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Test your basic knowledge |
SAT Math: Concepts And Tricks
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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. Change in y/ change in x rise/run
Evaluating an Expression
Using Two Points to Find the Slope
Percent Increase and Decrease
Part-to-Part Ratios and Part-to-Whole Ratios
2. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Part-to-Part Ratios and Part-to-Whole Ratios
Negative Exponent and Rational Exponent
Percent Increase and Decrease
Intersection of sets
3. 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
Direct and Inverse Variation
Intersection of sets
Rate
Counting the Possibilities
4. 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
Direct and Inverse Variation
Setting up a Ratio
Number Categories
Using the Average to Find the Sum
5. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Repeating Decimal
Volume of a Rectangular Solid
Setting up a Ratio
Using an Equation to Find an Intercept
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)
Multiplying Monomials
Using the Average to Find the Sum
Remainders
Length of an Arc
7. 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
Negative Exponent and Rational Exponent
Finding the Original Whole
Interior Angles of a Polygon
Adding and Subtraction Polynomials
8. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Adding/Subtracting Fractions
Similar Triangles
Negative Exponent and Rational Exponent
Average of Evenly Spaced Numbers
9. 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
Intersecting Lines
Triangle Inequality Theorem
Multiplying Monomials
Surface Area of a Rectangular Solid
10. 1. Re-express them with common denominators 2. Convert them to decimals
Multiplying Monomials
Exponential Growth
Number Categories
Comparing Fractions
11. The smallest multiple (other than zero) that two or more numbers have in common.
Average Rate
Using an Equation to Find the Slope
Number Categories
(Least) Common Multiple
12. 2pr
Circumference of a Circle
Multiplying and Dividing Powers
Adding/Subtracting Fractions
Reducing Fractions
13. 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
The 3-4-5 Triangle
(Least) Common Multiple
Pythagorean Theorem
Isosceles and Equilateral triangles
14. 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
Relative Primes
Multiplying and Dividing Roots
Using the Average to Find the Sum
Circumference of a Circle
15. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Finding the Original Whole
Triangle Inequality Theorem
Area of a Sector
Multiplying and Dividing Roots
16. The largest factor that two or more numbers have in common.
Length of an Arc
Using the Average to Find the Sum
Area of a Circle
Greatest Common Factor
17. Volume of a Cylinder = pr^2h
Simplifying Square Roots
Finding the Original Whole
Volume of a Cylinder
Tangency
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
Multiplying/Dividing Signed Numbers
Characteristics of a Parallelogram
Prime Factorization
Tangency
19. 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
Pythagorean Theorem
Repeating Decimal
Simplifying Square Roots
Adding/Subtracting Signed Numbers
20. To solve a proportion - cross multiply
Solving a Proportion
Adding/Subtracting Fractions
Part-to-Part Ratios and Part-to-Whole Ratios
Characteristics of a Rectangle
21. To divide fractions - invert the second one and multiply
Characteristics of a Rectangle
Mixed Numbers and Improper Fractions
Dividing Fractions
Identifying the Parts and the Whole
22. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
PEMDAS
Counting the Possibilities
Interior Angles of a Polygon
Raising Powers to Powers
23. 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
Length of an Arc
Part-to-Part Ratios and Part-to-Whole Ratios
Multiplying Fractions
Percent Increase and Decrease
24. 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
Length of an Arc
Counting the Possibilities
Solving a Proportion
Repeating Decimal
25. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Solving a Quadratic Equation
Combined Percent Increase and Decrease
Volume of a Rectangular Solid
26. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Length of an Arc
Counting the Possibilities
Volume of a Cylinder
Union of Sets
27. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Average Rate
Similar Triangles
Solving a System of Equations
Reducing Fractions
28. 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
Domain and Range of a Function
Factor/Multiple
Evaluating an Expression
Part-to-Part Ratios and Part-to-Whole Ratios
29. 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
Using the Average to Find the Sum
Simplifying Square Roots
Union of Sets
Mixed Numbers and Improper Fractions
30. Combine like terms
Volume of a Rectangular Solid
Adding and Subtraction Polynomials
Average of Evenly Spaced Numbers
Solving a Quadratic Equation
31. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Part-to-Part Ratios and Part-to-Whole Ratios
Adding and Subtracting monomials
Counting the Possibilities
Average Formula -
32. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Using an Equation to Find the Slope
Using the Average to Find the Sum
Multiples of 3 and 9
Percent Increase and Decrease
33. For all right triangles: a^2+b^2=c^2
Characteristics of a Rectangle
Domain and Range of a Function
Pythagorean Theorem
Prime Factorization
34. 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
Multiplying/Dividing Signed Numbers
Multiplying Monomials
Using the Average to Find the Sum
Characteristics of a Square
35. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Repeating Decimal
Greatest Common Factor
PEMDAS
Using Two Points to Find the Slope
36. Sum=(Average) x (Number of Terms)
Using an Equation to Find an Intercept
Counting the Possibilities
Percent Increase and Decrease
Using the Average to Find the Sum
37. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Using an Equation to Find the Slope
Factor/Multiple
Area of a Triangle
Interior Angles of a Polygon
38. 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
Function - Notation - and Evaulation
Area of a Circle
Percent Formula
Factor/Multiple
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
Multiples of 3 and 9
The 3-4-5 Triangle
Relative Primes
Percent Formula
40. 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
Counting the Possibilities
Average Formula -
Probability
Even/Odd
41. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Finding the Missing Number
Median and Mode
Multiples of 3 and 9
Parallel Lines and Transversals
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
Multiplying and Dividing Powers
Negative Exponent and Rational Exponent
(Least) Common Multiple
Volume of a Rectangular Solid
43. 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.
Number Categories
Intersecting Lines
Adding and Subtracting Roots
(Least) Common Multiple
44. 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)
Intersecting Lines
Area of a Sector
Counting Consecutive Integers
Remainders
45. Add the exponents and keep the same base
Multiplying and Dividing Powers
Using an Equation to Find the Slope
Characteristics of a Parallelogram
Counting Consecutive Integers
46. Surface Area = 2lw + 2wh + 2lh
Multiplying/Dividing Signed Numbers
Surface Area of a Rectangular Solid
Prime Factorization
Using an Equation to Find an Intercept
47. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Percent Increase and Decrease
Intersecting Lines
Solving an Inequality
Length of an Arc
48. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Greatest Common Factor
Finding the Distance Between Two Points
Dividing Fractions
Solving a Proportion
49. (average of the x coordinates - average of the y coordinates)
Intersection of sets
Intersecting Lines
Finding the midpoint
Characteristics of a Rectangle
50. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Adding and Subtracting monomials
Area of a Sector
Volume of a Rectangular Solid
Multiplying Monomials