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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. Probability= Favorable Outcomes/Total Possible Outcomes






2. 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






3. 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






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






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






6. 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






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






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






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






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






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






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






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






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






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






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






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






18. 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






19. Volume of a Cylinder = pr^2h






20. The whole # left over after division






21. 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)






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






23. 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.






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






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






26. 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






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






28. 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






29. 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






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






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






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






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






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






35. To solve a proportion - cross multiply






36. 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






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






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






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






40. 2pr






41. 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






42. 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






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






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






45. 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






46. 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






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






48. 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






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






50. Subtract the smallest from the largest and add 1