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. Factor out the perfect squares






2. 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.






3. Subtract the smallest from the largest and add 1






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






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






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






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






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






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






10. 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






11. 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






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






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






14. 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






15. 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






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






17. 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






18. 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






19. 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






20. 2pr






21. Volume of a Cylinder = pr^2h






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






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






24. 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






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






26. 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






27. Add the exponents and keep the same base






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






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






30. 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






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






32. pr^2






33. Combine like terms






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






35. 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






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






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






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






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






40. 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






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. 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






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






44. 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






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






46. The whole # left over after division






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






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






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






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