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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. 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
Dividing Fractions
Circumference of a Circle
Area of a Triangle
The 5-12-13 Triangle
2. To multiply fractions - multiply the numerators and multiply the denominators
Average Formula -
Simplifying Square Roots
Interior Angles of a Polygon
Multiplying Fractions
3. 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
Interior Angles of a Polygon
Part-to-Part Ratios and Part-to-Whole Ratios
Isosceles and Equilateral triangles
Volume of a Rectangular Solid
4. 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
Rate
Percent Formula
Raising Powers to Powers
Using an Equation to Find an Intercept
5. you can add/subtract when the part under the radical is the same
Even/Odd
Relative Primes
Adding and Subtracting Roots
Prime Factorization
6. 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
Isosceles and Equilateral triangles
Finding the Original Whole
Probability
Finding the midpoint
7. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Intersection of sets
Evaluating an Expression
Multiples of 2 and 4
Intersecting Lines
8. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Greatest Common Factor
Multiplying Monomials
Union of Sets
Surface Area of a Rectangular Solid
9. 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
Isosceles and Equilateral triangles
Tangency
Finding the Missing Number
Adding/Subtracting Signed Numbers
10. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Characteristics of a Rectangle
Negative Exponent and Rational Exponent
Multiples of 2 and 4
Multiplying Monomials
11. 2pr
Circumference of a Circle
Even/Odd
Greatest Common Factor
Multiplying and Dividing Powers
12. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Mixed Numbers and Improper Fractions
Intersection of sets
Tangency
Identifying the Parts and the Whole
13. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Exponential Growth
Intersecting Lines
Simplifying Square Roots
Volume of a Rectangular Solid
14. Domain: all possible values of x for a function range: all possible outputs of a function
Determining Absolute Value
Using an Equation to Find the Slope
Domain and Range of a Function
Part-to-Part Ratios and Part-to-Whole Ratios
15. 1. Re-express them with common denominators 2. Convert them to decimals
Solving a Proportion
Circumference of a Circle
Comparing Fractions
Triangle Inequality Theorem
16. 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
Using Two Points to Find the Slope
Adding and Subtracting monomials
The 3-4-5 Triangle
Counting the Possibilities
17. 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.
Exponential Growth
Function - Notation - and Evaulation
Intersection of sets
Number Categories
18. 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
Exponential Growth
Volume of a Rectangular Solid
Characteristics of a Rectangle
Relative Primes
19. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Interior and Exterior Angles of a Triangle
Multiplying Fractions
Using an Equation to Find the Slope
Intersection of sets
20. Multiply the exponents
Area of a Circle
Adding and Subtracting Roots
Finding the Original Whole
Raising Powers to Powers
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
Negative Exponent and Rational Exponent
Determining Absolute Value
Domain and Range of a Function
Interior and Exterior Angles of a Triangle
22. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
PEMDAS
Dividing Fractions
Intersection of sets
Characteristics of a Rectangle
23. (average of the x coordinates - average of the y coordinates)
Finding the midpoint
Using the Average to Find the Sum
Comparing Fractions
Multiplying and Dividing Powers
24. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Using an Equation to Find the Slope
Finding the Original Whole
Reducing Fractions
Dividing Fractions
25. Change in y/ change in x rise/run
Using the Average to Find the Sum
Using Two Points to Find the Slope
Dividing Fractions
Volume of a Cylinder
26. Subtract the smallest from the largest and add 1
Counting Consecutive Integers
Domain and Range of a Function
Even/Odd
Isosceles and Equilateral triangles
27. Combine like terms
Adding and Subtraction Polynomials
Percent Formula
Negative Exponent and Rational Exponent
Identifying the Parts and the Whole
28. To divide fractions - invert the second one and multiply
Characteristics of a Rectangle
Union of Sets
Rate
Dividing Fractions
29. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Number Categories
Area of a Triangle
Isosceles and Equilateral triangles
Intersection of sets
30. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
PEMDAS
Interior Angles of a Polygon
Parallel Lines and Transversals
Interior and Exterior Angles of a Triangle
31. 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
Multiplying Fractions
Isosceles and Equilateral triangles
Exponential Growth
32. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
(Least) Common Multiple
Union of Sets
Using Two Points to Find the Slope
Multiplying Monomials
33. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Reciprocal
Interior and Exterior Angles of a Triangle
Tangency
Solving a Quadratic Equation
34. The whole # left over after division
Similar Triangles
Direct and Inverse Variation
Remainders
Determining Absolute Value
35. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Finding the Missing Number
Length of an Arc
Similar Triangles
Characteristics of a Square
36. 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
Using an Equation to Find an Intercept
Multiples of 2 and 4
Multiples of 3 and 9
37. 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)
The 5-12-13 Triangle
Length of an Arc
Solving a Quadratic Equation
Interior and Exterior Angles of a Triangle
38. 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
Relative Primes
Solving an Inequality
Function - Notation - and Evaulation
Setting up a Ratio
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
Multiplying/Dividing Signed Numbers
Multiplying Monomials
Volume of a Cylinder
40. 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
Union of Sets
Isosceles and Equilateral triangles
(Least) Common Multiple
Using an Equation to Find the Slope
41. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Area of a Circle
Setting up a Ratio
Part-to-Part Ratios and Part-to-Whole Ratios
Using the Average to Find the Sum
42. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Setting up a Ratio
Using an Equation to Find the Slope
Average Formula -
Even/Odd
43. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Isosceles and Equilateral triangles
The 3-4-5 Triangle
Adding and Subtracting monomials
Pythagorean Theorem
44. Volume of a Cylinder = pr^2h
Volume of a Cylinder
Pythagorean Theorem
Multiplying and Dividing Roots
Average Formula -
45. Factor out the perfect squares
PEMDAS
Simplifying Square Roots
Factor/Multiple
Probability
46. To convert a mixed number to an improper fraction - multiply the whole number by the denominator - then add the numerator over the same denominator - to convert an improper fraction to a mixed number - divide the denominator into the numerator to get
Solving a Proportion
Multiplying and Dividing Powers
Mixed Numbers and Improper Fractions
Characteristics of a Square
47. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Function - Notation - and Evaulation
Solving a Quadratic Equation
Parallel Lines and Transversals
Characteristics of a Rectangle
48. 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
Counting the Possibilities
Using the Average to Find the Sum
PEMDAS
Union of Sets
49. 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
Volume of a Rectangular Solid
Negative Exponent and Rational Exponent
Direct and Inverse Variation
Area of a Circle
50. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Length of an Arc
Using the Average to Find the Sum
Dividing Fractions
Factor/Multiple