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SAT Math: Concepts And Tricks

Subjects : sat, math
Instructions:
  • Answer 50 questions in 30 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 find the reciprocal of a fraction switch the numerator and the denominator






2. The whole # left over after division






3. 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






4. 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






5. 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






6. pr^2






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






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






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






10. 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






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






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






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






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






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






16. 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






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






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






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






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






21. 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






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






23. 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.






24. To solve a proportion - cross multiply






25. 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






26. 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






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






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






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






30. 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






31. Part = Percent x Whole






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






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






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






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






36. 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






37. Multiply the exponents






38. 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






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






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






41. 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






42. A decimal with a sequence of digits that repeats itself indefinitely; to find a particular digit in the repetition - use the example: if there are 3 digits that repeat - every 3rd digit is the same. If you want the 31st digit - then the 30th digit is






43. 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






44. 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






45. 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






46. 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






47. 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






48. Subtract the smallest from the largest and add 1






49. 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)






50. 2pr






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