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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. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Comparing Fractions
Solving a Proportion
Multiples of 3 and 9
Union of Sets
2. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Median and Mode
Isosceles and Equilateral triangles
Raising Powers to Powers
Solving a Quadratic Equation
3. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
(Least) Common Multiple
Average Rate
The 5-12-13 Triangle
Isosceles and Equilateral triangles
4. Add the exponents and keep the same base
Adding/Subtracting Signed Numbers
Multiplying and Dividing Powers
Average Formula -
Triangle Inequality Theorem
5. 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
Solving a System of Equations
Greatest Common Factor
Adding and Subtracting Roots
6. Surface Area = 2lw + 2wh + 2lh
Direct and Inverse Variation
Number Categories
The 5-12-13 Triangle
Surface Area of a Rectangular Solid
7. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Length of an Arc
The 3-4-5 Triangle
Pythagorean Theorem
Tangency
8. 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
Characteristics of a Parallelogram
Finding the Original Whole
Comparing Fractions
Relative Primes
9. 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)
Intersection of sets
Function - Notation - and Evaulation
Area of a Sector
Multiplying and Dividing Powers
10. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Area of a Circle
Determining Absolute Value
Solving a System of Equations
PEMDAS
11. 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
Using an Equation to Find the Slope
The 5-12-13 Triangle
Combined Percent Increase and Decrease
Volume of a Cylinder
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
Function - Notation - and Evaulation
Area of a Sector
Area of a Circle
Percent Increase and Decrease
13. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Intersecting Lines
Interior Angles of a Polygon
Union of Sets
Average Formula -
14. 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.
Rate
Number Categories
Solving an Inequality
Multiplying Fractions
15. (average of the x coordinates - average of the y coordinates)
Remainders
The 5-12-13 Triangle
Mixed Numbers and Improper Fractions
Finding the midpoint
16. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Number Categories
Volume of a Rectangular Solid
Determining Absolute Value
Volume of a Cylinder
17. Part = Percent x Whole
Multiplying Fractions
Using an Equation to Find an Intercept
Percent Formula
Greatest Common Factor
18. 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
Volume of a Cylinder
Median and Mode
Simplifying Square Roots
19. 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
Average Formula -
The 3-4-5 Triangle
Triangle Inequality Theorem
Probability
20. 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
Interior Angles of a Polygon
Multiplying Monomials
PEMDAS
21. 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
Raising Powers to Powers
Dividing Fractions
Negative Exponent and Rational Exponent
(Least) Common Multiple
22. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
(Least) Common Multiple
Similar Triangles
Multiples of 2 and 4
Triangle Inequality Theorem
23. Factor out the perfect squares
Solving an Inequality
Adding and Subtraction Polynomials
Simplifying Square Roots
Using an Equation to Find the Slope
24. 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
Pythagorean Theorem
Function - Notation - and Evaulation
Number Categories
Isosceles and Equilateral triangles
25. 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
Pythagorean Theorem
Length of an Arc
Interior and Exterior Angles of a Triangle
Greatest Common Factor
26. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Combined Percent Increase and Decrease
Direct and Inverse Variation
Multiplying and Dividing Roots
Interior Angles of a Polygon
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
Percent Formula
Circumference of a Circle
Dividing Fractions
28. 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
Median and Mode
Even/Odd
Finding the Distance Between Two Points
Factor/Multiple
29. Sum=(Average) x (Number of Terms)
Tangency
Circumference of a Circle
Using the Average to Find the Sum
(Least) Common Multiple
30. 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
Probability
Multiplying/Dividing Signed Numbers
Even/Odd
Volume of a Rectangular Solid
31. 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 Proportion
Probability
Part-to-Part Ratios and Part-to-Whole Ratios
Using an Equation to Find the Slope
32. Area of Triangle = 1/2 (base)(height) - the height is the perpendicular distance between the side that's chosen as the base and the opposite vertex
Isosceles and Equilateral triangles
Finding the Distance Between Two Points
Area of a Triangle
Even/Odd
33. 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
Tangency
Area of a Triangle
Multiples of 2 and 4
Using an Equation to Find an Intercept
34. To solve a proportion - cross multiply
Adding and Subtraction Polynomials
Parallel Lines and Transversals
Solving a Proportion
Reducing Fractions
35. The smallest multiple (other than zero) that two or more numbers have in common.
(Least) Common Multiple
Raising Powers to Powers
Function - Notation - and Evaulation
Exponential Growth
36. 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
Multiples of 3 and 9
Relative Primes
Interior and Exterior Angles of a Triangle
Surface Area of a Rectangular Solid
37. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Percent Increase and Decrease
Using Two Points to Find the Slope
Characteristics of a Rectangle
Characteristics of a Parallelogram
38. 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 an Inequality
Circumference of a Circle
Finding the Original Whole
Volume of a Rectangular Solid
39. To multiply fractions - multiply the numerators and multiply the denominators
Determining Absolute Value
Multiplying Fractions
Finding the midpoint
Combined Percent Increase and Decrease
40. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Determining Absolute Value
Finding the Missing Number
Setting up a Ratio
Union of Sets
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
Multiples of 2 and 4
Adding/Subtracting Signed Numbers
Even/Odd
Solving a Quadratic Equation
42. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Solving a Quadratic Equation
Adding and Subtracting monomials
Surface Area of a Rectangular Solid
Characteristics of a Rectangle
43. 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
Interior Angles of a Polygon
Multiplying Monomials
Exponential Growth
Multiples of 3 and 9
44. The largest factor that two or more numbers have in common.
Surface Area of a Rectangular Solid
Greatest Common Factor
Identifying the Parts and the Whole
Percent Formula
45. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Evaluating an Expression
Remainders
Setting up a Ratio
Area of a Circle
46. 2pr
Circumference of a Circle
Using an Equation to Find an Intercept
Factor/Multiple
Finding the midpoint
47. A square is a rectangle with four equal sides; Area of Square = side*side
Length of an Arc
Characteristics of a Square
Solving a System of Equations
Greatest Common Factor
48. The whole # left over after division
Negative Exponent and Rational Exponent
Remainders
Greatest Common Factor
Area of a Sector
49. pr^2
Intersection of sets
Area of a Circle
Relative Primes
Percent Formula
50. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Finding the Original Whole
Tangency
Factor/Multiple
Negative Exponent and Rational Exponent