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






2. To multiply fractions - multiply the numerators and multiply the denominators






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






4. you can add/subtract when the part under the radical is the same






5. 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






6. Part = Percent x Whole






7. Probability= Favorable Outcomes/Total Possible Outcomes






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






9. A sector is a piece of the area of a circle. If n is the degree measure of the sector's central angle then the formula is: Area of a Sector = (n/360) (pr^2)






10. To multiply or divide integers - firstly ignore the sign and compute the problem - given 2 negatives make a positive - 2 positives make a positive - and one negative - and one positive make a negative attach the correct sign






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






12. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds






13. The whole # left over after division






14. Direct variation: equation: y=kx - where k is a nonzero constant trick: y changes directly as x does inverse variation: equation: xy=k trick: y doubles as x halves and vice-versa






15. 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






16. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.






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






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






19. 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






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






21. Multiply the exponents






22. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.






23. 2pr






24. Negative exponent: put number under 1 in a fraction and work out the exponent Rational exponent: square root it- 1. make the root of the problem whatever the denominator of the exponent is 2. the exponent under your root sign is the numerator of the






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






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






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






28. Surface Area = 2lw + 2wh + 2lh






29. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign






30. pr^2






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






32. Factor out the perfect squares






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






34. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive






35. Use units to keep things straight (make sure you use 1 unit for each thing) Example: use just inches in your cross multiplication - not inches and feet






36. Integers are whole numbers; they include negtavie whole numbers and zero - Rational numbers can be expressed as a ratio of two integers - irration numbers are real numbers that cant be expressed precisely as a fraction or decimal.






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






38. Volume of a Cylinder = pr^2h






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






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






41. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional






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






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






44. 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






45. Subtract the smallest from the largest and add 1






46. 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






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






48. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²






49. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions






50. Growth pattern in which the individuals in a population reproduce at a constant rate; j-curve graph-- logarithmic - FORMULA: y=a(1+r)^ EXPLANATION: a = initial amount before measuring growth/decay r = growth/decay rate (often a percent) x = number of