Test your basic knowledge |

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






2. 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






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






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






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






6. Start with 100 as a starting value - Example: A price rises by 10% one year and by 20% the next. What's the combined percent increase? - Say the original price is $100. Year one: $100 + (10% of 100) = 100 + 10 = 110 Year two: 110 + (20% of 110) = 110






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






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






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






10. Add the exponents and keep the same base






11. 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






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






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






14. The median is the value that falls in the middle of the set - the mode is the value that appears most often






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






16. 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






17. 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






18. 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






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






20. 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






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






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






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






24. 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






25. Volume of a Cylinder = pr^2h






26. 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






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






28. 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






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






30. 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.






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






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






33. 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






34. 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






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






36. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime






37. To solve a proportion - cross multiply






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






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






40. 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






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






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






43. 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






44. 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






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






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






48. Probability= Favorable Outcomes/Total Possible Outcomes






49. 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






50. Combine like terms