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






2. To increase: add decimal version of percent to one and times that # to the # you want to increase. Example: increase 40 by 25% Work: 1.25*40=? Answer: 50






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






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






5. 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






6. 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






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






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






9. 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






10. 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






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






12. Part = Percent x Whole






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






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






15. Factor out the perfect squares






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






17. Volume of a Cylinder = pr^2h






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






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






20. 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






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






22. 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






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






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






25. 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






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






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






28. 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






29. 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






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






31. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2






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






33. 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






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






35. 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)






36. 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






37. pr^2






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






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






40. 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






41. 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






42. To add or subtract fraction - first find a common denominator - then add or subtract the numerators






43. Add the exponents and keep the same base






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






45. The whole # left over after division






46. Subtract the smallest from the largest and add 1






47. Multiply the exponents






48. 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






49. 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






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