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SAT Math

Subjects : sat, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. Finding the Sum of the Interior Angles of a Polygon
Just add or subtract the coefficients in front of the radicals.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
The 3 interior angles of a any triangle add up to 180 degrees. An exterior angle of a triangle is equal to the sum of the remote - that is - non-adjacent - interior angles.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

2. If 4(x(2)-10x+25) - then what is the value of x?
Get the absolute value equation by itself. Solve.
Remember that any non-zero base to the power of zero is equal to one. Set the exponent equal to zero and solve for x.
Use the formula distance=rate*time and its variations to help in this question.
(x1+x2)/2 -(y1+y2)/2

3. Definition of a Rational Number
Fraction to a Decimal: Divide the Denominator into the numerator - Decimal to a Fraction: Set the decimal over 1 and multiply the numerator and denominator by 10 raised to the number of digits to the right of the decimal point.
Direct Variation- y=kx - where k is constant. As x gets larger - y gets larger. If the number of units of B were to double - the number of units of A would double - Inverse Variation- xy=k - where k is a constant. As x gets larger - y gets smaller. A
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

4. Multiplying Fractions
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Subtract the smallest from the largest and add 1
Multiply the numerators and multiply the denominators.

5. Adding and Subtracting Fractions
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Find a common denominator - then add or subtract the numerators.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Don't be confused by all the variables. Recall that (x-y)(x+y)=x(2)-y(2). Then - x(2)-y(2)=5*7=35. x(2)+1-y(2)=x(2)-y(2)+1=35+1=36.

6. Finding the LCM of Two or More Numbers

7. Solving a Radical Equation
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Multiply the numerators and multiply the denominators.
Multiply and/or divide positives and negatives treat the number parts as usual - and attach a negative sign if there is an odd number of negatives
Isolate the radical expression and use the standard rules of algebra.

8. Finding the Distance Between Two Points on a Coordinate Graph
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Four equal acute angles and four equal obtuse angles.
The value that falls in the middle of the set.

9. Properties of the Interior and Exterior Angles of a Triangle
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
A(2)+b(2)=c(2)
The 3 interior angles of a any triangle add up to 180 degrees. An exterior angle of a triangle is equal to the sum of the remote - that is - non-adjacent - interior angles.

10. Adding and Subtracting Monomials
Do whatever is necessary to both sides to isolate the variable.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Use the units to keep things straight - Snowfall inches/hours
If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side.

11. Solving an Inequality
The 3 interior angles of a any triangle add up to 180 degrees. An exterior angle of a triangle is equal to the sum of the remote - that is - non-adjacent - interior angles.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Put the equation into y=mx+b-- in which case b is the y-intercept.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

12. Finding the GCF of Two or More Numbers
Sector is a piece of the area of a circle. Area of a Sector: (n/360)((pie)r2) - n is the degree measure of the sector's central angle
The value that falls in the middle of the set.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

13. Solving a System of Equations
Two relatively prime numbers are integers that have no common factor other than 1.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Four equal acute angles and four equal obtuse angles.
Combine the equations so that one of the variables cancels out. 4x+3y=8 and x+y=3. Multiply equation 2 by -3... then add the two equations.

14. Average Rate and How Do You Find It
Adjacent angles are supplementary - Vertical angles are equal
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

15. Calculating Negative Exponents and Radical Exponents
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Scalene- No sides or angles are equal - Isosceles- Have two equal sides. The angles opposite the equal sides are also equal - Equilateral- All three sides and angles are equal.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

16. What is the value of x(2)+1-y(2) - if x-y=5 and x+y=7?

17. What is the Pythagorean Theorem?
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.
A(2)+b(2)=c(2)
VofaRS=lwh
The whole number left over after division.

