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SAT Math: Concepts And Tricks

Subjects : sat, math
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • Match each statement with the correct term.
  • Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. The 3 angles of any triangle add up to 180 degrees - an exterior angles of a triangle is equal to the sum of the remote interior angles - the 3 exterior angles add up to 360 degrees






2. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4






3. A parallelogram has two pairs of parallel sides - opposite sides are equal - opposite angles are equal - consecutive angles add up to 180 degrees; Area of Parallelogram = base x height






4. To find the reciprocal of a fraction switch the numerator and the denominator






5. To divide fractions - invert the second one and multiply






6. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3






7. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)






8. Example: If the ratio of males to females is 1 to 2 - then what is the ratio of males to people? - work: 1/(1+2) answer: 1/3






9. Factor out the perfect squares






10. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS






11. Change in y/ change in x rise/run






12. pr^2






13. If there are m ways one event can happen and n ways a second event can happen - then there are m × n ways for the 2 events to happen






14. For all right triangles: a^2+b^2=c^2






15. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime






16. If a right triangle's leg-to-leg ratio is 5:12 - or if the leg-to-hypotenuse ratio is 5:13 or 12:13 - it's a 5-12-13 triangle






17. To add a positive and negative integer first ignore the signs and find the positive difference between the two integers - attatch the sign of the original with higher absolute value - to subtract negative integers simply change it into an addition pr






18. Subtract the smallest from the largest and add 1






19. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them






20. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9






21. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b






22. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a






23. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3






24. Sum=(Average) x (Number of Terms)






25. Multiply the exponents






26. The whole # left over after division






27. The smallest multiple (other than zero) that two or more numbers have in common.






28. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width






29. A square is a rectangle with four equal sides; Area of Square = side*side






30. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact






31. Domain: all possible values of x for a function range: all possible outputs of a function






32. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180






33. Integers that have no common factor other than 1 - to determine whether two integers are relative primes break them both down to their prime factorizations






34. (average of the x coordinates - average of the y coordinates)






35. 1. Re-express them with common denominators 2. Convert them to decimals






36. To solve an inequality do whatever is necessary to both sides to isolate the variable. When you multiply or divide both sides by a negative number you must reverse the sign






37. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)






38. The largest factor that two or more numbers have in common.






39. Combine equations in such a way that one of the variables cancel out






40. Add the exponents and keep the same base






41. To solve a proportion - cross multiply






42. An isosceles triangle has 2 equal sides and the angles opposite the equal sides (base angles) are also equal - an equaliteral is a triangle where all 3 sides are equal - thus the angles are equal - regardless of side length the angle is always 60 deg






43. Part = Percent x Whole






44. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45






45. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides






46. This is the key to solving most fraction and percent word problems. Part is usually associated with the word is/are and whole is associated with the word of. Example: 'half of the boys are blonds' whole: all of the boys part: blonds






47. If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 or 4:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side






48. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal






49. An arc is a piece of the circumference. If n is the degree measure of the arc's central angle - then the formula is: Length of an Arc = 1 (n/360) (2pr)






50. 2pr