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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 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
Interior and Exterior Angles of a Triangle
Triangle Inequality Theorem
Multiplying and Dividing Powers
Area of a Circle
2. pr^2
Adding and Subtraction Polynomials
Area of a Circle
Relative Primes
Even/Odd
3. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Volume of a Cylinder
Evaluating an Expression
Finding the Missing Number
Repeating Decimal
4. To divide fractions - invert the second one and multiply
Percent Increase and Decrease
Dividing Fractions
Counting Consecutive Integers
Multiplying/Dividing Signed Numbers
5. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Characteristics of a Rectangle
Evaluating an Expression
Multiplying and Dividing Roots
Finding the Missing Number
6. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Percent Increase and Decrease
Identifying the Parts and the Whole
Multiples of 2 and 4
Factor/Multiple
7. 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
Characteristics of a Rectangle
Repeating Decimal
Multiplying Fractions
8. 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
Combined Percent Increase and Decrease
Using Two Points to Find the Slope
Direct and Inverse Variation
9. 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
Evaluating an Expression
Finding the Original Whole
Negative Exponent and Rational Exponent
Using the Average to Find the Sum
10. 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
Adding and Subtraction Polynomials
Percent Increase and Decrease
Identifying the Parts and the Whole
Surface Area of a Rectangular Solid
11. Part = Percent x Whole
Percent Formula
Number Categories
Volume of a Rectangular Solid
Remainders
12. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Factor/Multiple
Characteristics of a Rectangle
Parallel Lines and Transversals
Setting up a Ratio
13. Start with 100 as a starting value - Example: A price rises by 10% one year and by 20% the next. What's the combined percent increase? - Say the original price is $100. Year one: $100 + (10% of 100) = 100 + 10 = 110 Year two: 110 + (20% of 110) = 110
Combined Percent Increase and Decrease
Average of Evenly Spaced Numbers
The 3-4-5 Triangle
Characteristics of a Parallelogram
14. 2pr
Identifying the Parts and the Whole
Adding/Subtracting Signed Numbers
Average Formula -
Circumference of a Circle
15. Sum=(Average) x (Number of Terms)
Using the Average to Find the Sum
Surface Area of a Rectangular Solid
Pythagorean Theorem
Triangle Inequality Theorem
16. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Interior Angles of a Polygon
Multiples of 2 and 4
Volume of a Rectangular Solid
Union of Sets
17. For all right triangles: a^2+b^2=c^2
Pythagorean Theorem
Union of Sets
Interior Angles of a Polygon
Percent Formula
18. Subtract the smallest from the largest and add 1
Solving a Quadratic Equation
Reducing Fractions
Pythagorean Theorem
Counting Consecutive Integers
19. Factor out the perfect squares
PEMDAS
Simplifying Square Roots
Using an Equation to Find the Slope
Reducing Fractions
20. 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
Interior Angles of a Polygon
Average Rate
Even/Odd
Setting up a Ratio
21. 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
Percent Increase and Decrease
Counting the Possibilities
Interior Angles of a Polygon
22. 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
Number Categories
Direct and Inverse Variation
(Least) Common Multiple
The 5-12-13 Triangle
23. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Direct and Inverse Variation
Volume of a Rectangular Solid
Interior and Exterior Angles of a Triangle
Reducing Fractions
24. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Surface Area of a Rectangular Solid
Area of a Triangle
Triangle Inequality Theorem
Similar Triangles
25. 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
Interior and Exterior Angles of a Triangle
Average Formula -
Solving a Quadratic Equation
26. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Using the Average to Find the Sum
Mixed Numbers and Improper Fractions
Multiplying Monomials
Dividing Fractions
27. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Raising Powers to Powers
Comparing Fractions
Mixed Numbers and Improper Fractions
Intersecting Lines
28. The whole # left over after division
Adding/Subtracting Signed Numbers
Greatest Common Factor
Remainders
The 5-12-13 Triangle
29. 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)
(Least) Common Multiple
Pythagorean Theorem
Area of a Sector
Factor/Multiple
30. 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
Solving a System of Equations
Solving an Inequality
Simplifying Square Roots
Circumference of a Circle
31. (average of the x coordinates - average of the y coordinates)
Number Categories
Median and Mode
Finding the midpoint
Reciprocal
32. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
Solving a Proportion
Adding/Subtracting Signed Numbers
Adding and Subtracting Roots
33. 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
Surface Area of a Rectangular Solid
Relative Primes
Comparing Fractions
34. Volume of a Cylinder = pr^2h
Adding/Subtracting Fractions
Greatest Common Factor
Volume of a Cylinder
Pythagorean Theorem
35. The largest factor that two or more numbers have in common.
Adding and Subtraction Polynomials
Probability
Greatest Common Factor
Circumference of a Circle
36. 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
Adding/Subtracting Signed Numbers
Intersection of sets
Length of an Arc
Adding and Subtraction Polynomials
37. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Even/Odd
Number Categories
Factor/Multiple
Solving a System of Equations
38. Add the exponents and keep the same base
PEMDAS
Circumference of a Circle
Multiplying and Dividing Powers
Average of Evenly Spaced Numbers
39. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Parallel Lines and Transversals
Adding/Subtracting Fractions
Area of a Triangle
Dividing Fractions
40. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Domain and Range of a Function
Area of a Sector
Finding the Distance Between Two Points
Union of Sets
41. To multiply fractions - multiply the numerators and multiply the denominators
Intersection of sets
Interior and Exterior Angles of a Triangle
Using an Equation to Find the Slope
Multiplying Fractions
42. 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
Prime Factorization
Average Formula -
Solving an Inequality
43. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Surface Area of a Rectangular Solid
Isosceles and Equilateral triangles
Using Two Points to Find the Slope
Determining Absolute Value
44. 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
Prime Factorization
Multiplying and Dividing Powers
Negative Exponent and Rational Exponent
Adding and Subtracting monomials
45. 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
Greatest Common Factor
Exponential Growth
Prime Factorization
Solving a System of Equations
46. 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)
Length of an Arc
Finding the Original Whole
Intersection of sets
Union of Sets
47. you can add/subtract when the part under the radical is the same
Tangency
(Least) Common Multiple
Adding and Subtracting monomials
Adding and Subtracting Roots
48. 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
Adding and Subtraction Polynomials
Characteristics of a Parallelogram
Using the Average to Find the Sum
Isosceles and Equilateral triangles
49. 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
Multiplying and Dividing Roots
Characteristics of a Parallelogram
Repeating Decimal
50. 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
Relative Primes
Similar Triangles
Interior and Exterior Angles of a Triangle