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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 Missing Number in a Series When You are Given the Average
FOIL: First - Outer - Inner - Last... Combine Like Terms
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.

2. Properties of Similar Triangles
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.
Combine like terms.

3. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Average: Sum of the Terms/Number of the Terms
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

4. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Get the absolute value equation by itself. Solve.
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Use simple numbers like 1 and 2 and see what happens.

5. Characteristics of a Rectangle
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-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.

6. If r#t=t(r)-r(t) - then what is 4#3?
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.
Use the formula distance=rate*time and its variations to help in this question.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Get the absolute value equation by itself. Solve.

7. Finding a Term in a Geometric Sequence
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)
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.
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.

8. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
The whole number left over after division.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.

9. Definition of an Integer
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
The value that falls in the middle of the set.

10. Finding the Volume of a Rectangular Solid
VofaRS=lwh
Find a common denominator - then add or subtract the numerators.
Use the distributive property then combine the like terms.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

11. Converting from an Improper Fraction to a Mixed 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.
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

12. Adding and Subtracting Polynomials
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Combine like terms.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

13. Solving an Inequality
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Do whatever is necessary to both sides to isolate the variable.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

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

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15. Difference Between a Factor and a Multiple
Sum: Average x Number of Terms
Cancel factors common to the numerator and denominator.
Use the units to keep things straight - Snowfall inches/hours
-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.

16. Multiplying Binomials
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.
FOIL: First - Outer - Inner - Last... Combine Like 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.

17. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Four equal acute angles and four equal obtuse angles.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
The value that falls in the middle of the set.

18. Finding the LCM of Two or More Numbers

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19. Finding the Area of a Circle
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Get the absolute value equation by itself. Solve.
(pie)r(squared)

20. Converting from part-to-part ratios to part-to-whole ratios
Put each number in the original ratio over the sum of the numbers.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

21. Solving a Proportion
Cross multiply.
Do whatever is necessary to both sides to isolate the variable.
Express them with a common denominator.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

22. Definition of Remainder
The value that appears the most often.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
The whole number left over after division.
Do whatever is necessary to both sides to isolate the variable.

23. 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?
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Get the absolute value equation by itself. Solve.
Express them with a common denominator.

24. Finding the y-intercept When Given an Equation of a Line
Put the equation into y=mx+b-- in which case b is the y-intercept.
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
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
-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.

25. 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?
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
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Slope=change in y/change in x

26. What is the Triangle Inequality Theorem?
The value that appears the most often.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.

27. Multiplying Fractions
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.
Multiply the numerators and multiply the denominators.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

28. Simplifying an Algebraic Equation
The whole number left over after division.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
Cancel factors common to the numerator and denominator.

29. Calculating Negative Exponents and Radical Exponents
Isolate the radical expression and use the standard rules of algebra.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

30. What is a Function and how do you Evaluate one?

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31. Finding the GCF of Two or More Numbers
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Average: Sum of the Terms/Number of the Terms
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

32. Definition of a Rational Number
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
VofaC: (pie)r(2)h
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

33. Multiplying Expressions with Exponents that Have a Common Base
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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
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.

34. An Important Property of a Line Tangent to a Circle
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
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.

35. Formula Used to Find Percent
Part=Percent x Whole
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.

36. Finding the Circumference of a Circle
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Isolate the radical expression and use the standard rules of algebra.
-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

37. 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.
Use the formula distance=rate*time and its variations to help in this question.
Factor out and cancel all factors the numerator and denominator have in common.
Use simple numbers like 1 and 2 and see what happens.

38. Characteristics of a Square
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

39. Number of Groups - +1 Each Time
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.
Factor out and cancel all factors the numerator and denominator have in common.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.

40. Determining Absolute Value of a Number
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Sum: Average x Number of Terms

41. If (Square Root: x-1)+5=12 - what is the value of x/2?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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
VofaC: (pie)r(2)h
Adjacent angles are supplementary - Vertical angles are equal

42. Convert From a Fraction to a Decimal - Vice Versa
A(2)+b(2)=c(2)
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.
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 whole number part by the denominator - then add the numerator. Keep the same denominator.

43. Adding a Positive Number to a Negative Number
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 2 if the last digit is even - An integer is divisible by 4 if the last two digits form a multiple of 4.
Use simple numbers like 1 and 2 and see what happens.
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

44. Solving a System of Equations
Isolate the radical expression and use the standard rules of algebra.
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.
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.
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.

45. Solving a Problem Involving Rates
Multiply the numerators and multiply the denominators.
Express them with a common denominator.
Use the units to keep things straight - Snowfall inches/hours
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

46. Characteristics of a Parallelogram
Four equal acute angles and four equal obtuse angles.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.

47. What value of x is not in the domain of the function f(x)=x-2/x-3?
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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

48. 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
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.
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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.

49. Knowing if an Integer is a Multiple of 2 or 4
-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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Four equal acute angles and four equal obtuse angles.

50. Finding the Domain and Range of a Function
Combine like terms.
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.
Adjacent angles are supplementary - Vertical angles are equal
Average the smallest and largest number