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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Study First
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. Probability= Favorable Outcomes/Total Possible Outcomes
Adding/Subtracting Fractions
Area of a Triangle
Characteristics of a Parallelogram
Probability
2. Multiply the exponents
Raising Powers to Powers
Solving an Inequality
Finding the midpoint
Triangle Inequality Theorem
3. 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
Multiplying and Dividing Powers
Multiples of 2 and 4
Finding the Missing Number
4. 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.
Adding and Subtracting monomials
Volume of a Rectangular Solid
Multiplying/Dividing Signed Numbers
Number Categories
5. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Multiplying Monomials
Adding/Subtracting Signed Numbers
Reducing Fractions
Area of a Sector
6. 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
Prime Factorization
Mixed Numbers and Improper Fractions
Probability
Percent Increase and Decrease
7. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Finding the Missing Number
Interior and Exterior Angles of a Triangle
PEMDAS
Multiples of 2 and 4
8. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Area of a Triangle
Volume of a Cylinder
Finding the midpoint
Interior Angles of a Polygon
9. Subtract the smallest from the largest and add 1
Volume of a Rectangular Solid
Counting Consecutive Integers
Number Categories
Adding and Subtracting monomials
10. 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
Direct and Inverse Variation
Intersection of sets
Percent Increase and Decrease
Finding the Original Whole
11. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Average Formula -
Direct and Inverse Variation
Determining Absolute Value
Area of a Sector
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
Characteristics of a Rectangle
Reciprocal
Area of a Circle
Average Formula -
13. The smallest multiple (other than zero) that two or more numbers have in common.
(Least) Common Multiple
Reciprocal
Adding and Subtraction Polynomials
Parallel Lines and Transversals
14. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Adding and Subtraction Polynomials
Average Formula -
Characteristics of a Square
Evaluating an Expression
15. 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
Using an Equation to Find an Intercept
Even/Odd
Interior and Exterior Angles of a Triangle
Average Formula -
16. you can add/subtract when the part under the radical is the same
Union of Sets
Adding/Subtracting Fractions
Adding and Subtracting Roots
Function - Notation - and Evaulation
17. 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
Finding the midpoint
Using the Average to Find the Sum
Solving an Inequality
Union of Sets
18. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Tangency
Factor/Multiple
Similar Triangles
Reciprocal
19. 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
Setting up a Ratio
Characteristics of a Square
Repeating Decimal
20. (average of the x coordinates - average of the y coordinates)
Adding and Subtracting monomials
Repeating Decimal
Finding the Distance Between Two Points
Finding the midpoint
21. 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
Adding and Subtracting monomials
Triangle Inequality Theorem
Tangency
Setting up a Ratio
22. 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
Part-to-Part Ratios and Part-to-Whole Ratios
Volume of a Rectangular Solid
Solving a Quadratic Equation
Percent Increase and Decrease
23. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
Exponential Growth
Multiplying/Dividing Signed Numbers
Adding and Subtraction Polynomials
24. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Multiples of 2 and 4
Multiplying Monomials
Raising Powers to Powers
Finding the Original Whole
25. 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
Characteristics of a Square
Parallel Lines and Transversals
Area of a Circle
26. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Greatest Common Factor
Circumference of a Circle
Average Rate
Multiplying Monomials
27. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Using an Equation to Find the Slope
Finding the Missing Number
Adding and Subtracting monomials
Median and Mode
28. 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
Counting the Possibilities
Surface Area of a Rectangular Solid
Using the Average to Find the Sum
Greatest Common Factor
29. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Intersecting Lines
Volume of a Rectangular Solid
Counting the Possibilities
Mixed Numbers and Improper Fractions
30. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Solving a Proportion
Setting up a Ratio
Parallel Lines and Transversals
Adding and Subtraction Polynomials
31. 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
Domain and Range of a Function
Finding the Missing Number
Average of Evenly Spaced Numbers
Solving a Quadratic Equation
32. 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
Even/Odd
Multiplying and Dividing Powers
Length of an Arc
Comparing Fractions
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
Factor/Multiple
The 3-4-5 Triangle
Multiples of 2 and 4
Simplifying Square Roots
34. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Exponential Growth
Multiplying and Dividing Roots
Adding and Subtraction Polynomials
Number Categories
35. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Using the Average to Find the Sum
Adding and Subtracting monomials
Solving a Quadratic Equation
Intersection of sets
36. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Finding the Original Whole
Exponential Growth
Using an Equation to Find the Slope
Finding the Missing Number
37. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Characteristics of a Square
Solving a Quadratic Equation
Adding and Subtraction Polynomials
Multiples of 2 and 4
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
The 5-12-13 Triangle
Characteristics of a Rectangle
Exponential Growth
Simplifying Square Roots
39. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Finding the Missing Number
Tangency
Interior Angles of a Polygon
Raising Powers to Powers
40. To solve a proportion - cross multiply
Using Two Points to Find the Slope
Solving a Proportion
Domain and Range of a Function
Area of a Sector
41. Combine equations in such a way that one of the variables cancel out
Isosceles and Equilateral triangles
Dividing Fractions
Percent Formula
Solving a System of Equations
42. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Interior and Exterior Angles of a Triangle
The 3-4-5 Triangle
Adding/Subtracting Fractions
Circumference of a Circle
43. Sum=(Average) x (Number of Terms)
Simplifying Square Roots
Multiplying and Dividing Powers
Counting the Possibilities
Using the Average to Find the Sum
44. 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
Characteristics of a Parallelogram
Even/Odd
Adding/Subtracting Signed Numbers
The 5-12-13 Triangle
45. The whole # left over after division
Remainders
Probability
Solving a System of Equations
Multiplying/Dividing Signed Numbers
46. 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
Characteristics of a Square
Domain and Range of a Function
Area of a Circle
Interior and Exterior Angles of a Triangle
47. 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
Repeating Decimal
Using the Average to Find the Sum
Using an Equation to Find an Intercept
Reducing Fractions
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
Relative Primes
Number Categories
Combined Percent Increase and Decrease
49. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Reducing Fractions
Determining Absolute Value
Union of Sets
Percent Increase and Decrease
50. A square is a rectangle with four equal sides; Area of Square = side*side
Remainders
Function - Notation - and Evaulation
Characteristics of a Square
Union of Sets