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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. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Setting up a Ratio
Reducing Fractions
Solving a System of Equations
Circumference of a Circle
2. 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
Percent Formula
PEMDAS
Length of an Arc
Characteristics of a Parallelogram
3. 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
Adding and Subtracting Roots
Isosceles and Equilateral triangles
Greatest Common Factor
Evaluating an Expression
4. 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
Intersecting Lines
Multiples of 3 and 9
Finding the Original Whole
Determining Absolute Value
5. The smallest multiple (other than zero) that two or more numbers have in common.
The 3-4-5 Triangle
Volume of a Cylinder
(Least) Common Multiple
Remainders
6. 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
Union of Sets
Finding the Original Whole
Percent Increase and Decrease
Exponential Growth
7. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Greatest Common Factor
Prime Factorization
Number Categories
Percent Formula
8. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Average of Evenly Spaced Numbers
Multiples of 2 and 4
Solving a Proportion
Characteristics of a Square
9. 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
Multiplying and Dividing Powers
Adding and Subtracting monomials
Simplifying Square Roots
10. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Finding the Distance Between Two Points
Reciprocal
Factor/Multiple
Even/Odd
11. 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
Number Categories
Repeating Decimal
Remainders
Characteristics of a Parallelogram
12. 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
Direct and Inverse Variation
Characteristics of a Square
Percent Increase and Decrease
Multiplying and Dividing Powers
13. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Characteristics of a Square
Multiples of 2 and 4
Finding the Original Whole
Reciprocal
14. 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
Direct and Inverse Variation
Even/Odd
Characteristics of a Rectangle
Probability
15. 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
Multiplying/Dividing Signed Numbers
Finding the midpoint
Setting up a Ratio
Solving an Inequality
16. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Interior Angles of a Polygon
Adding/Subtracting Signed Numbers
Multiplying/Dividing Signed Numbers
Number Categories
17. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying/Dividing Signed Numbers
Multiplying Monomials
Triangle Inequality Theorem
Counting the Possibilities
18. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Multiples of 3 and 9
Relative Primes
Tangency
Characteristics of a Parallelogram
19. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Median and Mode
Union of Sets
Using an Equation to Find the Slope
Adding and Subtraction Polynomials
20. 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
Multiples of 2 and 4
Area of a Sector
Simplifying Square Roots
Rate
21. Sum=(Average) x (Number of Terms)
Rate
Solving a Proportion
Using the Average to Find the Sum
Negative Exponent and Rational Exponent
22. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Repeating Decimal
Percent Formula
Identifying the Parts and the Whole
Characteristics of a Rectangle
23. 1. Re-express them with common denominators 2. Convert them to decimals
Intersection of sets
Dividing Fractions
Comparing Fractions
Area of a Triangle
24. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Greatest Common Factor
Adding/Subtracting Signed Numbers
The 3-4-5 Triangle
Solving a Quadratic Equation
25. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Solving a Quadratic Equation
Factor/Multiple
Probability
Counting Consecutive Integers
26. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
Domain and Range of a Function
Adding/Subtracting Fractions
Parallel Lines and Transversals
27. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Reducing Fractions
Combined Percent Increase and Decrease
Multiplying and Dividing Roots
PEMDAS
28. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Intersecting Lines
Number Categories
Solving an Inequality
PEMDAS
29. 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
Intersecting Lines
Setting up a Ratio
Adding/Subtracting Signed Numbers
Tangency
30. 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
Identifying the Parts and the Whole
Solving a Proportion
Direct and Inverse Variation
Relative Primes
31. 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
Finding the midpoint
The 5-12-13 Triangle
Pythagorean Theorem
Combined Percent Increase and Decrease
32. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Average Formula -
Remainders
Characteristics of a Parallelogram
Probability
33. 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
Function - Notation - and Evaulation
Counting the Possibilities
Finding the Original Whole
Direct and Inverse Variation
34. To find the reciprocal of a fraction switch the numerator and the denominator
Using Two Points to Find the Slope
Reciprocal
Circumference of a Circle
Adding/Subtracting Signed Numbers
35. 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
Solving a System of Equations
Tangency
Average Formula -
36. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Finding the midpoint
Multiplying and Dividing Roots
Volume of a Rectangular Solid
Reducing Fractions
37. To solve a proportion - cross multiply
Solving a Proportion
Intersection of sets
Dividing Fractions
Characteristics of a Parallelogram
38. 2pr
Circumference of a Circle
Percent Increase and Decrease
Mixed Numbers and Improper Fractions
Using Two Points to Find the Slope
39. Probability= Favorable Outcomes/Total Possible Outcomes
Using an Equation to Find an Intercept
Probability
Adding and Subtracting Roots
The 5-12-13 Triangle
40. The whole # left over after division
Remainders
Multiples of 2 and 4
Multiplying and Dividing Roots
Characteristics of a Rectangle
41. pr^2
Using an Equation to Find an Intercept
Area of a Circle
Finding the Distance Between Two Points
Average Formula -
42. 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
Adding and Subtracting monomials
Area of a Triangle
Average of Evenly Spaced Numbers
Remainders
43. 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
Adding and Subtracting monomials
Relative Primes
Rate
Finding the Missing Number
44. A square is a rectangle with four equal sides; Area of Square = side*side
Raising Powers to Powers
Area of a Triangle
Repeating Decimal
Characteristics of a Square
45. Change in y/ change in x rise/run
Reciprocal
Factor/Multiple
Union of Sets
Using Two Points to Find the Slope
46. Multiply the exponents
Raising Powers to Powers
Number Categories
Finding the Original Whole
Percent Increase and Decrease
47. Factor out the perfect squares
Similar Triangles
Simplifying Square Roots
Finding the Missing Number
Solving a Quadratic Equation
48. 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
Multiples of 3 and 9
Interior and Exterior Angles of a Triangle
Area of a Circle
Mixed Numbers and Improper Fractions
49. 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
Comparing Fractions
Using the Average to Find the Sum
Triangle Inequality Theorem
Intersection of sets
50. Part = Percent x Whole
(Least) Common Multiple
The 3-4-5 Triangle
Percent Formula
Characteristics of a Rectangle