18. Converting from an Improper Fraction to a Mixed Number
Fraction to a Decimal: Divide the Denominator into the numerator - Decimal to a Fraction: Set the decimal over 1 and multiply the numerator and denominator by 10 raised to the number of digits to the right of the decimal point.
-The Factors of integer n are the positive integers that divide into n with no remainder - The Multiples of n are the positive integers that n divides into with no remainder.
Divide the denominator into the numerator to get a whole number quotient with a remainder. The quotient becomes the whole number of the mixed number. Remainder becomes the numerator.
FOIL: First - Outer - Inner - Last... Combine Like Terms

19. Finding a Term in a Geometric Sequence
Sum: Average x Number of Terms
The value that falls in the middle of the set.
Use the formula - a(n)=a(1)r(n-1) - where a(n) is the nth term - a1 is the first term - and r is the ratio between the terms.
An integer is divisible by 3 if the sum of its digits is divisible by 3 - - An integer is divisible by 9 is the sum of its digits is divisible by 9.

20. Finding the Area of a Circle
Combine like terms.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Four equal acute angles and four equal obtuse angles.
(pie)r(squared)

21. Let N represent the smallest positive integer that is a multiple of 6 and 8 - but leaves a remainder of 2 when divided by 7. What is the value of N?
Combine the equations so that one of the variables cancels out. 4x+3y=8 and x+y=3. Multiply equation 2 by -3... then add the two equations.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Average the smallest and largest number
(x1+x2)/2 -(y1+y2)/2

22. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Ue the formula y=mx+b - and remember that the value of m is the slope of the line. The slopes of two perpendicular lines are negative reciprocals of one another.
Variables that have an inverse relationship will always have the same product. As one value gets larger - the other gets smaller. Set up and solve the equation 310=6x. Answer: 5
Scalene- No sides or angles are equal - Isosceles- Have two equal sides. The angles opposite the equal sides are also equal - Equilateral- All three sides and angles are equal.
Plug in the given values for the unknowns and calculate according to PEMDAS.

23. Formula Used to Find Percent
If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side.
Part=Percent x Whole
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
2(pie)r

24. Calculating the Probability that an Event will Take Place
Use the sum... If the average of 4 numbers is 7 - then the sum of those 4 numbers is 4*7 - or 28. Suppose that 3 of the numbers are 3 -5 - and 9. These 3 numbers add up to 16 of that 28 - 12 is the fourth number.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Multiply the numerators and multiply the denominators.

25. Characteristics of a Square
Find a common denominator - then add or subtract the numerators.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Set the quadratic equation equal to zero with the terms in order of decreasing exponents - and solve for the roots by factoring. Don't forget to then find the difference in the roots by subtracting them. Ans: 2

26. Finding the Volume of a Rectangular Solid
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Ue the formula y=mx+b - and remember that the value of m is the slope of the line. The slopes of two perpendicular lines are negative reciprocals of one another.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
VofaRS=lwh

27. Identifying Which Number of a Fraction is the Part and Which Number is the Whole

28. Finding the Circumference of a Circle
Set the quadratic equation equal to zero with the terms in order of decreasing exponents - and solve for the roots by factoring. Don't forget to then find the difference in the roots by subtracting them. Ans: 2
Use the formula - a(n)=a(1)r(n-1) - where a(n) is the nth term - a1 is the first term - and r is the ratio between the terms.
Ue the formula y=mx+b - and remember that the value of m is the slope of the line. The slopes of two perpendicular lines are negative reciprocals of one another.
2(pie)r

29. Factoring a Polynomial ('FOIL in Reverse')
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

30. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Don't be confused by all the variables. Recall that (x-y)(x+y)=x(2)-y(2). Then - x(2)-y(2)=5*7=35. x(2)+1-y(2)=x(2)-y(2)+1=35+1=36.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

31. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Multiply and/or divide positives and negatives treat the number parts as usual - and attach a negative sign if there is an odd number of negatives
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

32. Multiply and Divide Positive and Negative Numbers
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Do whatever is necessary to both sides to isolate the variable.
Multiply and/or divide positives and negatives treat the number parts as usual - and attach a negative sign if there is an odd number of negatives

33. Numbers that are Relatively Prime
Use the units to keep things straight - Snowfall inches/hours
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Two relatively prime numbers are integers that have no common factor other than 1.
The length of one side of a triangle must be greater than the difference and less of the sum of the lengths of the other two sides.

34. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Combine like terms.
An integer is divisible by 3 if the sum of its digits is divisible by 3 - - An integer is divisible by 9 is the sum of its digits is divisible by 9.

35. What is the positive difference between the answers to the equation 35+x(2)=12x?

36. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Put each number in the original ratio over the sum of the numbers.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Four equal acute angles and four equal obtuse angles.

37. Finding the Rate of Speed
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Use the formula distance=rate*time and its variations to help in this question.
Use the units to keep things straight - Snowfall inches/hours
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

38. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Variables that have an inverse relationship will always have the same product. As one value gets larger - the other gets smaller. Set up and solve the equation 310=6x. Answer: 5
Use simple numbers like 1 and 2 and see what happens.
VofaC: (pie)r(2)h
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

39. Solving a Problem Involving Rates
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Combine the equations so that one of the variables cancels out. 4x+3y=8 and x+y=3. Multiply equation 2 by -3... then add the two equations.
Use the units to keep things straight - Snowfall inches/hours
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

40. Formula to Find Average
Slope=change in y/change in x
Fraction to a Decimal: Divide the Denominator into the numerator - Decimal to a Fraction: Set the decimal over 1 and multiply the numerator and denominator by 10 raised to the number of digits to the right of the decimal point.
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.
Average: Sum of the Terms/Number of the Terms

41. Converting from part-to-part ratios to part-to-whole ratios
Multiply the numerators and multiply the denominators.
Put each number in the original ratio over the sum of the numbers.
Use the sum... If the average of 4 numbers is 7 - then the sum of those 4 numbers is 4*7 - or 28. Suppose that 3 of the numbers are 3 -5 - and 9. These 3 numbers add up to 16 of that 28 - 12 is the fourth number.
Two relatively prime numbers are integers that have no common factor other than 1.

42. Multiplying and Dividing Roots
Use the formula - a(n)=a(1)r(n-1) - where a(n) is the nth term - a1 is the first term - and r is the ratio between the terms.
Multiplying: Multiply the numbers under the different radicals. The product goes under one radical - Dividing: The quotient of more than one square root is equal to the square root of their total quotient.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Divide the denominator into the numerator to get a whole number quotient with a remainder. The quotient becomes the whole number of the mixed number. Remainder becomes the numerator.

43. Increasing and Decreasing a Number by a Certain Percentage
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Subtract the smallest from the largest and add 1
-Increasing: Add the percent to 100 percent - convert to a decimal - and multiply - Decrease: Subtract the percent from 100 percent - convert to a decimal - and multiply.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

44. Finding the Volume of a Cylinder
-Increasing: Add the percent to 100 percent - convert to a decimal - and multiply - Decrease: Subtract the percent from 100 percent - convert to a decimal - and multiply.
2(pie)r
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
VofaC: (pie)r(2)h

45. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Put the equation into y=mx+b-- in which case b is the y-intercept.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Multiply and/or divide positives and negatives treat the number parts as usual - and attach a negative sign if there is an odd number of negatives
VofaC: (pie)r(2)h

46. Finding the Length of an Arc in a Circle

47. Finding the Reciprocal of a Fraction
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.
The value that appears the most often.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Switch the numerator and denominator.

48. Evaluating an Algebraic Expression
Plug in the given values for the unknowns and calculate according to PEMDAS.
Cross multiply.
Find a common denominator - then add or subtract the numerators.
Cancel factors common to the numerator and denominator.

49. Simplifying an Algebraic Equation
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Cancel factors common to the numerator and denominator.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

50. Properties of a 45-45-90 Triangle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
When a line is tangent to a circle - or touches the circle at just one point - the radius of the circle is perpendicular to the line at the point of contact.
Area of a Triangle=1/29(base)(height) - The height is the perpendicular distance between the side that's chosen as the base and the opposite vertex.
Plug in the given values for the unknowns and calculate according to PEMDAS.