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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. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
Two relatively prime numbers are integers that have no common factor other than 1.

2. Definition of an Irrational Number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

3. If the average of a - b - and 48 is 48 - what is the value of a + b?
Average the smallest and largest number
Switch the numerator and denominator.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

4. Convert From a Fraction to a Decimal - Vice Versa
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
Factor out and cancel all factors the numerator and denominator have in common.

5. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
Find a common denominator - then add or subtract the numerators.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

6. Adding and Subtracting Polynomials
Combine like terms.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Find a common denominator - then add or subtract the numerators.
Switch the numerator and denominator.

7. Characteristics of a Parallelogram
Get the absolute value equation by itself. Solve.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

8. Dividing Expressions with Exponents that Have a Common Base
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.

9. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
The whole number left over after division.

10. Multiplying Fractions
The whole number left over after division.
Multiply the numerators and multiply the denominators.
Two relatively prime numbers are integers that have no common factor other than 1.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

11. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
(pie)r(squared)
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

12. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

13. Direct Variation and Inverse Variation
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.
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
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
Two relatively prime numbers are integers that have no common factor other than 1.

14. Finding the Area of a Sector

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15. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

16. Finding the Volume of a Rectangular Solid
A(2)+b(2)=c(2)
VofaRS=lwh
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.

17. Finding the Mode of a Set of Numbers
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
The value that appears the most often.
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.
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. Properties of Similar Triangles
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
Slope=change in y/change in x
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

19. Counting Consecutive Integers
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
VofaRS=lwh
Isolate the radical expression and use the standard rules of algebra.
Subtract the smallest from the largest and add 1

20. Solving a Linear Equation
Factor out and cancel all factors the numerator and denominator have in common.
Do whatever is necessary to both sides to isolate the variable.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Combine like terms.

21. An Important Property of a Line Tangent to a Circle
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.
VofaC: (pie)r(2)h
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Values of x the take the denominator of a faction equal to zero - thereby dividing by zero which is not possible - are not in the domain of a function. Set the denominator equal to zero and solve for x. Ans: 3

22. Finding the Circumference of a Circle
2(pie)r
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

23. If x varies directly with y - and the value of x is 12 when y is 11 - what is the value of y when x is 66?
(pie)r(squared)
Switch the numerator and denominator.
Average the smallest and largest number
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

24. Increasing and Decreasing a Number by a Certain Percentage
Put the equation into y=mx+b-- in which case b is the y-intercept.
-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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

25. Definition of Remainder
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
The whole number left over after division.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

26. How do you know if an integer is a multiple of 3 or 9?
Subtract the smallest from the largest and add 1
Use the units to keep things straight - Snowfall inches/hours
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.
-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.

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

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28. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
In a 30-60-90 triangle - the measure of the longer leg is 7(square root: 3) - then the length of the shorter side or shorter leg must be 7.
The value that appears the most often.
Use simple numbers like 1 and 2 and see what happens.

29. Number of Groups - +1 Each Time
Use the formula distance=rate*time and its variations to help in this question.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

30. If r#t=t(r)-r(t) - then what is 4#3?
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Part=Percent x Whole
Sum: Average x Number of Terms

31. 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?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
(x1+x2)/2 -(y1+y2)/2
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Part=Percent x Whole

32. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Get the absolute value equation by itself. Solve.
Slope=change in y/change in x
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 radical expression and use the standard rules of algebra.

33. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Switch the numerator and denominator.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
-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.

34. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Express them with a common denominator.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

35. Raising a Power to a Power
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Multiply the exponents - (x^3)^4=x^3*4=x^12
-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.

36. Solving a System of Equations
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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
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.

37. Multiplying and Dividing Roots
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Do whatever is necessary to both sides to isolate the variable.
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

38. Knowing if an Integer is a Multiple of 5 or 10
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Part=Percent x Whole
-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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

39. Adding and Subtracting Roots
Use simple numbers like 1 and 2 and see what happens.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Just add or subtract the coefficients in front of the radicals.
Use the distributive property then combine the like terms.

40. Scalene - Isosceles - and Equilateral Triangles
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Cancel factors common to the numerator and denominator.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

41. Finding a Term in a Geometric Sequence
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
Average the smallest and largest number

42. Dividing Fractions
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

43. Finding the y-intercept When Given an Equation of a Line
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Average the smallest and largest number
Put the equation into y=mx+b-- in which case b is the y-intercept.
Adjacent angles are supplementary - Vertical angles are equal

44. Characteristics of a Square
Isolate the radical expression and use the standard rules of algebra.
VofaRS=lwh
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Express them with a common denominator.

45. Properties of the Interior and Exterior Angles of a Triangle
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.
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.
Use the distributive property then combine the like terms.
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.

46. Finding the Slope of a Line When Given Two Points on the Line
Factor out and cancel all factors the numerator and denominator have in common.
Slope=change in y/change in x
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.
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.

47. Prime Factorization of a Number
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
A(2)+b(2)=c(2)
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.

48. Finding the Distance Between Two Points on a Coordinate Graph
A(2)+b(2)=c(2)
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
-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.

49. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.

50. If (Square Root: x-1)+5=12 - what is the value of x/2?
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 variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Average: Sum of the Terms/Number of the Terms
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25