutions does the quadratic x^2 + 3x - 4 = 0 have?
• Using sin^2 θ + cos^2 θ = 1, if cos θ = 1/2 and θ is in the first quadrant, what is sin θ?
• Solve for x: 2^x = 32.
• 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%?
• 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?
• If an isosceles right triangle has leg length 6, what is its perimeter?
• Using the same distance-time relation, what is d when t = 7?
• 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?
• What is the mean of the set 2, 4, 6, 8?
• The graphs of f(x) = (x - 3)^2 + 2 and g(x) = (1/2)x + 1 intersect at exactly how many x-values?
• What is the median of the set {1, 3, 3, 3, 7}?
• Which equation represents the line perpendicular to y = x that passes through (0,1)?
• 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?
• The mode of the data set {5, 5, 7, 9, 9, 9, 11} is?
• 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?
• A fair coin is flipped twice. What is the probability of at least one heads?
• 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?
• In scientific notation, 670,000,000 + 700,000,000 equals which of the following?
• Solve the system 2x + y = 5 and x - y = 1. What are the values of x and y?
• 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?
• On a map where 1/2 inch represents 18 miles, about how many miles apart are two towns that are 2.5 inches apart?
• Flip a fair coin twice. What is the probability of getting exactly one head?
• If the average of 4, 7, x, and 11 is 9, what is x?
• Domain of f(x) = sqrt(x - 1) is which of the following?
• 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?
• From the system x + y = 7 and 2x - y = 1, what is the value of x?
• In a study of 150 people, what is the probability that a randomly selected person has Type A or Type AB blood?
• If f(x) = 3x + 4, what is f^{-1}(7)?
• In a 30-60-90 right triangle, with hypotenuse length 2, what are the lengths of the legs?
• What is f(2) for f(x) = (3x + 7)^2?
• A parabola with vertex at (0, -4) passes through (1, -3). What is its equation?
• The data set {1,1,2,2,2,3} has which mode?
• In a diagram, ∠BAC = x + 20°, ∠BAD = 90°. What is ∠CAD?
• Isosceles right triangle has a hypotenuse of 8√2 inches. What is its perimeter?
• Find the area of a trapezoid with bases 3 and 9 and height 5.
• A sector of a circle has radius 8 and central angle 120 degrees. What is its area?
• On the same map, how many miles are 3 inches apart?
• For f(x) = (x - 2)^2, what is the minimum value?
• A rectangular floor measures 18 feet by 12 feet. Cabinets cover 36 square feet. What area must be tiled?
• How many ways are there to choose 3 items from 5 when order does not matter?
• Compute (3 + 4)^2.
• 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?
• Evaluate sin 60°.
• The circumference of a circle with radius 6 is 12π. Which expression gives the circumference?
• Compute the product (-3i + 4)(3i + 4).
• 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?
• The quotient and remainder when dividing x^3 - x^2 + x - 4 by (x - 2) are respectively?
• A circle has diameter 6. What is its area?
• Solve 2x + 3 = 7. What is x?
• What is the slope of a line perpendicular to y = x?
• What is the mean of the numbers 3, 8, 10, and 15?
• Using the relation d = 6t + 14, what is d when t = 5?
• 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?
• In a box containing 750 regular pieces and 5 extras, what is the probability of selecting a normal piece?
• If the radius is tripled, by what factor does the circle's area increase?
• In a triangle with side lengths 14 cm, 18 cm, and 20 cm, which angle is smallest?
• In a 45-45-90 triangle, if a leg length is 6, what is the length of the hypotenuse?
• The area of a triangle with base 8 and height 5 is 20 square units. What is the area?
• Divide (2x^3 - 3x^2 + x - 5) by (x - 2). What is the quotient and remainder?
• What is the equation of the parabola with vertex at (0, -4) that passes through (3, 5)?
• What is the rate, in cans per day, at which the dog eats?
• What is cos 60 degrees?
• Find the intersection points of the circle x^2 + y^2 = 16 and the line x + y = 0.
• The slope of the line through (0,2) and (4,6) is?
• In a right triangle with legs 6 and 8, what is the length of the hypotenuse?
• The expression (x^2 - 16)/(x^2 - 4x) simplifies to what, for x ≠ 0, 4?
• Which statement describes the solution set for the inequality |x - 5| < -1?
• What is the distance between the points (0,0) and (3,4)?
• The circumference of a circle with radius 6 is 12π. What is the circumference for a circle with radius 3?
• Simplify sqrt(50).
• What is the sum of the first 20 positive integers?
• Solve for x: (x - 2)/(x + 4) = 3/5, with x ≠ -4.
• In a right triangle with legs 5 and 12, the hypotenuse is 13. Which value is the hypotenuse?
• The geometric sequence starts with 1, -3, 9, -27, ... What is the seventh term?
• The area of a triangle with base 12 and height 5 is?
• What is the area of a circle with radius 6?
• The median of the data set {3, 7, 8, 12, 14} is?
• The slope of CD is sought for points C(9,4) and D(12,1). What is the slope of CD?
