## Test your basic knowledge |

# SAT Math: Concepts And Tricks

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

**2. 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**

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

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

**5. 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**

**6. 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)**

**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 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**

**9. To solve a proportion - cross multiply**

**10. 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**

**11. 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**

**12. 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**

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

**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. 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**

**16. 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.**

**17. Add the exponents and keep the same base**

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

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

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

**21. 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**

**22. Surface Area = 2lw + 2wh + 2lh**

**23. 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**

**24. 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**

**25. The whole # left over after division**

**26. 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**

**27. 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**

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

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

**30. Probability= Favorable Outcomes/Total Possible Outcomes**

**31. 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**

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

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

**34. Subtract the smallest from the largest and add 1**

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

**37. 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**

**38. 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**

**39. 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**

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

**41. 2pr**

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

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

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

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

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

**47. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).**

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

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

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