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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Subjects
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sat
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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. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Prime Factorization
Counting Consecutive Integers
Rate
PEMDAS
2. 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
Solving a System of Equations
Finding the Original Whole
The 3-4-5 Triangle
Remainders
3. 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.
Number Categories
The 3-4-5 Triangle
Interior and Exterior Angles of a Triangle
Function - Notation - and Evaulation
4. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Isosceles and Equilateral triangles
Evaluating an Expression
Using the Average to Find the Sum
Multiples of 2 and 4
5. Factor out the perfect squares
Raising Powers to Powers
Identifying the Parts and the Whole
Simplifying Square Roots
Prime Factorization
6. 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
Determining Absolute Value
Multiplying/Dividing Signed Numbers
The 5-12-13 Triangle
Area of a Circle
7. 1. Re-express them with common denominators 2. Convert them to decimals
Comparing Fractions
Using the Average to Find the Sum
Relative Primes
Parallel Lines and Transversals
8. 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
Length of an Arc
Probability
The 3-4-5 Triangle
Determining Absolute Value
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
Remainders
Intersection of sets
Multiplying/Dividing Signed Numbers
Repeating Decimal
10. The whole # left over after division
Area of a Sector
Adding and Subtraction Polynomials
Interior Angles of a Polygon
Remainders
11. The largest factor that two or more numbers have in common.
Multiplying and Dividing Roots
Comparing Fractions
Negative Exponent and Rational Exponent
Greatest Common Factor
12. 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
Tangency
Function - Notation - and Evaulation
Domain and Range of a Function
Area of a Triangle
13. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
Adding and Subtracting monomials
Reducing Fractions
Characteristics of a Rectangle
14. Probability= Favorable Outcomes/Total Possible Outcomes
Parallel Lines and Transversals
Domain and Range of a Function
Negative Exponent and Rational Exponent
Probability
15. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Median and Mode
Percent Increase and Decrease
Characteristics of a Rectangle
Finding the Original Whole
16. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Interior Angles of a Polygon
Average Formula -
Prime Factorization
Evaluating an Expression
17. 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 midpoint
Circumference of a Circle
Solving a System of Equations
Using an Equation to Find the Slope
18. 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
Adding/Subtracting Fractions
Pythagorean Theorem
Prime Factorization
19. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Mixed Numbers and Improper Fractions
Adding/Subtracting Fractions
Comparing Fractions
Interior Angles of a Polygon
20. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Determining Absolute Value
Part-to-Part Ratios and Part-to-Whole Ratios
Union of Sets
Interior and Exterior Angles of a Triangle
21. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Adding/Subtracting Signed Numbers
Determining Absolute Value
Average Formula -
22. 2pr
Circumference of a Circle
Similar Triangles
Domain and Range of a Function
Surface Area of a Rectangular Solid
23. 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
Counting the Possibilities
Exponential Growth
Intersecting Lines
Prime Factorization
24. 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
Interior Angles of a Polygon
Circumference of a Circle
Comparing Fractions
25. 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
Percent Increase and Decrease
Mixed Numbers and Improper Fractions
Finding the Missing Number
Reducing Fractions
26. 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)
Area of a Sector
Median and Mode
Percent Formula
Probability
27. 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
Multiples of 2 and 4
Circumference of a Circle
Counting Consecutive Integers
28. 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
Raising Powers to Powers
Using an Equation to Find an Intercept
Similar Triangles
Median and Mode
29. 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
PEMDAS
Repeating Decimal
Isosceles and Equilateral triangles
Volume of a Cylinder
30. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Multiplying and Dividing Roots
Intersection of sets
Adding and Subtracting monomials
Prime Factorization
31. 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
Prime Factorization
Counting the Possibilities
Reducing Fractions
Surface Area of a Rectangular Solid
32. 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
Remainders
Direct and Inverse Variation
Part-to-Part Ratios and Part-to-Whole Ratios
Relative Primes
33. Domain: all possible values of x for a function range: all possible outputs of a function
Rate
Finding the Distance Between Two Points
Multiples of 3 and 9
Domain and Range of a Function
34. Part = Percent x Whole
Area of a Sector
Multiplying Monomials
Percent Formula
Characteristics of a Parallelogram
35. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Parallel Lines and Transversals
Exponential Growth
Intersection of sets
Domain and Range of a Function
36. 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
Counting the Possibilities
Adding and Subtracting monomials
Surface Area of a Rectangular Solid
37. To divide fractions - invert the second one and multiply
Raising Powers to Powers
Triangle Inequality Theorem
Even/Odd
Dividing Fractions
38. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Multiples of 2 and 4
Direct and Inverse Variation
Factor/Multiple
Finding the midpoint
39. 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 Formula -
Rate
Number Categories
40. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Multiplying Fractions
Mixed Numbers and Improper Fractions
Determining Absolute Value
Solving a Proportion
41. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Tangency
Circumference of a Circle
Raising Powers to Powers
Factor/Multiple
42. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Solving an Inequality
Average Rate
Volume of a Rectangular Solid
Finding the Original Whole
43. 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
Interior Angles of a Polygon
Finding the Missing Number
Solving a Proportion
Characteristics of a Parallelogram
44. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Solving a Quadratic Equation
Finding the Distance Between Two Points
Percent Increase and Decrease
Multiplying and Dividing Roots
45. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Setting up a Ratio
Factor/Multiple
Interior Angles of a Polygon
Adding/Subtracting Fractions
46. Combine like terms
Circumference of a Circle
Reciprocal
Adding and Subtraction Polynomials
Using the Average to Find the Sum
47. 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
Greatest Common Factor
Adding/Subtracting Fractions
Intersecting Lines
48. For all right triangles: a^2+b^2=c^2
(Least) Common Multiple
Multiples of 2 and 4
Pythagorean Theorem
Union of Sets
49. 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
Interior and Exterior Angles of a Triangle
Multiples of 2 and 4
Rate
Using an Equation to Find an Intercept
50. Surface Area = 2lw + 2wh + 2lh
Using Two Points to Find the Slope
Adding/Subtracting Fractions
Surface Area of a Rectangular Solid
Dividing Fractions