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. 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






2. 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






3. 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)






4. 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






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






6. 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






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






8. 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






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






10. Combine like terms






11. 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






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






13. 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






14. 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






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






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






17. 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






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






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






20. 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






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






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






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






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






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






26. 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






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






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






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






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






31. Volume of a Cylinder = pr^2h






32. 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






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






34. To solve a proportion - cross multiply






35. 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






36. 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






37. 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






38. Add the exponents and keep the same base






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






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






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






42. Factor out the perfect squares






43. 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






44. Probability= Favorable Outcomes/Total Possible Outcomes






45. 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






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






47. 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






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






49. Multiply the exponents






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