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






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






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






4. Multiply the exponents






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






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. 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






8. Part = Percent x Whole






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






10. 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






11. 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






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






13. 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






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






15. Probability= Favorable Outcomes/Total Possible Outcomes






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






17. 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






18. 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






19. 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






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






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






23. 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






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






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






26. 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






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






28. 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






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






30. 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






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






32. 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






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






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






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






36. 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






37. Subtract the smallest from the largest and add 1






38. 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






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






40. 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






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






42. Add the exponents and keep the same base






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






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






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






46. 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






47. 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






48. 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






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






50. 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