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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. To convert a mixed number to an improper fraction - multiply the whole number by the denominator - then add the numerator over the same denominator - to convert an improper fraction to a mixed number - divide the denominator into the numerator to get






2. 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






3. Combine like terms






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






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






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






7. 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






8. 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






9. To solve a proportion - cross multiply






10. Volume of a Cylinder = pr^2h






11. 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






12. Add the exponents and keep the same base






13. Use this example: Example: after a 5% increase - the population was 59 -346. What was the population before the increase? Work: 1.05x=59 -346 Answer: 56 -520






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






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






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






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






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






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






20. Factor out the perfect squares






21. pr^2






22. Notation: f(x) read: 'f of x' evaluation: if you want to evaluate the function for f(4) - replace x with 4 everywhere in the equation






23. Part = Percent x Whole






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






25. 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






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






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






28. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common






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






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






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






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






33. Area of Triangle = 1/2 (base)(height) - the height is the perpendicular distance between the side that's chosen as the base and the opposite vertex






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






35. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).






36. 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






37. The median is the value that falls in the middle of the set - the mode is the value that appears most often






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






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






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






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






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






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






44. Multiply the exponents






45. 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






46. The length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides






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






48. 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






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






50. 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