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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. (average of the x coordinates - average of the y coordinates)
Finding the midpoint
Using an Equation to Find an Intercept
Characteristics of a Square
Multiplying and Dividing Roots
2. Sum=(Average) x (Number of Terms)
Using the Average to Find the Sum
Reducing Fractions
Combined Percent Increase and Decrease
Repeating Decimal
3. 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
Isosceles and Equilateral triangles
Part-to-Part Ratios and Part-to-Whole Ratios
Multiplying/Dividing Signed Numbers
Direct and Inverse Variation
4. 2pr
Characteristics of a Parallelogram
Circumference of a Circle
Characteristics of a Square
Multiples of 3 and 9
5. 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
Solving a Quadratic Equation
Interior and Exterior Angles of a Triangle
Characteristics of a Parallelogram
Union of Sets
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
Similar Triangles
Adding and Subtracting monomials
Isosceles and Equilateral triangles
Function - Notation - and Evaulation
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
Using an Equation to Find an Intercept
Using an Equation to Find the Slope
The 5-12-13 Triangle
Negative Exponent and Rational Exponent
8. 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
Finding the Distance Between Two Points
Similar Triangles
Characteristics of a Square
Finding the Original Whole
9. For all right triangles: a^2+b^2=c^2
Multiplying Fractions
Greatest Common Factor
Pythagorean Theorem
Identifying the Parts and the Whole
10. 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
Characteristics of a Rectangle
Finding the Distance Between Two Points
Relative Primes
Mixed Numbers and Improper Fractions
11. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Tangency
Solving an Inequality
Union of Sets
Multiplying Monomials
12. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Simplifying Square Roots
Evaluating an Expression
Characteristics of a Rectangle
Median and Mode
13. Factor out the perfect squares
Simplifying Square Roots
Finding the Missing Number
Surface Area of a Rectangular Solid
Adding/Subtracting Signed Numbers
14. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Adding/Subtracting Fractions
PEMDAS
Rate
Evaluating an Expression
15. 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
Finding the Original Whole
Rate
Finding the Distance Between Two Points
Counting Consecutive Integers
16. 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
Part-to-Part Ratios and Part-to-Whole Ratios
Counting the Possibilities
Setting up a Ratio
Union of Sets
17. 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
Intersection of sets
Negative Exponent and Rational Exponent
18. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Multiples of 3 and 9
Multiples of 2 and 4
Multiplying Fractions
Average Formula -
19. 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
Intersecting Lines
Combined Percent Increase and Decrease
The 5-12-13 Triangle
Mixed Numbers and Improper Fractions
20. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Solving a Quadratic Equation
Multiplying Fractions
Parallel Lines and Transversals
Raising Powers to Powers
21. 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
Median and Mode
Parallel Lines and Transversals
Length of an Arc
Interior and Exterior Angles of a Triangle
22. Multiply the exponents
Raising Powers to Powers
Determining Absolute Value
Interior and Exterior Angles of a Triangle
Solving a Quadratic Equation
23. Part = Percent x Whole
Length of an Arc
Combined Percent Increase and Decrease
Relative Primes
Percent Formula
24. you can add/subtract when the part under the radical is the same
Domain and Range of a Function
Intersection of sets
Average of Evenly Spaced Numbers
Adding and Subtracting Roots
25. Combine like terms
Multiplying Monomials
Using Two Points to Find the Slope
Adding and Subtraction Polynomials
Volume of a Cylinder
26. 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
Exponential Growth
Average of Evenly Spaced Numbers
Adding/Subtracting Fractions
Multiplying and Dividing Powers
27. To divide fractions - invert the second one and multiply
Finding the Missing Number
Dividing Fractions
Multiples of 2 and 4
Solving an Inequality
28. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Exponential Growth
Volume of a Rectangular Solid
Repeating Decimal
Multiplying Monomials
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
Mixed Numbers and Improper Fractions
Volume of a Rectangular Solid
Using Two Points to Find the Slope
Adding/Subtracting Fractions
30. 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
Direct and Inverse Variation
Tangency
Volume of a Rectangular Solid
Finding the Missing Number
31. 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
Domain and Range of a Function
Repeating Decimal
Counting Consecutive Integers
Surface Area of a Rectangular Solid
32. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Using the Average to Find the Sum
Reciprocal
Solving an Inequality
33. 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
Characteristics of a Rectangle
Evaluating an Expression
Average Formula -
The 3-4-5 Triangle
34. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Similar Triangles
Finding the Missing Number
Factor/Multiple
Median and Mode
35. Domain: all possible values of x for a function range: all possible outputs of a function
Finding the Original Whole
Union of Sets
Domain and Range of a Function
Multiplying and Dividing Roots
36. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Average Rate
Using the Average to Find the Sum
Area of a Circle
Relative Primes
37. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Setting up a Ratio
Adding and Subtraction Polynomials
Adding and Subtracting monomials
Raising Powers to Powers
38. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Circumference of a Circle
Multiplying/Dividing Signed Numbers
Adding/Subtracting Fractions
Surface Area of a Rectangular Solid
39. 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
Domain and Range of a Function
Exponential Growth
Surface Area of a Rectangular Solid
40. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Reducing Fractions
Percent Formula
Using an Equation to Find an Intercept
Similar Triangles
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
Greatest Common Factor
Adding/Subtracting Signed Numbers
Solving a Proportion
Surface Area of a Rectangular Solid
42. 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
Domain and Range of a Function
Part-to-Part Ratios and Part-to-Whole Ratios
Determining Absolute Value
Identifying the Parts and the Whole
43. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Finding the midpoint
PEMDAS
Finding the Original Whole
Median and Mode
44. 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
Relative Primes
Even/Odd
Characteristics of a Rectangle
Identifying the Parts and the Whole
45. 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.
Part-to-Part Ratios and Part-to-Whole Ratios
Number Categories
Counting the Possibilities
Median and Mode
46. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Similar Triangles
Combined Percent Increase and Decrease
Multiplying and Dividing Powers
Comparing Fractions
47. pr^2
Rate
Area of a Circle
Multiples of 2 and 4
Counting Consecutive Integers
48. 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
Negative Exponent and Rational Exponent
Length of an Arc
Factor/Multiple
Area of a Triangle
49. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Multiplying and Dividing Powers
Prime Factorization
(Least) Common Multiple
50. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Counting the Possibilities
Adding/Subtracting Signed Numbers
Finding the Distance Between Two Points
Solving a Proportion