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






2. 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






3. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






6. 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






7. 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






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






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






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






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






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






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






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






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






16. 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






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






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






19. To solve a proportion - cross multiply






20. Factor out the perfect squares






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






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






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






24. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45






25. Add the exponents and keep the same base






26. Combine like terms






27. 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






28. 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






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






30. 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






31. 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






32. 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






33. Multiply the exponents






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






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






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






37. Subtract the smallest from the largest and add 1






38. Volume of a Cylinder = pr^2h






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






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






41. 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






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






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






44. 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






45. A sector is a piece of the area of a circle. If n is the degree measure of the sector's central angle then the formula is: Area of a Sector = (n/360) (pr^2)






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






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






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






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






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