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






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






3. 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






4. 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






5. 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






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






7. Add the exponents and keep the same base






8. 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.






9. To solve a proportion - cross multiply






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






11. Multiply the exponents






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






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






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






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. 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






18. 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






19. 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






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






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






22. pr^2






23. 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






24. 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






25. Subtract the smallest from the largest and add 1






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






27. 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






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






29. The whole # left over after division






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






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






32. 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






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






34. Factor out the perfect squares






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






36. 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






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






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






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






40. Probability= Favorable Outcomes/Total Possible Outcomes






41. 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






42. 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






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






44. 2pr






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






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






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






48. Combine like terms






49. 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)






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