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






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






3. Probability= Favorable Outcomes/Total Possible Outcomes






4. 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






5. 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






6. 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






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






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






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






10. 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)






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






12. 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






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






14. 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






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






16. 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






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






18. 2pr






19. 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






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






21. Multiply the exponents






22. 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






23. 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






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






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






26. 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






27. 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






28. 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






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






30. Volume of a Cylinder = pr^2h






31. pr^2






32. 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






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






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






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






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






37. Combine like terms






38. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common






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






40. Subtract the smallest from the largest and add 1






41. Add the exponents and keep the same base






42. 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






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






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






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






46. 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






47. The whole # left over after division






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






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