PSAT 8/9 Math Practice Test

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• What is the mode of the numbers 1, 2, 2, 3, 5?
• Area of trapezoid with bases 8 and 5 and height 4?
• What is the equation of the vertical line through x = -7?
• Which letter is commonly used to denote an unknown value in algebra?
• Solve 2^x = 16 for x.
• Find the midpoint of the line segment with endpoints (2, -3) and (8, 7).
• Dave is d years old. Tracy is twice Dave's age. What is the SUM of Dave and Tracy's ages, in terms of d ?
• Find the equation of the line with slope 3 that passes through the point (0, -2).
• In mathematical statements, the word 'of' typically indicates which operation?
• The distance between (0,0) and (3,4) is 5.
• Perpendicular lines have which type of slopes?
• If a = 2 and c = 6 in the quadratic ax^2 + bx + c = 0, what is the product of the roots?
• Factor x^2 - 5x + 6.
• Factor out the greatest common factor from 3x^2 - 12x - 36; which of the following is the correct factored form?
• Which equation represents inverse variation, where the product of two variables remains constant?
• Simplify: (3x^2 - 12x) / (3x) for x ≠ 0.
• If two angles of a triangle measure 50 degrees and 60 degrees, what is the measure of the third angle?
• What is the probability of drawing an ace from a standard deck on a single draw?
• What is the y-intercept of y = -2x + 7?
• If a circle has radius 5, its circumference is 2πr. Which expression gives the circumference?
• What is Sonya's age in terms of Dave's age d, given Sonya is three times Dave's age?
• Solve for x: 3x + 7 = 22.
• The sum of an arithmetic sequence with first term 2, common difference 1, and n terms is 35. What is n?
• What is the fully factored form of 3x^2 - 12x - 36?
• Which term describes a percentage of a sale price paid to a salesperson?
• What is the mean (average) of the numbers 4, 7, 9, and 13?
• A circle with radius 4 has area 16π. Which of the following is equal to the area?
• Which expression gives the perimeter of a square with side length s?
• What does percent mean in arithmetic?
• Simplify (3r)^3
• What is the fifth term of the arithmetic sequence that starts with 2 and has a common difference of 3?
• The slope of a horizontal line is?
• If a square has side length 5, its perimeter is?
• A triangle has base 12 and height 5. What is its area?
• The equation 2x + 3y = 12 in slope-intercept form is y = mx + b. Which equation correctly represents it?
• Factor x^2 - 4x - 5.
• Solve the system: x + y = 7 and x - y = 1. What are x and y?
• What is the minimum value of f(x) = (x - 3)²?
• What is the slope-intercept form of a line with slope -2 that passes through (0, 5)?
• A rectangular prism has length 3, width 4, and height h. If its volume is 72 cubic units, what is h?
• A triangle has two angles measuring 30 degrees and 70 degrees. What is the measure of the third angle?
• The slope of the line through (1,2) and (3,8) is which?
• Solve 3x + 9 = 0.
• In similar triangles, what is true about the ratio of corresponding sides?
• Solve 3x^2 = 27 for the positive value of x.
• If two angles of a triangle are 60° and 60°, the third angle is?
• For a quadratic equation ax^2 + bx + c = 0, the sum of the roots is given by which expression?
• What is the common difference of the arithmetic sequence 2, 5, 8, 11, ... ?
• What is 2^0?
• The vertex of the parabola y = (x - 3)² + 1 is at
• In similar triangles, the shorter side of the small triangle is 4, and the ratio small:large is 2:5. What is the corresponding length of the larger side?
• The mean of the numbers 4, 8, 12 is what?
• Is a triangle with sides 7, 7, 7 equilateral?
• What is the value of (6y)^3 in simplest form?
• The y-intercept of the line 3x - 2y = 6 is what point?
• What is the average of the numbers 2, 8, 10, and 14?
• The distance between points (1,2) and (4,6) is?
• Which trig ratio is opposite over hypotenuse?
