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






2. Probability= Favorable Outcomes/Total Possible Outcomes






3. pr^2






4. 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






5. 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






6. Add the exponents and keep the same base






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






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






9. Factor out the perfect squares






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






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






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






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






14. 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






15. 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






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






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






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






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






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. 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






22. 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






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






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






25. 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






26. Multiply the exponents






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






28. 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






29. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.






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






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






32. 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






33. 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






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






35. 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






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






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. 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






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






40. 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






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. Negative exponent: put number under 1 in a fraction and work out the exponent Rational exponent: square root it- 1. make the root of the problem whatever the denominator of the exponent is 2. the exponent under your root sign is the numerator of the






43. 2pr






44. 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






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






46. 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






47. 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.






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






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






50. Subtract the smallest from the largest and add 1