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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. 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






3. 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






4. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b






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






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






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






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






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






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






11. Volume of a Cylinder = pr^2h






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






13. 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






14. 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






15. pr^2






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






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






18. The whole # left over after division






19. 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






20. 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






21. 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






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






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






24. 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






25. 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






26. 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






27. 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.






28. 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






29. 2pr






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






31. 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






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






33. 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)






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






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. 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






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






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






39. 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)






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






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






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






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






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






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






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






47. Add the exponents and keep the same base






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






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






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