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SAT Math

Subjects : sat, math

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Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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1. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Sum: Average x Number of Terms
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Use the formula distance=rate*time and its variations to help in this question.

2. Solving a Radical Equation
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Isolate the radical expression and use the standard rules of algebra.

3. Multiplying Fractions
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Multiply the numerators and multiply the denominators.

4. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
Use the formula distance=rate*time and its variations to help in this question.
Cross multiply.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

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

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6. Simplifying Square Roots
Average: Sum of the Terms/Number of the Terms
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

7. Finding the y-intercept When Given an Equation of a Line
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Put the equation into y=mx+b-- in which case b is the y-intercept.
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%

8. Properties of Similar Triangles
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.
(pie)r(squared)
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

9. Factoring the Difference of Two Squares
Cross multiply.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

10. If 4(x(2)-10x+25) - then what is the value of x?
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.

11. Convert From a Fraction to a Decimal - Vice Versa
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.
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.
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

12. Formula to Find Average
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Average: Sum of the Terms/Number of the Terms
Consecutive odd integers are odd integers in order in a row - such as 1 - 3 - and 5. The difference between any two consecutive odd integers is 2. Translate the question into an equation that expresses the relationship between the integers.

13. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Switch the numerator and denominator.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

14. Properties of a 30-60-90 Triangle
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Adjacent angles are supplementary - Vertical angles are equal

15. Converting From a Mixed Number to an Improper Fraction
Subtract the smallest from the largest and add 1
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
The whole number left over after division.

16. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Two relatively prime numbers are integers that have no common factor other than 1.
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 the formula distance=rate*time and its variations to help in this question.

17. What Does Solving In Terms of Mean?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Subtract the smallest from the largest and add 1
Consecutive odd integers are odd integers in order in a row - such as 1 - 3 - and 5. The difference between any two consecutive odd integers is 2. Translate the question into an equation that expresses the relationship between the integers.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

18. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
(pie)r(squared)
Multiply the exponents - (x^3)^4=x^3*4=x^12

19. Finding the Surface Area of a Rectangular Solid
Do whatever is necessary to both sides to isolate the variable.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Express them with a common denominator.

20. Setting Up a Ratio
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
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

21. Comparing the values of two or more Fractions
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
Express them with a common denominator.
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.

22. Definition of an Integer
The value that appears the most often.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Get the absolute value equation by itself. Solve.

23. Definition of a Rational Number
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Plug in the given values for the unknowns and calculate according to PEMDAS.
2(pie)r
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

24. Raising a Power to a Power
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
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

25. Finding the Area of a Sector

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26. Characteristics of a Square
Use the distributive property then combine the like terms.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

27. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
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.

28. Finding the Circumference of a Circle
Standard function notation is written f(x) and read 'f of x.' To evaluate the function f(x)=2x+3 for f(4) - replace every x with 4 and simplify. f(4)=2(4)+3=11.
Average the smallest and largest number
2(pie)r
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.

29. Sale Price of a Jacket Marked Down 30% Each Week for 3 Weeks - What % of the Original Price is the Cost of the Jacket After the 3 Week Sale Period
Factor out and cancel all factors the numerator and denominator have in common.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Four equal acute angles and four equal obtuse angles.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

30. Finding the Midpoint Between Two Points
Four equal acute angles and four equal obtuse angles.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Use simple numbers like 1 and 2 and see what happens.
(x1+x2)/2 -(y1+y2)/2

31. Finding the Area of a Circle
Just add or subtract the coefficients in front of the radicals.
(pie)r(squared)
-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.
Use the formula distance=rate*time and its variations to help in this question.

32. Knowing if an Integer is a Multiple of 5 or 10
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
-An integer is divisible by 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.
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
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

33. Direct Variation and Inverse Variation
-An integer is divisible by 2 if the last digit is even - An integer is divisible by 4 if the last two digits form a multiple of 4.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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

34. Finding the Domain and Range of a Function
Domain- The domain of a a function is the set of values for which the function is defined - Range- The range of a function is the set of outputs or results of the function.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Subtract the smallest from the largest and add 1

35. How do you know if an integer is a multiple of 3 or 9?
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.
Multiply the numerators and multiply the denominators.
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.
Express them with a common denominator.

36. Converting from part-to-part ratios to part-to-whole ratios
Put each number in the original ratio over the sum of the numbers.
The value that falls in the middle of the set.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.

37. Expressing the Union and Intersection of Sets
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
The union of Set A and Set B is the set of elements that are in either or both Set A and Set B - The intersection of Set A and Set B is the set of elements common to both Set A and Set B

38. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
Multiply the numerators and multiply the denominators.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.

39. Simplifying a Fraction to Lowest Terms
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Sum: Average x Number of Terms
Factor out and cancel all factors the numerator and denominator have in common.
Get the absolute value equation by itself. Solve.

40. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Average the smallest and largest number
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

41. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

42. Multiply and Divide Positive and Negative Numbers
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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
VofaRS=lwh
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

43. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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.
Sum: Average x Number of Terms
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

44. Finding a Term in a Geometric Sequence
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.
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.
VofaRS=lwh
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.

45. Finding the LCM of Two or More Numbers

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46. An Important Property of a Line Tangent to a Circle
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.
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.
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.
Consecutive odd integers are odd integers in order in a row - such as 1 - 3 - and 5. The difference between any two consecutive odd integers is 2. Translate the question into an equation that expresses the relationship between the integers.

47. Finding the Sum of the Interior Angles of a Polygon
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

48. Finding the Volume of a Cylinder
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.
VofaC: (pie)r(2)h
Slope=change in y/change in x
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.

49. Solving a Linear Equation
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Do whatever is necessary to both sides to isolate the variable.
-An integer is divisible by 2 if the last digit is even - An integer is divisible by 4 if the last two digits form a multiple of 4.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

50. Definition of Remainder
Find a common denominator - then add or subtract the numerators.
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
The whole number left over after division.

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