Officer Aptitude Rating (OAR) Formulas Practice Test

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• What is the formula for the volume of a cone with radius r and height h?
• If 750 g of mass occupies 300 mL, what is the density in g/mL?
• If the mass doubles while velocity and radius remain constant, how does the angular momentum L change given L = m v r?
• The distance between two points (x1, y1) and (x2, y2) is given by which of the following formulas?
• In projectile motion with no distance, which relation holds between final velocity, initial velocity, acceleration, and time?
• If a circle's radius is halved, how does the area change relative to the original area?
• A cylinder has radius 5 units and height 10 units. What is its lateral surface area?
• In a simple machine, mechanical advantage MA is defined as what?
• A product is bought for 100 and sold for 120. What is the percent profit?
• A savings account earns simple interest at 5% per year. If you start with P = 1000 and t = 3 years, what is the amount A using A = P(1 + rt)?
• If a car's fuel efficiency is 35 miles per gallon, how many gallons are needed to travel 420 miles?
• Which statement correctly defines velocity?
• For molarity, which option correctly identifies its unit?
• In the formula A = 4πr², how does the area change if the radius is doubled?
• A cylinder has radius 3 units and height 7 units. What is its lateral surface area?
• Convert 60 minutes to hours.
• For an arithmetic series with first term a1 = 2 and sixth term a6 = 12, what is S6?
• Compute the area of a triangle with base 6 units and height 4 units.
• Which form correctly defines hydrostatic pressure at a depth in a liquid?
• If the distance traveled increases while height stays fixed, what happens to the friction coefficient μ defined as height / distance traveled?
• Which is the formula for compound interest with annual compounding?
• Which unit correctly represents a joule?
• If three items have values 50, 70, and 80, what is the weighted average with weights 2, 3, and 1 respectively?
• In projectile motion with no final velocity, distance is given by which expression?
• A notebook contains 60 pages, 25 of which are blank. What is the percent of blank pages?
• What is the permutation formula P(n, r)?
• What is the area formula for a trapezoid with height h and bases b1 and b2?
• Which equation correctly defines kinetic energy?
• A rectangular prism has length 2, width 3, height 6. What is its volume?
• For R1 = 16 Ω and R2 = 8 Ω in parallel, which is the correct equivalent resistance?
• What is the area of a circle with radius 7?
• The weight of a 1-kilogram mass on Earth is approximately how many newtons?
• If a block weighs W and is moved up a ramp with height H and base D, which formula gives the required force along the ramp?
• In projectile motion, distance d is given by which expression?
• Find the volume of a rectangular prism with length 3, width 4, and height 5.
• In the simple interest formula, what does p stand for?
• The equivalent resistance of two resistors R1 and R2 in parallel is given by which expression?
• What is the probability of blue when drawing a ball from a bag containing 3 red and 2 blue balls?
• A map scale is 1 inch represents 40 miles. If the map distance is 2.5 inches, what real distance does it represent?
• The mean of data set {2, 4, 6, 8, 10} is what?
• The unit of work, given W = F × d, is which of the following?
• Which formula computes the area of a circle?
• The median of the set {1, 3, 7, 7, 9} is what?
• Which expression uses A given B to compute P(A and B)?
• Which equation expresses Hooke's law for a spring?
• The total surface area of a cylinder with radius 3 and height 7 is what?
• One kilogram weighs approximately how many newtons on Earth?
• Which statement about torque sign convention is correct?
• What is the percent error formula?
• What is the work (potential energy) stored in a spring stretched by displacement x?
• A cone has radius 4 units and height 9 units. What is its volume?
• Which formula gives the area of a regular hexagon with side length s?
• In the weighted average example, which expression represents the weighted average?
• If five numbers have a total of 30, what is their mean?
• A parallelogram has base 10 units and height 4 units. What is its area?
• Which formula defines flow rate as a product of velocity and cross-sectional area?
• If gear A has N_A teeth and gear B has N_B teeth, the ratio of revolutions of B to A is equal to which quantity?
• Which expression equals the volume of a cone?
• A sphere has radius 6 units. What is its surface area?
• Acceleration is defined as which of the following?
• A train travels 180 miles at 60 mph. How long does the trip take?
• Under a scaling transformation with factor k = 3, what is the image of the point (2, -4)?
• If height remains constant and gravity unchanged, how does doubling mass affect potential energy?
