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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. Properties of a 45-45-90 Triangle
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Average the smallest and largest number
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

2. If the average of a - b - and 48 is 48 - what is the value of a + b?
Sum: Average x Number of Terms
-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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
-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.

3. Solving a System of Equations
Just add or subtract the coefficients in front of the radicals.
A(2)+b(2)=c(2)
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.

4. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
Cancel factors common to the numerator and denominator.
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
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

5. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Factor out and cancel all factors the numerator and denominator have in common.
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.
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.
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.

6. Finding the Domain and Range of a Function
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.
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.

7. Scalene - Isosceles - and Equilateral Triangles
Multiply the numerators and multiply the denominators.
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
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.
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.

8. Comparing the values of two or more Fractions
VofaC: (pie)r(2)h
2(pie)r
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.
Express them with a common denominator.

9. What is the Pythagorean Theorem?
FOIL: First - Outer - Inner - Last... Combine Like Terms
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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(2)+b(2)=c(2)

10. Solving a Problem Involving Rates
The whole number left over after division.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Use the units to keep things straight - Snowfall inches/hours
-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.

11. Definition of an Irrational Number
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
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Average: Sum of the Terms/Number of the Terms

12. Finding the Distance Between Two Points on a Coordinate Graph
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

13. Increasing and Decreasing a Number by a Certain Percentage
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
-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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

14. Finding the Missing Number in a Series When You are Given the Average
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 - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
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

15. Finding the Volume of a Rectangular Solid
-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.
VofaRS=lwh
2(pie)r
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.

16. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
The whole number left over after division.
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
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.

17. Finding the Circumference of 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.
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.
2(pie)r
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

18. Converting from part-to-part ratios to part-to-whole ratios
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Express them with a common denominator.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Put each number in the original ratio over the sum of the numbers.

19. Determining Absolute Value of a Number
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.
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

20. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
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.
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

21. What types of angles are formed when two lines intersect?
Part=Percent x Whole
Adjacent angles are supplementary - Vertical angles are equal
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

22. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

23. Finding the LCM of Two or More Numbers

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24. Dividing Expressions with Exponents that Have a Common Base
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Put the equation into y=mx+b-- in which case b is the y-intercept.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

25. 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
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

26. Finding the Area of a Triangle

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27. Number of Groups - +1 Each Time
The value that appears the most often.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

28. What are Two Special Pythagorean Triples?

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29. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Two relatively prime numbers are integers that have no common factor other than 1.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

30. Solving an Inequality
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

31. If (Square Root: x-1)+5=12 - what is the value of x/2?
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Plug in the given values for the unknowns and calculate according to PEMDAS.

32. Simplifying an Algebraic Equation
VofaRS=lwh
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.
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.

33. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
(x1+x2)/2 -(y1+y2)/2
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
VofaC: (pie)r(2)h
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

34. Finding the Reciprocal of a Fraction
-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.
Find a common denominator - then add or subtract the numerators.
Switch the numerator and denominator.
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.

35. Solving a Radical Equation
Factor out and cancel all factors the numerator and denominator have in common.
Isolate the radical expression and use the standard rules of algebra.
-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.
Multiply the numerators and multiply the denominators.

36. Finding the Sum of the Interior Angles of a Polygon
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

37. What types of angles are formed when a transversal cross parallel lines?
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.
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.
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
Four equal acute angles and four equal obtuse angles.

38. Finding the GCF of Two or More Numbers
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 whole number part by the denominator - then add the numerator. Keep the same denominator.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

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

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40. Finding the Area of a Circle
Cross multiply.
(pie)r(squared)
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)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.

41. 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?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Get the absolute value equation by itself. Solve.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

42. 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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Factor out and cancel all factors the numerator and denominator have in common.

43. Adding a Positive Number to a Negative Number
Just add or subtract the coefficients in front of the radicals.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Cancel factors common to the numerator and denominator.

44. Multiplying and Dividing Roots
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.
Subtract the smallest from the largest and add 1

45. Direct Variation and Inverse Variation
Find a common denominator - then add or subtract the numerators.
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

46. Finding the y-intercept When Given an Equation of a Line
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

47. Finding the Slope of a Line When Given Two Points on the Line
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Put each number in the original ratio over the sum of the numbers.
Slope=change in y/change in x
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.

48. Multiplying Expressions with Exponents that Have a Common Base
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

49. What is the greatest of three consecutive odd integers where the sum of the third and twice the first is equal to nine more than twice the second?
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Two relatively prime numbers are integers that have no common factor other than 1.
-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.
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.

50. Adding and Subtracting Roots
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Just add or subtract the coefficients in front of the radicals.
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)