• The distance between (0,0) and (3,4) is?
• Convert 0.75 to a fraction.
• Solve for x: 4x + 3 = 19.
• Dave is d years old. Sonya is three times Dave's age. Gavin is 20 years old. What is the sum of their ages in terms of d?
• A rectangle has length 10 and width w. If the area is 40, what is w?
• Simplify (5r)^2
• The area of a trapezoid with bases 6 and 2 and height 4 is?
• Which symbol represents 'less than or equal to'?
• A percentage fee of the sales price paid to a salesperson is known as a _______.
• What is the slope of the line through the points (2, -1) and (5, 4)?
• If a = 3 and b = -6 in the quadratic ax^2 + bx + c = 0, the sum of the roots equals what?
• Parallel lines have what type of slopes?
• A bag contains 3 red and 2 blue balls. What is the probability of drawing a red ball?
• The perimeter of a square is 28. What is the side length?
• What is the y-intercept of the line that passes through (0,0) and (2,3)?
• In a right triangle with legs 3 and 4, the length of the hypotenuse is which of the following?
• Solve for x: 2x - 3 = x + 4.
• What is Sonya's age minus Dave's age in terms of d?
• What is the greatest common factor that can be factored from 3x^2 - 12x - 36?
• A line passing through origin with slope -2 has equation?
• If x:y = 3:5, what fraction of the total does x represent?
• A price increases by 20% to become 60. What was the original price?
• If a smaller triangle has a shorter side of 6 and the ratio small:large is 2:5, what is the corresponding length of the larger side?
• Dave is four years old. Tracy is twice Dave's age. How old is Tracy?
• Solve the system: 3x - y = 7 and x + y = 5. Find x and y.
• If two numbers have sum 11 and difference 3, what are the numbers?
• 10% as a decimal equals which value?
• A line has slope -3/4. What is the slope of a line perpendicular to it?
• What is the standard formula for the surface area of a rectangular prism with length l, width w, and height h?
• If f(x) = 2x - 5, what is f(4)?
• In the equation 3y - 4x = 12, solve for y in terms of x.
• The area of a circle with radius 3 is which of the following?
• For the line y = -2x + 5, what is the y-intercept?
• For the equation 3x - 4y = 12 written in standard form Ax + By = C, what is the slope of the line?
• Which mnemonic helps remember the sine, cosine, and tangent ratios?
• Expand (x + 3)(x + 5).
• If a fair coin is flipped twice, what is the probability of exactly one head?
• Simplify (2x)^2
• Evaluate y = 2x^2 - 3x + 1 at x = -1.
• If the ratio of boys to girls is 3:4 and there are 21 boys, how many girls are there?
• If y is proportional to x and y = 12 when x = 4, what is y when x = 8?
• What is the area of a triangle with base 8 units and height 5 units?
• The discriminant of x^2 + 4x + 5 is negative; which statement about the roots is true?
• Which equation represents a circle with center (4, -1) and radius 5?
• Dave is d years old. Sonya is three times Dave's age. Which expression represents the sum of their ages in terms of d?
• What is the equation of a vertical line through x = -4?
• Expand (x - 2)(x + 4).
• In a right triangle, the sine of an angle is defined as which ratio?
• What is the circumference of a circle with radius 6?
• A store buys items at $12 and sells at $15. What is the percent markup on cost?
• Solve for x: 3x - 5 = 16.
• A circle with radius 5 has area in terms of π equal to:
• In the system 2x + y = 9 and x - y = 1, what is x?
• The slope of a vertical line is?
• What is the perimeter of an equilateral triangle with side length 7?
• If two numbers have sum 15 and difference 5, what are the numbers?
• In a triangle, two angles are 50° and 60°. What is the measure of the third angle?
• Solve x^2 = 49.
• Which of the following is the expanded form of (x - 4)(x + 5)?
• f(x) = m x. If f(5) = 15, find m.
