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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 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
Relative Primes
Identifying the Parts and the Whole
Adding and Subtracting monomials
Multiplying/Dividing Signed Numbers
2. 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
Percent Formula
Finding the midpoint
Adding/Subtracting Signed Numbers
Average of Evenly Spaced Numbers
3. Volume of a Cylinder = pr^2h
Volume of a Cylinder
Finding the midpoint
Pythagorean Theorem
Adding and Subtracting Roots
4. 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)
Function - Notation - and Evaulation
Adding/Subtracting Signed Numbers
Pythagorean Theorem
Area of a Sector
5. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Repeating Decimal
Adding/Subtracting Fractions
PEMDAS
Multiplying Monomials
6. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
Percent Formula
Using an Equation to Find the Slope
Greatest Common Factor
7. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Median and Mode
The 5-12-13 Triangle
Multiples of 3 and 9
Identifying the Parts and the Whole
8. Subtract the smallest from the largest and add 1
Repeating Decimal
Counting Consecutive Integers
Length of an Arc
Multiplying Monomials
9. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Adding and Subtraction Polynomials
Average Rate
Factor/Multiple
Using an Equation to Find the Slope
10. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Reducing Fractions
Characteristics of a Square
Even/Odd
Multiplying and Dividing Roots
11. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Average of Evenly Spaced Numbers
Characteristics of a Parallelogram
Using the Average to Find the Sum
Using an Equation to Find the Slope
12. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Adding and Subtracting Roots
Exponential Growth
The 5-12-13 Triangle
Similar Triangles
13. 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
Setting up a Ratio
Intersecting Lines
Finding the Original Whole
Combined Percent Increase and Decrease
14. Surface Area = 2lw + 2wh + 2lh
Multiplying and Dividing Powers
Multiples of 2 and 4
Characteristics of a Rectangle
Surface Area of a Rectangular Solid
15. 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
Part-to-Part Ratios and Part-to-Whole Ratios
Domain and Range of a Function
Isosceles and Equilateral triangles
Interior and Exterior Angles of a Triangle
16. 2pr
Circumference of a Circle
Domain and Range of a Function
Exponential Growth
Union of Sets
17. 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)
Simplifying Square Roots
Length of an Arc
Even/Odd
Number Categories
18. 1. Re-express them with common denominators 2. Convert them to decimals
Comparing Fractions
Function - Notation - and Evaulation
Simplifying Square Roots
Triangle Inequality Theorem
19. 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
Solving a Proportion
(Least) Common Multiple
Identifying the Parts and the Whole
Multiples of 3 and 9
20. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Raising Powers to Powers
Using an Equation to Find an Intercept
Multiples of 2 and 4
Solving a System of Equations
21. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
The 3-4-5 Triangle
Multiplying and Dividing Roots
Parallel Lines and Transversals
Number Categories
22. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Area of a Sector
Raising Powers to Powers
Multiplying and Dividing Roots
Percent Increase and Decrease
23. 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
Median and Mode
Characteristics of a Rectangle
Mixed Numbers and Improper Fractions
Characteristics of a Parallelogram
24. 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
The 5-12-13 Triangle
Multiplying and Dividing Powers
Percent Formula
25. Part = Percent x Whole
Counting the Possibilities
Part-to-Part Ratios and Part-to-Whole Ratios
Percent Formula
Parallel Lines and Transversals
26. 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
Determining Absolute Value
Exponential Growth
Even/Odd
Multiplying Fractions
27. 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
Negative Exponent and Rational Exponent
The 3-4-5 Triangle
The 5-12-13 Triangle
Raising Powers to Powers
28. Factor out the perfect squares
Function - Notation - and Evaulation
Simplifying Square Roots
Part-to-Part Ratios and Part-to-Whole Ratios
Counting Consecutive Integers
29. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Remainders
Average Formula -
Solving a System of Equations
Domain and Range of a Function
30. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Determining Absolute Value
Tangency
Counting the Possibilities
Percent Formula
31. Multiply the exponents
Number Categories
Setting up a Ratio
Raising Powers to Powers
Dividing Fractions
32. 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
Percent Increase and Decrease
Probability
Using an Equation to Find an Intercept
Multiplying Fractions
33. 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
Setting up a Ratio
Percent Formula
Solving a System of Equations
Even/Odd
34. pr^2
Probability
Area of a Circle
Multiplying/Dividing Signed Numbers
Simplifying Square Roots
35. For all right triangles: a^2+b^2=c^2
Intersection of sets
Mixed Numbers and Improper Fractions
Negative Exponent and Rational Exponent
Pythagorean Theorem
36. Sum=(Average) x (Number of Terms)
Characteristics of a Parallelogram
Using an Equation to Find an Intercept
Reciprocal
Using the Average to Find the Sum
37. To solve a proportion - cross multiply
Area of a Triangle
Solving a Proportion
Multiplying/Dividing Signed Numbers
Average of Evenly Spaced Numbers
38. Use the sum - Example: if the average of 4 #s is 7 - and the #s are 3 - 5 - 8 - and ____ - what is the fourth #? Work: sum= 4*7 =28 3+5+8=16 28-16=? Answer: 12
Triangle Inequality Theorem
Finding the Missing Number
Solving a Proportion
Combined Percent Increase and Decrease
39. 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.
Mixed Numbers and Improper Fractions
Multiplying Fractions
Dividing Fractions
Number Categories
40. Probability= Favorable Outcomes/Total Possible Outcomes
Solving a System of Equations
Evaluating an Expression
Comparing Fractions
Probability
41. you can add/subtract when the part under the radical is the same
Characteristics of a Square
Adding and Subtracting Roots
Percent Increase and Decrease
Comparing Fractions
42. 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
Using an Equation to Find an Intercept
Multiplying/Dividing Signed Numbers
The 3-4-5 Triangle
Triangle Inequality Theorem
43. 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 Proportion
Length of an Arc
Characteristics of a Square
44. To find the reciprocal of a fraction switch the numerator and the denominator
Using an Equation to Find an Intercept
Multiples of 2 and 4
Adding/Subtracting Fractions
Reciprocal
45. Combine like terms
Adding and Subtraction Polynomials
Volume of a Cylinder
Average of Evenly Spaced Numbers
Area of a Triangle
46. 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
Pythagorean Theorem
Counting Consecutive Integers
Multiplying and Dividing Roots
The 3-4-5 Triangle
47. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Tangency
Setting up a Ratio
Finding the midpoint
48. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Multiplying/Dividing Signed Numbers
Adding and Subtracting monomials
Intersecting Lines
Finding the Original Whole
49. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Setting up a Ratio
Number Categories
Probability
Evaluating an Expression
50. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Simplifying Square Roots
Negative Exponent and Rational Exponent
Characteristics of a Rectangle
Adding/Subtracting Fractions