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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. 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
Tangency
Even/Odd
Adding/Subtracting Signed Numbers
2. Combine like terms
Adding and Subtraction Polynomials
Intersecting Lines
PEMDAS
Solving a Quadratic Equation
3. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Parallel Lines and Transversals
Adding and Subtracting monomials
Average Formula -
Triangle Inequality Theorem
4. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
The 5-12-13 Triangle
Adding/Subtracting Fractions
Mixed Numbers and Improper Fractions
5. 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)
Surface Area of a Rectangular Solid
Length of an Arc
Simplifying Square Roots
Reciprocal
6. 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
Relative Primes
Parallel Lines and Transversals
Area of a Sector
Exponential Growth
7. 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
Mixed Numbers and Improper Fractions
Interior and Exterior Angles of a Triangle
Using Two Points to Find the Slope
Domain and Range of a Function
8. pr^2
Greatest Common Factor
Area of a Circle
Volume of a Rectangular Solid
Circumference of a Circle
9. 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
Relative Primes
Number Categories
Finding the Original Whole
Multiplying/Dividing Signed Numbers
10. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Reciprocal
Volume of a Rectangular Solid
Using an Equation to Find an Intercept
Similar Triangles
11. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Multiplying and Dividing Roots
Finding the Missing Number
Volume of a Rectangular Solid
Solving a Quadratic Equation
12. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Using Two Points to Find the Slope
Parallel Lines and Transversals
Characteristics of a Rectangle
Median and Mode
13. To solve a proportion - cross multiply
Isosceles and Equilateral triangles
Solving a Proportion
Multiplying and Dividing Roots
Domain and Range of a Function
14. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Greatest Common Factor
Area of a Circle
Adding and Subtracting monomials
Function - Notation - and Evaulation
15. 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
Determining Absolute Value
Area of a Circle
Reducing Fractions
16. The smallest multiple (other than zero) that two or more numbers have in common.
(Least) Common Multiple
Percent Increase and Decrease
Adding and Subtraction Polynomials
Adding/Subtracting Fractions
17. Probability= Favorable Outcomes/Total Possible Outcomes
Counting Consecutive Integers
Intersecting Lines
Circumference of a Circle
Probability
18. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Domain and Range of a Function
Similar Triangles
Raising Powers to Powers
19. Domain: all possible values of x for a function range: all possible outputs of a function
Average Formula -
Multiplying Fractions
Domain and Range of a Function
Counting Consecutive Integers
20. 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)
Setting up a Ratio
The 5-12-13 Triangle
Area of a Sector
(Least) Common Multiple
21. 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
Mixed Numbers and Improper Fractions
Determining Absolute Value
Function - Notation - and Evaulation
Triangle Inequality Theorem
22. 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
Area of a Sector
Volume of a Cylinder
Rate
Interior and Exterior Angles of a Triangle
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
Identifying the Parts and the Whole
Similar Triangles
Multiples of 3 and 9
Comparing Fractions
24. 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
Reciprocal
Area of a Triangle
Even/Odd
Raising Powers to Powers
25. Multiply the exponents
Pythagorean Theorem
Multiples of 2 and 4
(Least) Common Multiple
Raising Powers to Powers
26. 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
Characteristics of a Square
Finding the Distance Between Two Points
Tangency
Percent Increase and Decrease
27. Volume of a Cylinder = pr^2h
Similar Triangles
Repeating Decimal
Volume of a Cylinder
Area of a Sector
28. 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
Determining Absolute Value
Median and Mode
Counting Consecutive Integers
29. 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
Multiplying Monomials
Probability
Prime Factorization
Part-to-Part Ratios and Part-to-Whole Ratios
30. 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
Isosceles and Equilateral triangles
Interior and Exterior Angles of a Triangle
Solving a Proportion
31. The whole # left over after division
Negative Exponent and Rational Exponent
Reciprocal
Remainders
Average Formula -
32. (average of the x coordinates - average of the y coordinates)
Average Formula -
Intersecting Lines
The 5-12-13 Triangle
Finding the midpoint
33. 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
Comparing Fractions
Area of a Circle
Direct and Inverse Variation
Multiplying/Dividing Signed Numbers
34. Sum=(Average) x (Number of Terms)
Determining Absolute Value
Characteristics of a Rectangle
Using the Average to Find the Sum
Adding/Subtracting Fractions
35. 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
Adding and Subtraction Polynomials
Solving a Proportion
Circumference of a Circle
36. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Pythagorean Theorem
Reducing Fractions
Median and Mode
Interior and Exterior Angles of a Triangle
37. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Multiplying and Dividing Roots
Multiplying/Dividing Signed Numbers
Direct and Inverse Variation
38. 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
Exponential Growth
Multiplying Fractions
Mixed Numbers and Improper Fractions
Dividing Fractions
39. A square is a rectangle with four equal sides; Area of Square = side*side
Area of a Sector
Area of a Triangle
Length of an Arc
Characteristics of a Square
40. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Area of a Triangle
Volume of a Rectangular Solid
Average Rate
The 3-4-5 Triangle
41. 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
Interior and Exterior Angles of a Triangle
Circumference of a Circle
The 3-4-5 Triangle
Domain and Range of a Function
42. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Mixed Numbers and Improper Fractions
Using an Equation to Find the Slope
Multiples of 2 and 4
Isosceles and Equilateral triangles
43. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Circumference of a Circle
Finding the Distance Between Two Points
Setting up a Ratio
Repeating Decimal
44. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Intersection of sets
Similar Triangles
Using an Equation to Find an Intercept
Parallel Lines and Transversals
45. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Evaluating an Expression
Counting Consecutive Integers
Counting the Possibilities
Using an Equation to Find an Intercept
46. 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
Length of an Arc
Counting the Possibilities
Using an Equation to Find an Intercept
Characteristics of a Parallelogram
47. 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
Multiplying Monomials
Isosceles and Equilateral triangles
Rate
Multiplying and Dividing Roots
48. 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
Adding and Subtraction Polynomials
Intersecting Lines
Circumference of a Circle
Multiplying/Dividing Signed Numbers
49. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
(Least) Common Multiple
Multiplying Monomials
Factor/Multiple
Area of a Sector
50. Change in y/ change in x rise/run
Using an Equation to Find an Intercept
Using Two Points to Find the Slope
Characteristics of a Rectangle
Average Formula -