• In the exponential expression y = 40 × (0.75)³, what is the initial amount?
• What is the base (common ratio) of the exponential expression y = 40 × (0.75)³?
• A rectangle has length 7 and width 3. What is its perimeter?
• The sum of the interior angles of a triangle is 180°. If two angles are 35° and 75°, the third angle is?
• If a square has side length s, its perimeter is?
• The maximum (or minimum) point of a quadratic graph is called the _____ .
• Find the equation of the line with slope -1/2 passing through (2,3).
• For what value of x does f(x) = (x - 3)² + 1 reach its minimum?
• If |x - 4| = 0, what is x?
• A rectangle has length 9 and width 4. What is its area?
• What is the slope-intercept form of the line passing through (0,0) and (2,3)?
• If a price increases by 20% and then decreases by 20% of the new amount, is it back to the original price?
• If sin θ = 1/2 and cos θ = sqrt(3)/2 for some acute angle θ, then tan θ equals which value?
• Which trig ratio is adjacent over hypotenuse?
• A car travels at 60 mph for 2 hours and 75 mph for 1 hour. What is the average speed for the trip?
• Which symbol represents 'at least, greater than or equal to'?
• What is the sum of the interior angles in any triangle?
• If y is proportional to x and y = 15 when x = 3, what is y when x = 9?
• Factor x^2 - 5x + 6.
• If line 2x - 3y = 6, what is y when x = 3?
• What is the volume of a prism with base area 12 and height 5?
• What is b^0 for a nonzero b?
• The distance between points (1, 4) and (4, -2) is which of the following expressions?
• A cube with side length 4 has surface area which of the following?
• If a square has area 64, what is its side length?
• If the area of a rectangle is 42 and the length is 7, find width.
• For what value of x does f(x) = x² reach its minimum?
• In a right triangle with legs 6 and 8, what is the length of the hypotenuse?
• Solve (x + 1)(x - 4) = 0. What are the solutions for x?
• What is m if f(x) = m x and f(7) = 21?
• Solve for y: 2y - 5 = 3y + 7.
• Solve for x in the equation 2x - 3 = 7. What is x?
• Area of a trapezoid with bases 10 and 4 and height 3 is?
• What is 7 - 5^0?
• If the circumference of a circle is 12π, what is the radius?
• The slope of the line through (1, 2) and (5, -6) is?
• If a line has slope m, which is the slope of a line perpendicular to it (assuming m ≠ 0)?
• If a rectangle has length 9 and area 63, what is the width?
• The graph of a quadratic function resembles which letter?
• The distance between (1,2) and (4,6) is which value?
• A circle with radius 3 has area in terms of π equal to:
• What is the range of the data set 2, 9, 5, 12, 7?
• Does the triangle with sides 6, 8, and 10 form a right triangle?
• Solve the system: 2x + 3y = 12 and x - y = 1. Find x and y.
• Figures that are the same shape but not necessarily the same size are called
• What is the slope of the line through (0, 4) and (3, -2)?
• Which term is defined as the most frequently occurring score(s) in a distribution?
• Which equation represents the circle with center at (0, 0) and radius 3?
• If a saleswoman rents you a car for x dollars getting a 10% commission, what is her commission in terms of x?
• The expression x^2 + 4x + 4 is a perfect square trinomial. Factor it.
• Dave is d years old. Tracy is twice Dave's age. What is Tracy's age, in terms of d ?
• The sum of interior angles in a triangle is 180 degrees. If one angle is 50 and another is 60, what is the third angle?
• If a rectangle has length 8 and area 48, what is the width?
• What is the sum of the first six terms of the sequence 2, 5, 8, 11, 14, 17, ...?
• What is the distance between (0,0) and (6,8)?
• Are quadratic function graphs symmetrical with respect to their axis of symmetry?
• Any non-zero number raised to the zero power equals 1. Which of the following expresses this fact?
• If you know two sides of a right triangle, what formula will help you find the third side?
