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






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






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






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






5. 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






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






7. 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






8. To solve a proportion - cross multiply






9. Add the exponents and keep the same base






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






11. 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






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






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






14. 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






15. 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)






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






17. 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






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






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






20. 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






21. 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






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






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






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






26. Probability= Favorable Outcomes/Total Possible Outcomes






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






28. Volume of a Cylinder = pr^2h






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






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






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






32. 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






33. 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






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






35. 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






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






37. 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






38. 2pr






39. 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






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






41. 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






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






43. 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






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






45. 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






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






47. pr^2






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






49. The whole # left over after division






50. Subtract the smallest from the largest and add 1