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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
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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. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Parallel Lines and Transversals
Area of a Triangle
Comparing Fractions
Reducing Fractions
2. 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
Simplifying Square Roots
Repeating Decimal
Interior and Exterior Angles of a Triangle
Exponential Growth
3. 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)
Prime Factorization
Area of a Sector
Evaluating an Expression
Multiples of 2 and 4
4. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Finding the Distance Between Two Points
Finding the Missing Number
Parallel Lines and Transversals
Evaluating an Expression
5. 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
Comparing Fractions
Area of a Circle
Relative Primes
Finding the Missing Number
6. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Union of Sets
Intersection of sets
Average Formula -
Finding the midpoint
7. 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 Rate
Solving a Proportion
Similar Triangles
The 3-4-5 Triangle
8. 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
Multiplying Monomials
Identifying the Parts and the Whole
Median and Mode
Finding the midpoint
9. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Parallel Lines and Transversals
Finding the Original Whole
Finding the Distance Between Two Points
Volume of a Rectangular Solid
10. 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.
Area of a Sector
Counting the Possibilities
Number Categories
Volume of a Cylinder
11. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Intersecting Lines
Average of Evenly Spaced Numbers
Adding/Subtracting Fractions
Pythagorean Theorem
12. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Evaluating an Expression
Area of a Sector
Multiples of 2 and 4
Tangency
13. 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
Rate
Repeating Decimal
Solving a Proportion
Average of Evenly Spaced Numbers
14. 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
Average Formula -
Average Rate
Characteristics of a Parallelogram
Multiplying/Dividing Signed Numbers
15. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Solving an Inequality
The 5-12-13 Triangle
Multiplying/Dividing Signed Numbers
Tangency
16. 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
The 5-12-13 Triangle
Multiplying Monomials
Counting Consecutive Integers
Interior and Exterior Angles of a Triangle
17. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Repeating Decimal
Area of a Sector
Surface Area of a Rectangular Solid
Prime Factorization
18. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Using an Equation to Find the Slope
Setting up a Ratio
Multiples of 3 and 9
Multiples of 2 and 4
19. 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
Using an Equation to Find an Intercept
Adding/Subtracting Signed Numbers
Exponential Growth
Solving a Proportion
20. Add the exponents and keep the same base
Multiplying and Dividing Powers
Interior and Exterior Angles of a Triangle
Interior Angles of a Polygon
Evaluating an Expression
21. 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
Dividing Fractions
Solving a Quadratic Equation
Number Categories
22. 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
Area of a Triangle
Adding/Subtracting Signed Numbers
Even/Odd
Area of a Circle
23. Combine like terms
Adding and Subtraction Polynomials
Circumference of a Circle
Repeating Decimal
Solving a Proportion
24. 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
Combined Percent Increase and Decrease
Area of a Sector
The 5-12-13 Triangle
Solving a System of Equations
25. 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
Direct and Inverse Variation
Mixed Numbers and Improper Fractions
Counting Consecutive Integers
26. Part = Percent x Whole
Comparing Fractions
Length of an Arc
The 5-12-13 Triangle
Percent Formula
27. 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
Average of Evenly Spaced Numbers
Function - Notation - and Evaulation
Finding the Missing Number
Circumference of a Circle
28. For all right triangles: a^2+b^2=c^2
Pythagorean Theorem
Factor/Multiple
Probability
Intersecting Lines
29. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Adding/Subtracting Fractions
Using Two Points to Find the Slope
Counting Consecutive Integers
Factor/Multiple
30. 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
Volume of a Cylinder
Domain and Range of a Function
Finding the Original Whole
Identifying the Parts and the Whole
31. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Raising Powers to Powers
Using an Equation to Find an Intercept
Isosceles and Equilateral triangles
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
Length of an Arc
Volume of a Cylinder
Adding/Subtracting Signed Numbers
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
Factor/Multiple
Using an Equation to Find an Intercept
Evaluating an Expression
Combined Percent Increase and Decrease
34. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Finding the Original Whole
Mixed Numbers and Improper Fractions
Characteristics of a Rectangle
Remainders
35. Probability= Favorable Outcomes/Total Possible Outcomes
Repeating Decimal
Isosceles and Equilateral triangles
Probability
Adding and Subtracting Roots
36. To find the reciprocal of a fraction switch the numerator and the denominator
Greatest Common Factor
Reciprocal
Multiples of 2 and 4
Remainders
37. To solve a proportion - cross multiply
Area of a Circle
Surface Area of a Rectangular Solid
Intersecting Lines
Solving a Proportion
38. 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
Solving a Quadratic Equation
Greatest Common Factor
Percent Increase and Decrease
Volume of a Cylinder
39. 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
Triangle Inequality Theorem
Interior and Exterior Angles of a Triangle
Function - Notation - and Evaulation
Reciprocal
40. you can add/subtract when the part under the radical is the same
Solving a System of Equations
Adding and Subtracting Roots
Similar Triangles
Finding the Distance Between Two Points
41. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Finding the Missing Number
Area of a Circle
Parallel Lines and Transversals
Finding the Distance Between Two Points
42. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Evaluating an Expression
Adding/Subtracting Fractions
Triangle Inequality Theorem
Average Rate
43. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Simplifying Square Roots
Intersecting Lines
Adding and Subtracting Roots
Raising Powers to Powers
44. The smallest multiple (other than zero) that two or more numbers have in common.
(Least) Common Multiple
Volume of a Cylinder
Simplifying Square Roots
Comparing Fractions
45. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Percent Formula
Counting the Possibilities
Union of Sets
Characteristics of a Rectangle
46. Change in y/ change in x rise/run
Using Two Points to Find the Slope
Probability
Comparing Fractions
Area of a Sector
47. 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
Negative Exponent and Rational Exponent
The 5-12-13 Triangle
Characteristics of a Square
48. 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
Isosceles and Equilateral triangles
Using the Average to Find the Sum
Area of a Circle
Interior Angles of a Polygon
49. The whole # left over after division
Using an Equation to Find the Slope
Remainders
Negative Exponent and Rational Exponent
Volume of a Rectangular Solid
50. 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
Direct and Inverse Variation
Solving an Inequality
Adding/Subtracting Fractions
Remainders