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






2. Multiply the exponents






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






4. 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






5. Subtract the smallest from the largest and add 1






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






7. 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






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






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






10. Part = Percent x Whole






11. 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






12. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.






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






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






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






16. 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






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






18. 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






19. The whole # left over after division






20. 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






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






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






24. Factor out the perfect squares






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






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






27. 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






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






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






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






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 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






34. To solve a proportion - cross multiply






35. 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






36. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






39. 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






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






41. If there are m ways one event can happen and n ways a second event can happen - then there are m × n ways for the 2 events to happen






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






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






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






45. 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






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






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






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






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






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