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SAT Math Questions Test Prep.docx
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What is the order of operations? - correct answer Parentheses, exponents, multiplication, division, addition, subtraction What are natural numbers? - correct answer All whole numbers except for 0 How to determine if a number is prime - correct answer Approximate a square root, then try to divide the number by all prime numbers below the approximated root What are relatively prime numbers? - correct answer The greatest common factor is 1, but the numbers are not necessarily prime. Formula for calculation exponential growth - correct answer final amount = original amount x (1+growth rate)^number of changes Supplementary angles add up to - correct answer 180° Complimentary angles add up to - correct answer 90° What is the triangle inequality rule? - correct answer The length of a side of a triangle is less than the sum of and greater than the difference of the other two sides. Scalene triangle - correct answer No equal sides and no equal angles Isosceles Triangles - correct answer Two sides and two angle are equal
30-60-90 triangle - correct answer Hypotenuse is 2x, short side is x, long side is x√ 45-45-90 triangle - correct answer Hypotenuse is x√2, and the sides are x. What is the sum of the interior angles for a polygon with n sides? - correct answer (n-2) Formula for the area of a trapezoid - correct answer A = ((s₁ + s₂)h) / 2 How can you determine the arc degree or central angle of an inscribed angle? - correct answer Multiply the inscribed angle by 2 Formula for arc length - correct answer Arc length equals = (degree of the arc / 360)(circumference) Formula for the area of a sector - correct answer A = (degree of the arc / 360)(area of a circle) Formula for the diagonal length of a rectangular prism - correct answer d = √(l²+w²+h²) Formula for the diagonal length of a cube - correct answer d= s√ Formula for the volume of a cone - correct answer V= (1/3) (πr²h) Surface area of a cone - correct answer SA = πr² +πrl Volume of a pyramid - correct answer V = (1/3)bh
How to find the distance between two points in 3d plane? - correct answer Square the differences between each coordinate, then square root the sum What is the form of a polar coordinate? - correct answer (r, θ), where r is the distance from the origin and θ is the angle from the positive x-axis How can multiple polar coordinates be made? - correct answer Adding or subtracting 180 to θ and reversing the sign of r. What are the conversion equations for polar coordinates to normal coordinates? - correct answer x=rcosθ y=rsinθ Where is tangent positive/negative? - correct answer Positive: Quadrants 1 and 3 Negative: Quadrants 2 and 4 Pythagorean Identities - correct answer sin²x+cos²x = 1 sec²x = 1+tan²x csc²x = 1+cot²x Double Angle Formulas - correct answer sin2x= 2sinxcosx cos2x = cos²x − sin²x = 2cos²x − 1 = 1 − sin²x Sum of 2 Angles Formulas - correct answer sin(a+b) = sin(a)cos(b) + sin(b)cos(a) cos(a+b) = cos(a)cos(b) - sin(a)sin(b) tan(a+b) = [tan(a) + tan(b)] / [1-tan(a)tan(b)] Difference between 2 Angles formulas - correct answer sin(a- b) = sin(a)cos(b) - sin(b)cos(a)
cos(a-b) = cos(a)cos(b) + sin(a)sin(b) tan(a-b) = [tan(a) - tan(b)] / [1+tan(a)tan(b)] Law of Cosines - correct answer c² = a² + b² - 2abcos(C) If a function is of the nth degree, what is the maximum number of extreme bumps it can have? - correct answer n- Define an even function. - correct answer f(x) = f(-x) Define an odd function. - correct answer f(x) = -f(-x) How many ways can n elements be ordered? - correct answer n! Permutation formula (ordering) - correct answer nPr = n! / (n- r)! Combination formula - correct answer nCr = nPr / r! = n! / (n- r)!r! Formula for arithmetic sequence - correct answer an = a₁ + (n-1)d Formula for geometric sequence - correct answer an = a₁rⁿ⁻¹ Sum of finite geometric series - correct answer ∑ of n terms = a₁ (1-rⁿ/1-r) Sum of n terms of an arithmetic sequence - correct answer ∑ = (n/2)(a₁ + an)