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






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






3. 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






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






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






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






7. To solve a proportion - cross multiply






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






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






10. 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






11. Add the exponents and keep the same base






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






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






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






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






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






17. pr^2






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






19. 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)






20. 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






21. 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






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






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






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






25. 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)






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






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






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






29. 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






30. Factor out the perfect squares






31. 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






32. 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






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






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






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. 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






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






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






39. 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






40. 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






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






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






43. 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






44. 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






45. 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






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






47. 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






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






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. 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