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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. 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/Subtracting Signed Numbers
Determining Absolute Value
Triangle Inequality Theorem
Circumference of a Circle
2. Subtract the smallest from the largest and add 1
Counting Consecutive Integers
Parallel Lines and Transversals
Counting the Possibilities
Characteristics of a Rectangle
3. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Parallel Lines and Transversals
Percent Formula
Determining Absolute Value
Intersecting Lines
4. 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
Raising Powers to Powers
Adding/Subtracting Signed Numbers
The 5-12-13 Triangle
Volume of a Rectangular Solid
5. Combine like terms
Adding and Subtraction Polynomials
Finding the Missing Number
Multiplying and Dividing Roots
Pythagorean Theorem
6. The whole # left over after division
Remainders
The 3-4-5 Triangle
Characteristics of a Rectangle
Finding the Original Whole
7. you can add/subtract when the part under the radical is the same
Adding and Subtracting Roots
Parallel Lines and Transversals
Length of an Arc
Triangle Inequality Theorem
8. 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
Triangle Inequality Theorem
Identifying the Parts and the Whole
Interior and Exterior Angles of a Triangle
9. 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
Surface Area of a Rectangular Solid
Multiples of 2 and 4
Multiplying/Dividing Signed Numbers
Evaluating an Expression
10. 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
Characteristics of a Rectangle
Negative Exponent and Rational Exponent
Similar Triangles
Evaluating an Expression
11. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Solving a Proportion
Using an Equation to Find the Slope
Solving a System of Equations
Parallel Lines and Transversals
12. 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
Even/Odd
Triangle Inequality Theorem
Counting the Possibilities
Relative Primes
13. 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.
Characteristics of a Square
Dividing Fractions
Interior Angles of a Polygon
Number Categories
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
Solving a Quadratic Equation
Prime Factorization
Part-to-Part Ratios and Part-to-Whole Ratios
Median and Mode
15. Domain: all possible values of x for a function range: all possible outputs of a function
Adding and Subtracting Roots
Domain and Range of a Function
Mixed Numbers and Improper Fractions
Rate
16. Combine equations in such a way that one of the variables cancel out
Multiplying and Dividing Roots
Solving a System of Equations
Factor/Multiple
Reducing Fractions
17. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Length of an Arc
Multiplying Monomials
Using an Equation to Find an Intercept
Combined Percent Increase and Decrease
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
Using an Equation to Find an Intercept
Circumference of a Circle
Characteristics of a Parallelogram
Area of a Triangle
19. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Circumference of a Circle
Intersecting Lines
Dividing Fractions
Identifying the Parts and the Whole
20. 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
Reducing Fractions
Remainders
Direct and Inverse Variation
Percent Formula
21. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Multiplying and Dividing Powers
Finding the Distance Between Two Points
Remainders
Triangle Inequality Theorem
22. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Area of a Sector
Average Formula -
Solving an Inequality
Percent Formula
23. To find the reciprocal of a fraction switch the numerator and the denominator
Adding and Subtraction Polynomials
Reciprocal
Finding the Missing Number
Probability
24. 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
Finding the midpoint
The 3-4-5 Triangle
Greatest Common Factor
Factor/Multiple
25. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Using an Equation to Find the Slope
Isosceles and Equilateral triangles
Adding and Subtraction Polynomials
PEMDAS
26. # 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
Surface Area of a Rectangular Solid
Volume of a Cylinder
Simplifying Square Roots
27. 1. Re-express them with common denominators 2. Convert them to decimals
Probability
Finding the Original Whole
Multiplying Monomials
Comparing Fractions
28. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Solving an Inequality
Using an Equation to Find the Slope
Dividing Fractions
Intersecting Lines
29. 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
Function - Notation - and Evaulation
Characteristics of a Parallelogram
Average of Evenly Spaced Numbers
Exponential Growth
30. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Adding and Subtracting Roots
Average Rate
Union of Sets
Evaluating an Expression
31. To divide fractions - invert the second one and multiply
Dividing Fractions
Intersection of sets
Solving a Quadratic Equation
Median and Mode
32. The smallest multiple (other than zero) that two or more numbers have in common.
Isosceles and Equilateral triangles
Counting the Possibilities
(Least) Common Multiple
Intersection of sets
33. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Pythagorean Theorem
Multiples of 2 and 4
Counting the Possibilities
Determining Absolute Value
34. 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
Intersecting Lines
Interior and Exterior Angles of a Triangle
Adding and Subtraction Polynomials
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
Adding and Subtracting monomials
Adding/Subtracting Signed Numbers
Using an Equation to Find the Slope
Intersecting Lines
36. Sum=(Average) x (Number of Terms)
Using the Average to Find the Sum
Adding/Subtracting Signed Numbers
Repeating Decimal
Adding and Subtracting Roots
37. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Counting the Possibilities
Volume of a Rectangular Solid
Length of an Arc
Adding and Subtracting monomials
38. 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
Identifying the Parts and the Whole
Characteristics of a Square
Similar Triangles
Adding and Subtraction Polynomials
39. For all right triangles: a^2+b^2=c^2
Finding the Missing Number
Percent Increase and Decrease
Pythagorean Theorem
Counting the Possibilities
40. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Repeating Decimal
Volume of a Rectangular Solid
Combined Percent Increase and Decrease
Prime Factorization
41. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Median and Mode
Multiplying and Dividing Roots
Function - Notation - and Evaulation
Solving a System of Equations
42. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Average Formula -
Reducing Fractions
Solving a Proportion
Multiplying/Dividing Signed Numbers
43. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Function - Notation - and Evaulation
Intersection of sets
Negative Exponent and Rational Exponent
Adding/Subtracting Fractions
44. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Multiplying and Dividing Roots
Direct and Inverse Variation
The 5-12-13 Triangle
Average Formula -
45. The largest factor that two or more numbers have in common.
PEMDAS
Surface Area of a Rectangular Solid
Adding and Subtraction Polynomials
Greatest Common Factor
46. 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
Characteristics of a Square
Rate
Number Categories
Volume of a Cylinder
47. 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
Area of a Triangle
The 5-12-13 Triangle
Counting the Possibilities
48. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Using Two Points to Find the Slope
Raising Powers to Powers
Using the Average to Find the Sum
Union of Sets
49. 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
Intersecting Lines
Reducing Fractions
Counting the Possibilities
Percent Increase and Decrease
50. A square is a rectangle with four equal sides; Area of Square = side*side
Adding and Subtracting monomials
Characteristics of a Parallelogram
Characteristics of a Square
Tangency