/* */

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. 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






2. 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






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






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






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






6. 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






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






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






9. 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






10. 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






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






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






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






14. 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






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






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






17. 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






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






19. 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






20. 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






21. To increase: add decimal version of percent to one and times that # to the # you want to increase. Example: increase 40 by 25% Work: 1.25*40=? Answer: 50






22. 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






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






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






27. 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






28. 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






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






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






31. 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






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






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






34. 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






35. 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






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






37. Part = Percent x Whole






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






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






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






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






42. Subtract the smallest from the largest and add 1






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






44. 2pr






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






46. Add the exponents and keep the same base






47. 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)






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






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






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






//