• If tan theta = 3/4 and theta is in the first quadrant, what is sin theta?
• The range of the data set {2, 4, 9, 9, 15} is?
• Convert 0.75 to a fraction.
• Factor the polynomial 6x^2 - 9x.
• What is the inverse function of f(x) = 3x - 7?
• If ∠BAC = 60° in the same configuration as the previous angle-question, what is ∠BAD?
• 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?
• For the system x + y = 7 and 2x - y = 1, what is y?
• Solve |2x - 5| = 7 for x.
• Which description matches the graph of the region defined by 1 < x + y < 2?
• 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?
• If sin θ = 3/5 and θ is in Quadrant II, what is cos θ?
• Compute 2^3 * 2^4.
• 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?
• If x:y = 5:2 and y:z = 3:2, what is the ratio x:z?
• Compute (a + b)^2 when a = 3 and b = 4.
• Solve 3y - 4 = 2y + 9.
• What is the distance between the two intersection points of the circle x^2 + y^2 = 16 and the line x + y = 0?
• For f(x) = (x - 2)^2, what is the x-coordinate of the vertex?
• If f(x) = 4 * 2^x, what is f(3)?
• 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?
• What is sin 30 degrees?
• If a point at (3, -7) is reflected across the y-axis, which are its coordinates after the reflection?
• Solve |2x - 5| = 7.
• 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?
• The volume of a rectangular prism with length 3, width 4, height 5 is 60. Which value is the volume?
• What is the radius of the circle defined by x^2 + y^2 = 25?
• The range of the data set {6, 10, 14, 14, 20} is?
• Simplify the rational expression (x^2 - 9)/(x^2 - 3x) for x ≠ 0, 3. Which expression is equivalent?
• Evaluate cos 30°.
• From the system 2x + 3y = 12 and x - y = 1, what is y?
• 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?
• Find the slope of the line through (0,0) and (4,6).
• What is the mean of the monthly fees for the five colleges: 370, 310, 380, 340, and 310?
• The quotient and remainder when dividing x^3 - 6x^2 + 11x - 6 by (x - 1) are?
• If f(x) = sqrt(x) and g(x) = x - 1, the domain of f(g(x)) is:
• If sin θ = 3/5 and θ is in the first quadrant, what is cos θ?
• If tan theta = 5/12 and theta is in the first quadrant, what is sin theta?
• 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?
• What fraction lies exactly halfway between 2/3 and 3/4?
• Find the area of a semicircle with radius 7.
• Evaluate f(-2) for f(x) = 2x^2 - 3x + 1.
• Evaluate the product (-2i + 5)(2i + 5).
• The 5th term of the geometric sequence 1, -3, 9, -27, ... is what?
• How many permutations exist for four distinct items?
• What is the larger root of x^2 - 5x + 6 = 0?
• 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?
• 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 tan 45 degrees?
• 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?
• A rectangle has width 6 and area 60. What is its length?
• Given f = c d^3, with f = 450 and d = 10, what is c?
• What is sin 0 degrees?
• How many days would it take the dog to eat 28 cans at that rate?
• If y = 2x + 5 and x = -3, what is y?
• The mean of numbers 3, 7, 7, 7, 9 is what?
• 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?
• 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?
• A rectangle has area 54 square centimeters and length 9 cm. What is its perimeter?
• Which of the following is the correct ascending order of the numbers 1/2, 5/6, and 5/8?
• If f(x) = 2x + 3 and g(x) = x^2, what is (f ∘ g)(2)?
• If two similar triangles have a linear scale factor of 3:5, what is the ratio of their areas?
• If two events A and B are independent with P(A)=0.5 and P(B)=0.6, what is P(A ∩ B)?
• The quotient and remainder when dividing x^3 - 6x^2 + 11x - 6 by (x - 2) are?
• 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 a plane, lines AB and CD intersect at A with A between C and D. If ∠BAC = 47°, what is ∠BAD?
• Using the Law of Cosines, with a = 5, b = 7, and included angle C = 60 degrees, what is c?
• Which of the following is the y-intercept of the line y = -x + 1?
• Evaluate 4/√2 + 2/√3 and select its equivalent expression from the options.
• If the average of the numbers 4, 7, x, and 13 is 9, what is x?
• 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?
• How many ways to arrange 4 distinct letters A, B, C, D?
• Which expression is equivalent to 1/2 y^2 (6x + 2y + 12x - 2y)?
• In a circle graph representing hours, if a sector has a central angle of 160°, what percent of the circle does it represent?
• What is the probability of drawing a red card from a standard deck?
• A dog eats 7 cans of food in 3 days. At this rate, how many cans are eaten in 3 + d days?
• 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?
• If two triangles are similar with scale factor 3:2, what is the ratio of their areas?
• A fair six-sided die is rolled. What is the probability of getting an even number?
• Which of the following describes the solution set of the inequality x^2 - 4x - 5 > 0?
• If a = 3 and b = 4, what is (a + b)^2?
• A line passes through the points (0, 2) and (3, 8). What is its slope?