• Which formula gives the volume of a sphere with radius r?
• A line has slope 3 and passes through (0, 2). What is the equation in slope-intercept form?
• For two resistors in parallel, the equivalent resistance is always which relation to the smallest resistor?
• Which expression equals the volume of a sphere?
• Impulse has the same dimension as which of the following?
• Which formula gives the area of a circle in terms of the diameter d?
• Which formula would you use to compute the surface area of a cylinder?
• Which equation represents the ideal gas law?
• The area of a circle with diameter 14 units is what?
• Which formula gives the volume of a cube with side length s?
• Work is defined as which product?
• If a rectangle has one side of 8 units and a diagonal of 10 units, what is the length of the other side?
• Which value is equivalent to 1 cubic meter in liters?
• In the spring force equation F = -k x, what does x denote?
• In a fair coin flip, what is the probability of not getting heads on a single flip?
• Which formula expresses resistance in terms of resistivity, length, and cross-sectional area?
• Which formula calculates the volume of a cylinder with radius r and height h?
• If a square has side length s, what is its diagonal length in terms of s?
• Using C = (F - 32) * 5/9, what is the Celsius temperature when F = 68?
• Which expression is the correct formula for the volume of a rectangular prism?
• In the simple interest formula, what does r stand for?
• If the side length of a regular hexagon is doubled, by what factor does the area increase?
• In the simple machine context, which statement is true?
• In projectile motion with no acceleration, distance is given by which formula?
• What is the standard formula for P(n, r) (permutation)?
• Which expression represents the area of a circle with radius r?
• Convert 135 minutes to hours.
• In the projectile displacement formula d = v_f t − (1/2) a t^2, what does v_f stand for?
• For a fixed volumetric flow rate, how does reducing pipe cross-sectional area affect velocity?
• Which conversion is correct for liters to cubic meters?
• If y = k/x^2 and x = 2 yields y = 3, what is the value of k?
• If a circle has a radius of 5 units and a central angle of 180 degrees, what is the arc length?
• In a right triangle the legs are 3 and 4 units. What is the length of the hypotenuse?
• In a fluid system, which form expresses work as pressure × change in volume?
• Which expression is a valid formula for P(A or B)?
• Scaling a polygon by a factor k maps a point (x, y) to which coordinates?
• In the friction formula F = μ × weight × 9.81, the weight term is interpreted as which of the following in the given context?
• A sphere has radius 2 units. What is its volume?
• If the diameter of a circle doubles, by what factor does the area increase?
• In a lever with fulcrum, which expression gives input force F given load R, with L1 as effort arm and L2 as load arm?
• A circle has radius 9 units. What is its area?
• A scientist mixes 3 L of 20% saline with 2 L of 60% saline. What is the final concentration?
• A speed problem: If you drive at 55 mph for 2.5 hours, what distance do you cover?
• Using the slant height you computed, what is the cone's total surface area?
• The angular velocity ω is defined as which ratio when the velocity is perpendicular to the radius?
• The circumference of a circle with radius r is given by which formula?
• If the tangential speed stays the same but the radius doubles, the angular velocity ω will which of the following?
• Which equation describes displacement during projectile motion with no initial velocity?
• If a stock increases by 30% and then decreases by 25%, what is the overall percentage change?
• With annual compounding at 5% over 2 years, the amount is A = ?
• Which formula defines machine efficiency?
• In the simple interest formula, what does t stand for?
• In data analysis, which statement defines an outlier using the interquartile range (IQR) method?
• A mass of 6 kg occupies a volume of 2 m^3. What is the density?
• The force needed to move an object against friction is given by which formula?
• What is the formula for the z-score of a value x given the mean and standard deviation?
• Which expression represents P(A and B) as the product of P(A) and P(B)?
• A rectangle has one side of 6 units and a diagonal of 10 units. What is the length of the other side?
• Which expression represents the mechanical advantage in a screw jack with threaded portion length L, thread pitch p, and lever length R?
• If resistivity increases while length and cross-sectional area stay the same, what happens to resistance?
• In fluid work, which expression is a correct form for the work done by the fluid?
• Momentum is defined as which product?
• The distance equals speed times time. If a vehicle travels 500 meters in 20 seconds, what is its speed?
• The conductivity of a material is the reciprocal of its resistivity. Which expression correctly shows this relationship?
• Which equation expresses the time required for a trip, given distance and speed?