• If f(x) = 3x + 1, what is f(-2)?
• The slope of the line through (2, -1) and (5, 4) is what?
• Does the triple 9-12-15 form a right triangle?
• Evaluate 3^2 + 4^2.
• If the height of the trapezoid is doubled from 4 to 8 while bases remain 8 and 5, what is the area?
• Find the equation of a line with slope 2 passing through the origin.
• If g(x) = 2x + 7, what is g(a+1) in terms of a?
• Which term is defined as the middle score in a distribution?
• For a quadratic equation ax^2 + bx + c = 0, the product of the roots is given by which expression?
• Similar triangles have which properties?
• If four numbers have a mean of 10, what is their total sum?
• If Dave is four years old, what is the sum of Dave's and Tracy's ages?
• If log10 t = 2, what is t?
• What is the sum of the first four terms of the sequence 2, 5, 8, 11, ...?
• Does a triangle with sides 5, 12, and 13 form a right triangle?
• What is the expression inside the parentheses after factoring out the GCF from 3x^2 - 12x - 36?
• In a right triangle, the legs measure 3 and 4. What is the length of the hypotenuse?
• Factoring is rewriting an expression as which operation?
• Compute the mean of the numbers 2, 4, 6, 8, 10.
• If two fair six-sided dice are rolled, what is the probability the sum is 7?
• If 2x - 5 = 0, what is x?
• What is 20 percent of 50?
• Compute the surface area of a rectangular prism with length 2, width 3, and height 4.
• Evaluate f(x) = x^2 at x = -3. What is f(-3)?
• What is the sum of the first five terms of the arithmetic sequence 2, 5, 8, ...?
• Simplify 2√18.
• In a right triangle with legs 6 and 8, what is the length of the hypotenuse?
• What describes a function? Each input maps to exactly one output.
• If f(x) = x^2 - 4x, what is f(3)?
• If a quadratic y = a(x-2)^2 - 5 opens upward, what is the sign of a?
• A rectangle has length 9 units and width w. If its area is 63 square units, what is w?
• If a recipe calls for 3/4 cup sugar and you triple the recipe, how many cups of sugar are needed?
• What is the median of the numbers 2, 4, 4, 7, 9?
• The slope of the line through (-2, 3) and (4, -5) is?
• The area of a triangle with base 8 and height 5 is what?
• If f(x) = m x and f(0) = 0, what is f(1)?
• What is the median of the numbers 1, 3, 7, 7, 9?
• If a line has slope -2, what is the slope of a line perpendicular to it?
• In a right triangle, if the side opposite the angle is 3 and the hypotenuse is 5, what is sin(angle)?
• What tool can you use to find solutions to equations such as 2x^2 - 13x + 18?
• If a saleswoman rents you a car for $1000 getting a 10% commission, what is her commission in dollars?
• If a circle has diameter 10, what is its circumference?
• What is the slope-intercept form of the line through (0,0) and (2,3)?
• If you have a two-part ratio 7:3, what decimal represents the first part of the total?
• If f(x) = 3x, what is f(6)?
• A 4-sided die is rolled. What is the probability of getting an even number?
• A bag contains r red and b blue balls. If r/(r+b) = 1/3 and r = 2, what is b?
• In a triangle, two angles measure 40° and 70°. What is the measure of the third angle?
• Which symbol is used to denote equality in equations?
• Solve for x: |2x - 5| = 11.
• Which statement describes a line with undefined slope?
• A 40°-60°-80° triangle is similar to a triangle that is five times as large. What are the angles of the new triangle?
• A price increases by 50% and then decreases by 50% of the new amount. Is it back to the original price?
• Solve 2x^2 = 32.
• The area of a triangle with base 10 and height h is 25. Find h.
• Find the slope of the line through the points (0, 2) and (4, 6).
• For what value of x does f(x) = (x - 3)² reach its minimum?
• What is the distance between points (1, 2) and (4, 6) in the plane?