• How many ways to choose 3 items from 6 without regard to order?
• How many permutations exist for five distinct items?
• If f(x) = x − 1/x and g(x) = 1/x, what is f(g(1/2))?
• In a right triangle with legs 5 and 12, the square of the hypotenuse equals what?
• In a right triangle with legs 9 and 12, what is the hypotenuse?
• Which statement about h(x) = |x - 3| is true?
• Using d = 6t + 14, what is d when t = 7?
• What is the slope of the line through points (4, -3) and (7, 5)?
• If f(x) = 2x + 3 and g(x) = x^2, what is (g ∘ f)(1)?
• If log base 10 of x equals 2, what is x?
• What is the area of a circle with radius 6?
• 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?
• If f(x) = x^2, what is f(5)?
• The line through (0,-1) and (2,3) has slope 2. Which equation represents that line?
• A line perpendicular to y = -2x + 7 has what slope?
• Find the sum of the arithmetic sequence with first term 5, common difference 3, and 7 terms.
• What is the equation of the line through (2,-3) that is perpendicular to y = x?
• What is the measure of each interior angle of a regular octagon?
• If a dog eats 7 cans in 3 days, how many cans are eaten in 9 days?
• 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?
• Factor and solve: x^2 - 5x + 6 = 0. Which of the following expresses the solutions?
• If a, b, and c are positive integers such that a^b = x and c^b = y, then xy = ?
• Compute 3^4 * 3^(-2).
• Which inequality describes the interior of a circle with center (1, 2) and radius 3?
• Simplify sqrt(50).
• What is the inverse function of f(x) = 2x + 3?
• 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?
• Solve 3x - 5 = 16.
• On a map with scale 1 inch represents 2 feet, an object 18 feet long would be how many inches long on the map?
• If f(x) = (3x + 7)^2, what is f(1)?
• What is the sum of the solutions to |2x - 5| = 7?
• For f(x) = 3x + 4, which is f(2)?
• Write the equation of the circle with center at (2, -1) and radius 5.
• How many ways to choose 2 items from 5 without regard to order?
• Factor the quadratic expression x^2 - 4x - 5.
• Which equation expresses the Law of Cosines for the angle opposite the largest side 20 in a triangle with sides 14, 18, and 20?
• If two similar triangles have a linear scale factor of 2:7, what is the ratio of their areas?
• Solve 2(x - 3) = 4x + 1 for x.
• The minimum value of f(x) = (x - 2)^2 is which value?
• The vertex of the parabola y = x^2 - 4x + 5 is at:
• Solve by quadratic formula: 2x^2 - 4x - 6 = 0. Which are the solutions?
• How many intersection points does the line y = 2x + 3 have with the circle x^2 + y^2 = 25?
• Find the area of a trapezoid with bases 5 and 9 and height 4.
• The area of a circle with radius 3 is 9π. Which option equals the area?
• What is the probability of rolling a 5 or a 6 on a fair six-sided die?
• Using f(x) = (3x + 7)^2, what is f(-1)?
• Solve the system: 2x + 3y = 12 and x - y = 1. What are the values of x and y?
• 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?
• 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?
• Factor by grouping: x^3 - 3x^2 + 2x - 6.
• For f(x) = (x - 2)^2, what is the y-coordinate of the vertex?
• Find the equation of the line through points (0,-1) and (2,3).
• Which equation represents the line through (0, 2) with slope 2?
• Solve for x: 3x - 7 = 2x + 5.
• A rope of length 30 units is cut into two pieces such that the longer piece is twice the shorter. What are the lengths?
• A line parallel to the line y = -2x + 7 has which slope?
• What is (f ∘ g)(3) for f(x) = 2x + 3 and g(x) = x^2?
• 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?
• A fair die is rolled. What is the probability of rolling an even number?
• 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?
• The slope of the line through (0,2) and (4,-2) is what?
• Which statement describes the domain of y = sqrt(x - 1)?
• What is the value of g(2) if g(x) = 1/x?
• Which of the following expresses the solution set for the compound inequality -5 < 1 - 3x < 10?
• 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?
• 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?
• Compute (2/3) ÷ (4/5). Which fraction is the result?
• If point D has coordinates (12, 1) and is reflected across the y-axis to D', what are the coordinates of D’?
• If f(x) = x^2 and g(x) = 2x + 1, what is f(g(2))?
• 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?
• Solve the system 3x - y = 5 and x + y = 3.
• If a car travels at 60 mph for 2 hours and 40 minutes, how far does it travel?
• If the radius of a circle is doubled, by what factor does its area increase?
• If two triangles are similar with scale factor 2:1, what is the ratio of their areas?
• Write the equation of the circle with center at (0,0) and radius 5.
• Evaluate f(0) for f(x) = 2x^2 - 3x + 1.
• Simplify ((2^3)^4).
• What is the distance between the points (1,2) and (4,6)?
• A rectangular solid has surface area A = 2lw + 2lh + 2wh. If each dimension is doubled, by what factor is the surface area multiplied?