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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. Adding and Subtracting Fractions
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Slope=change in y/change in x
Find a common denominator - then add or subtract the numerators.

2. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

3. Simplifying a Fraction to Lowest Terms
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.
Factor out and cancel all factors the numerator and denominator have in common.
VofaRS=lwh
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.

4. Finding the Reciprocal of a Fraction
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Four equal acute angles and four equal obtuse angles.
Switch the numerator and denominator.

5. Definition of an Irrational Number
Use the distributive property then combine the like terms.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Average the smallest and largest number

6. Solving a Problem Involving Rates
Express them with a common denominator.
Use the units to keep things straight - Snowfall inches/hours
Find a common denominator - then add or subtract the numerators.
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

7. Finding the Area of a Sector

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8. Factoring the Difference of Two Squares
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

9. Finding the Distance Between Two Points on a Coordinate Graph
Use the formula distance=rate*time and its variations to help in this question.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

10. Solving a Linear Equation
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.
Do whatever is necessary to both sides to isolate the variable.
Use the distributive property then combine the like terms.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

11. Multiplying Monomials
Express them with a common denominator.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

12. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Get the absolute value equation by itself. Solve.
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

13. If 3(3x)=9(x+2) - what is the value of x?
Get the absolute value equation by itself. Solve.
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.
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 units to keep things straight - Snowfall inches/hours

14. Converting from part-to-part ratios to part-to-whole ratios
Put each number in the original ratio over the sum of the numbers.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
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.

15. If (Square Root: x-1)+5=12 - what is the value of x/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.
Express them with a common denominator.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Do whatever is necessary to both sides to isolate the variable.

16. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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.
Do whatever is necessary to both sides to isolate the variable.
2(pie)r
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

17. What is the Pythagorean Theorem?
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
(x1+x2)/2 -(y1+y2)/2
Probability: Number of Favorable Outcomes/Total Possible Outcomes
A(2)+b(2)=c(2)

18. Adding a Positive Number to a Negative Number
FOIL: First - Outer - Inner - Last... Combine Like Terms
Cancel factors common to 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
Cross multiply.

19. What is the Triangle Inequality Theorem?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Average the smallest and largest number
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.

20. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
-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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.

21. Finding the Slope When Given an Equation of a Line
Use the distributive property then combine the like terms.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Adjacent angles are supplementary - Vertical angles are equal

22. Factoring a Polynomial ('FOIL in Reverse')
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.
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.
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

23. General Procedure for Multiplying Polynomials
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Use the distributive property then combine the like terms.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

24. 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
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.
Switch the numerator and denominator.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

25. Formula to Find Average
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Average: Sum of the Terms/Number of the Terms
The whole number left over after division.
'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 Circle
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
(pie)r(squared)
Probability: Number of Favorable Outcomes/Total Possible Outcomes
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

27. Finding the Rate of Speed
Just add or subtract the coefficients in front of the radicals.
Use the formula distance=rate*time and its variations to help in this question.
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.
Cancel factors common to the numerator and denominator.

28. 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
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

29. Comparing the values of two or more Fractions
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Express them with a common denominator.

30. Finding the Volume of a Rectangular Solid
-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.
VofaRS=lwh
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Probability: Number of Favorable Outcomes/Total Possible Outcomes

31. Finding the Mode of a Set of Numbers
The value that falls in the middle of the set.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.
The value that appears the most often.

32. If x(2)=7x+18 - what is the positive value of x?
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
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

33. Increasing and Decreasing a Number by a Certain Percentage
-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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

34. Adding and Subtracting Monomials
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

35. Definition of a Rational Number
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Find a common denominator - then add or subtract the numerators.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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

36. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
Cross multiply.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

37. Convert From a Fraction to a Decimal - Vice Versa
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

38. Calculating the Probability that an Event will Take Place
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Sum: Average x Number of Terms
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

39. Scalene - Isosceles - and Equilateral Triangles
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 coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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 2 if the last digit is even - An integer is divisible by 4 if the last two digits form a multiple of 4.

40. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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

41. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

42. Finding the Surface Area of a Rectangular Solid
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
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

43. Calculating Negative Exponents and Radical Exponents
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Put each number in the original ratio over the sum of the numbers.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Just add or subtract the coefficients in front of the radicals.

44. Adding and Subtracting Roots
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
(x1+x2)/2 -(y1+y2)/2
Just add or subtract the coefficients in front of the radicals.

45. Definition of Remainder
The whole number left over after division.
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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. Multiplying Expressions with Exponents that Have a Common Base
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
Isolate the radical expression and use the standard rules of algebra.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

47. 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.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Multiply the exponents - (x^3)^4=x^3*4=x^12

48. If the average of a - b - and 48 is 48 - what is the value of a + b?
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
Average: Sum of the Terms/Number of the Terms
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

49. 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?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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 exponents - (x^3)^4=x^3*4=x^12
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.

50. Finding the Volume of a Cylinder
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
VofaC: (pie)r(2)h
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)