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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 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
Solving a System of Equations
Adding/Subtracting Signed Numbers
Surface Area of a Rectangular Solid
Adding and Subtracting Roots
2. Add the exponents and keep the same base
Finding the Distance Between Two Points
Multiplying and Dividing Powers
Pythagorean Theorem
Solving a Quadratic Equation
3. 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
Solving a System of Equations
Determining Absolute Value
Even/Odd
Counting the Possibilities
4. 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
Area of a Sector
Similar Triangles
Isosceles and Equilateral triangles
5. 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
Similar Triangles
Greatest Common Factor
Percent Increase and Decrease
Area of a Sector
6. The median is the value that falls in the middle of the set - the mode is the value that appears most often
The 5-12-13 Triangle
Median and Mode
Determining Absolute Value
Circumference of a Circle
7. 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
Even/Odd
Relative Primes
Solving a System of Equations
Interior and Exterior Angles of a Triangle
8. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Multiplying and Dividing Powers
Characteristics of a Square
Finding the Distance Between Two Points
Adding and Subtracting monomials
9. 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
Tangency
Function - Notation - and Evaulation
Relative Primes
Multiples of 2 and 4
10. 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
Finding the Distance Between Two Points
(Least) Common Multiple
Negative Exponent and Rational Exponent
11. 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
Counting the Possibilities
Exponential Growth
Interior Angles of a Polygon
Evaluating an Expression
12. 1. Re-express them with common denominators 2. Convert them to decimals
Characteristics of a Square
Solving a Quadratic Equation
Comparing Fractions
Multiplying Monomials
13. 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
The 3-4-5 Triangle
Setting up a Ratio
Characteristics of a Rectangle
Direct and Inverse Variation
14. The largest factor that two or more numbers have in common.
Prime Factorization
Adding and Subtraction Polynomials
Greatest Common Factor
Raising Powers to Powers
15. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Solving a Proportion
Volume of a Rectangular Solid
Prime Factorization
Average of Evenly Spaced Numbers
16. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Greatest Common Factor
Average of Evenly Spaced Numbers
Reducing Fractions
Characteristics of a Rectangle
17. For all right triangles: a^2+b^2=c^2
Remainders
Finding the Original Whole
Pythagorean Theorem
Using an Equation to Find an Intercept
18. A square is a rectangle with four equal sides; Area of Square = side*side
Determining Absolute Value
Characteristics of a Square
Comparing Fractions
Setting up a Ratio
19. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Volume of a Rectangular Solid
Intersecting Lines
Adding and Subtraction Polynomials
Multiples of 3 and 9
20. Part = Percent x Whole
Median and Mode
Percent Formula
Percent Increase and Decrease
Evaluating an Expression
21. 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
Using Two Points to Find the Slope
Direct and Inverse Variation
Using an Equation to Find the Slope
Average of Evenly Spaced Numbers
22. Multiply the exponents
(Least) Common Multiple
Negative Exponent and Rational Exponent
Raising Powers to Powers
Dividing Fractions
23. Factor out the perfect squares
Multiples of 2 and 4
Percent Increase and Decrease
Prime Factorization
Simplifying Square Roots
24. pr^2
Median and Mode
Average of Evenly Spaced Numbers
Intersection of sets
Area of a Circle
25. The whole # left over after division
Number Categories
Average Rate
Setting up a Ratio
Remainders
26. The smallest multiple (other than zero) that two or more numbers have in common.
Volume of a Rectangular Solid
Using an Equation to Find the Slope
(Least) Common Multiple
Finding the Original Whole
27. 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)
Percent Increase and Decrease
Direct and Inverse Variation
Comparing Fractions
Length of an Arc
28. To find the reciprocal of a fraction switch the numerator and the denominator
Adding and Subtraction Polynomials
Reciprocal
Interior Angles of a Polygon
Pythagorean Theorem
29. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Parallel Lines and Transversals
Multiplying and Dividing Roots
PEMDAS
Adding/Subtracting Fractions
30. 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
Factor/Multiple
Finding the Original Whole
Median and Mode
31. 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
Percent Increase and Decrease
Solving an Inequality
Determining Absolute Value
Isosceles and Equilateral triangles
32. Combine like terms
Adding/Subtracting Fractions
Adding and Subtraction Polynomials
Probability
Interior Angles of a Polygon
33. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Direct and Inverse Variation
Probability
Parallel Lines and Transversals
Average Rate
34. Combine equations in such a way that one of the variables cancel out
Combined Percent Increase and Decrease
Interior and Exterior Angles of a Triangle
Part-to-Part Ratios and Part-to-Whole Ratios
Solving a System of Equations
35. Subtract the smallest from the largest and add 1
Counting Consecutive Integers
Multiplying and Dividing Powers
Multiples of 3 and 9
Finding the Original Whole
36. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Percent Increase and Decrease
Union of Sets
Evaluating an Expression
Adding and Subtracting monomials
37. 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
Circumference of a Circle
Interior and Exterior Angles of a Triangle
Comparing Fractions
38. 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
Number Categories
Multiplying/Dividing Signed Numbers
Solving a Quadratic Equation
Function - Notation - and Evaulation
39. 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
Adding and Subtracting Roots
Characteristics of a Square
Circumference of a Circle
40. 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
Area of a Sector
Prime Factorization
Even/Odd
Solving an Inequality
41. 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
Dividing Fractions
Combined Percent Increase and Decrease
Length of an Arc
Circumference of a Circle
42. 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
Multiplying Monomials
Multiples of 2 and 4
Determining Absolute Value
43. 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)
Reciprocal
Greatest Common Factor
Simplifying Square Roots
Area of a Sector
44. 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
Using an Equation to Find an Intercept
Average Formula -
Multiples of 3 and 9
Greatest Common Factor
45. (average of the x coordinates - average of the y coordinates)
Tangency
Finding the midpoint
Surface Area of a Rectangular Solid
Parallel Lines and Transversals
46. 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
Adding and Subtracting Roots
Finding the Missing Number
Part-to-Part Ratios and Part-to-Whole Ratios
Characteristics of a Rectangle
47. 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
Multiplying Monomials
Negative Exponent and Rational Exponent
Evaluating an Expression
Union of Sets
48. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Parallel Lines and Transversals
Reciprocal
Evaluating an Expression
Characteristics of a Square
49. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Intersection of sets
Isosceles and Equilateral triangles
Similar Triangles
Determining Absolute Value
50. 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
Area of a Triangle
Finding the Original Whole
Rate
Multiplying Fractions