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






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






3. Volume of a Cylinder = pr^2h






4. To solve a proportion - cross multiply






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






6. Probability= Favorable Outcomes/Total Possible Outcomes






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






8. Use the sum - Example: if the average of 4 #s is 7 - and the #s are 3 - 5 - 8 - and ____ - what is the fourth #? Work: sum= 4*7 =28 3+5+8=16 28-16=? Answer: 12






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






10. 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






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






12. Add the exponents and keep the same base






13. The whole # left over after division






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






15. 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






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






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






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






19. 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






20. 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






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






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






23. To find the y-intercept: put the equation into slope-intercept form (b is the y-intercept): y=mx+b or plug x=0 and solve for y - To find the x-intercept: plug y=0 and solve for x






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






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






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






27. 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)






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






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






30. 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






31. 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






32. pr^2






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






34. 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






35. 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






36. 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






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






38. 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






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






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






41. Multiply the exponents






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






43. 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






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






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






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






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






48. Part = Percent x Whole






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






50. 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