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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. For all right triangles: a^2+b^2=c^2
The 3-4-5 Triangle
Tangency
Pythagorean Theorem
Circumference of a Circle
2. Multiply the exponents
Finding the Distance Between Two Points
Isosceles and Equilateral triangles
Solving a Quadratic Equation
Raising Powers to Powers
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)
Area of a Sector
Median and Mode
Average of Evenly Spaced Numbers
Surface Area of a Rectangular Solid
4. Combine equations in such a way that one of the variables cancel out
Dividing Fractions
Rate
Solving a System of Equations
Adding/Subtracting Signed Numbers
5. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Factor/Multiple
Adding and Subtracting monomials
Relative Primes
Finding the Original Whole
6. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Probability
Combined Percent Increase and Decrease
Solving a Quadratic Equation
Intersecting Lines
7. 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
Tangency
Determining Absolute Value
Multiplying/Dividing Signed Numbers
Remainders
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
Characteristics of a Square
Union of Sets
Even/Odd
Identifying the Parts and the Whole
9. 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
Adding/Subtracting Fractions
Triangle Inequality Theorem
Raising Powers to Powers
10. 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
Determining Absolute Value
Percent Increase and Decrease
Direct and Inverse Variation
Number Categories
11. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Area of a Sector
Solving a Proportion
Dividing Fractions
Finding the Distance Between Two Points
12. 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
Prime Factorization
Finding the midpoint
Adding/Subtracting Signed Numbers
Similar Triangles
13. you can add/subtract when the part under the radical is the same
Domain and Range of a Function
Adding and Subtracting Roots
Intersecting Lines
Length of an Arc
14. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Combined Percent Increase and Decrease
Volume of a Cylinder
Solving a Proportion
Tangency
15. 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
Identifying the Parts and the Whole
Using an Equation to Find the Slope
Percent Increase and Decrease
Exponential Growth
16. 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
Exponential Growth
Simplifying Square Roots
Reducing Fractions
17. 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
Characteristics of a Rectangle
Adding/Subtracting Fractions
Area of a Triangle
Solving an Inequality
18. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Area of a Triangle
Negative Exponent and Rational Exponent
Tangency
Intersection of sets
19. Factor out the perfect squares
Using Two Points to Find the Slope
Characteristics of a Parallelogram
Simplifying Square Roots
Multiplying and Dividing Powers
20. 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
Negative Exponent and Rational Exponent
The 3-4-5 Triangle
Multiplying/Dividing Signed Numbers
Adding and Subtracting monomials
21. 2pr
Union of Sets
Tangency
Circumference of a Circle
Remainders
22. Domain: all possible values of x for a function range: all possible outputs of a function
Combined Percent Increase and Decrease
Domain and Range of a Function
Dividing Fractions
Multiplying and Dividing Roots
23. 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
Circumference of a Circle
Adding and Subtraction Polynomials
Interior Angles of a Polygon
24. Part = Percent x Whole
Percent Formula
Solving a Quadratic Equation
Multiplying Monomials
Identifying the Parts and the Whole
25. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Repeating Decimal
Triangle Inequality Theorem
Characteristics of a Rectangle
Multiplying/Dividing Signed Numbers
26. 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
Finding the Original Whole
Even/Odd
(Least) Common Multiple
Circumference of a Circle
27. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Prime Factorization
Solving a Proportion
Length of an Arc
Probability
28. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Using the Average to Find the Sum
Probability
Average Formula -
Tangency
29. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Adding/Subtracting Fractions
Intersecting Lines
Setting up a Ratio
Comparing Fractions
30. 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
Using an Equation to Find the Slope
Simplifying Square Roots
Relative Primes
Area of a Sector
31. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
PEMDAS
Average Rate
Using the Average to Find the Sum
Factor/Multiple
32. 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
Percent Formula
Direct and Inverse Variation
The 3-4-5 Triangle
Interior Angles of a Polygon
33. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Determining Absolute Value
Greatest Common Factor
Adding/Subtracting Signed Numbers
Intersecting Lines
34. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Evaluating an Expression
Determining Absolute Value
Negative Exponent and Rational Exponent
Adding/Subtracting Signed Numbers
35. (average of the x coordinates - average of the y coordinates)
Finding the midpoint
Solving a System of Equations
Using an Equation to Find the Slope
Average of Evenly Spaced Numbers
36. The whole # left over after division
Number Categories
Characteristics of a Square
Remainders
Average Rate
37. Subtract the smallest from the largest and add 1
Parallel Lines and Transversals
Reducing Fractions
Multiplying and Dividing Powers
Counting Consecutive Integers
38. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Percent Increase and Decrease
Finding the midpoint
Average of Evenly Spaced Numbers
The 3-4-5 Triangle
39. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Adding and Subtracting Roots
Adding/Subtracting Fractions
Triangle Inequality Theorem
Tangency
40. 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
Interior and Exterior Angles of a Triangle
Prime Factorization
Counting Consecutive Integers
Using an Equation to Find an Intercept
41. 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
Triangle Inequality Theorem
Using an Equation to Find an Intercept
Identifying the Parts and the Whole
42. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Pythagorean Theorem
Adding/Subtracting Signed Numbers
Function - Notation - and Evaulation
43. 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
Solving an Inequality
Similar Triangles
Triangle Inequality Theorem
Relative Primes
44. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Multiplying and Dividing Roots
Percent Increase and Decrease
Reducing Fractions
Union of Sets
45. Add the exponents and keep the same base
Multiplying and Dividing Powers
Triangle Inequality Theorem
Adding/Subtracting Fractions
Adding and Subtraction Polynomials
46. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Multiplying and Dividing Roots
Finding the midpoint
Multiples of 2 and 4
Interior Angles of a Polygon
47. Surface Area = 2lw + 2wh + 2lh
Multiplying and Dividing Roots
Surface Area of a Rectangular Solid
Circumference of a Circle
Parallel Lines and Transversals
48. Change in y/ change in x rise/run
Part-to-Part Ratios and Part-to-Whole Ratios
Using Two Points to Find the Slope
Remainders
Solving an Inequality
49. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Pythagorean Theorem
Mixed Numbers and Improper Fractions
Exponential Growth
Multiplying Monomials
50. pr^2
Using Two Points to Find the Slope
Characteristics of a Rectangle
Area of a Circle
Average Formula -