• A liquid mixture contains 40% solute. If you have 200 mL of solution, how many mL of solute are present?
• Which expression gives the area of a trapezoid?
• Which formula gives the slant height l of a right circular cone?
• Which equation defines current in terms of charge and time?
• Two workers complete a job in 4 hours and 6 hours respectively. If they work together, how long to finish the job?
• A triangle with sides 5, 12, and 13 is a right triangle. Verify using Pythagoras.
• The impulse of a force is defined as which of the following?
• The angular momentum L of a particle with mass m moving with velocity v perpendicular to the radius r is given by which expression?
• Which statement defines work in physics?
• Which expression relates velocity squared to work and mass for a given object?
• If two quantities are inversely proportional, y = k/x and x = 4 when y = 6, what is k?
• Which expression defines density?
• Three workers complete a job with rates of 1/8, 1/6, and 1/12 job per hour, respectively. What is the total time for all three to finish the job?
• The angular momentum for a rotating point mass can be written as L = I ω. For a point mass, which expression is equivalent?
• What is the formula for the total surface area of a cone in terms of radius r and slant height l?
• Which expression defines electrical power in terms of work and time?
• In a 2nd class lever, which order correctly lists fulcrum, load, and effort?
• The angular momentum L can also be written as L = I ω. For a point mass, I = m r^2, so L equals which expression?
• Which equation correctly defines Ohm's law for voltage?
• If a system does 100 J of work in 4 seconds, what is the average power?
• Which formula gives arc length on a circle in terms of central angle and radius?
• What is the ratio of red balls to total balls in a bag containing 3 red and 2 blue balls?
• If y = k/x and y = 3 when x = 6, what is k?
• If 1 inch represents 40 miles, how many inches represent 100 miles?
• What is the expression for the combination C(n, r)?
• Which description correctly describes pressure around an airplane wing?
• A right circular cone with radius 4 and height 9, what is the slant height?
• In the ideal gas law, if temperature and moles are constant and the volume is doubled, what happens to pressure?
• Which formula expresses the force exerted on an object according to Newton's second law?
• In a wheel-and-axle system, which formula gives the input force F when the load is L, wheel radius is R, and axle radius is r?
• A complete revolution corresponds to how many radians?
• A 5-liter mixture contains 40% solute. How many liters of solute are present?
• What is the combination formula C(n, r)?
• In a 3rd class lever, which order correctly lists load, effort, and fulcrum?
• In a class of 200 students, 160 passed. What percent passed?
• In the inclined plane, sine of the angle is equal to which ratio?
• A loan with annual interest rate 6% compounded annually for 2 years on a principal of 1000. What is the amount A?
• In electrical circuits, which statement about current direction is correct?
• What determines the mechanical advantage of a pulley system?
• Which expression represents the simple interest formula?
• What is a Perfect Number?
• Which expression represents the area of a triangle with base b and height h?
• According to the given definition, what is μ equal to?
• A sphere has radius 6 units. What is its volume?
• The trapezoid has bases 8 and 3 units and height 4 units. What is its area?
• A class has 120 students; 90 passed. What percent passed?
• The tangential speed v at distance r from the rotation axis relates to angular velocity ω by which equation?
• A circle has radius 3 units. What is its circumference?
• In a 1st class lever, which order correctly lists load, fulcrum, and effort?
• Which formula represents max displacement as a function of time?
• A bag contains 3 red and 2 blue balls. If one ball is drawn at random, what is the probability of red?
• Molarity is defined as the amount of solute per liter of solution. What is the correct definition?
• A rectangle has length 8 units and width 3 units. What is its perimeter?
• Which formula gives P(A or B) in terms of P(A), P(B), and P(A and B)?
• What is the common base for logarithms?
• Which expression represents energy as the product of work and force?
• Which statement correctly describes a 3rd class lever based on the given sequence?
• A circle has radius 5 units. What is its circumference?
• Which equation correctly defines potential energy in a uniform gravitational field?
• Hydrostatic pressure at depth h in a fluid with density ρ is given by which expression?
• Density is mass per volume. If 500 g of material occupies 250 mL, what is the density in g/mL?
• Which expression represents the surface area of a sphere?
• If n, R, and T are constant in the ideal gas law, what happens to P V?
• The constant 9.81 m/s^2 in the friction formula is most directly associated with what physical quantity?
• If a stock increases by 25% and then decreases by 20%, what is the overall percentage change?