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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.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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 Roots
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Just add or subtract the coefficients in front of the radicals.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

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

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3. Finding the Sum of the Interior Angles of a Polygon
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Do whatever is necessary to both sides to isolate the variable.

4. Finding the Length of an Arc in a Circle

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5. 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.
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 A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.

6. Finding the Midpoint Between Two Points
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
(x1+x2)/2 -(y1+y2)/2
Cross multiply.
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

7. Multiplying Binomials
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.
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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
FOIL: First - Outer - Inner - Last... Combine Like Terms

8. Properties of the Interior and Exterior Angles of a Triangle
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.
-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.
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

9. Number of Groups - +1 Each Time
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Slope=change in y/change in x
-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.

10. An Important Property of a Line Tangent to a Circle
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Do whatever is necessary to both sides to isolate the variable.
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.
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.

11. Converting from an Improper Fraction to a Mixed Number
Multiply the numerators and multiply the denominators.
Use simple numbers like 1 and 2 and see what happens.
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.
(x1+x2)/2 -(y1+y2)/2

12. Evaluating an Algebraic Expression
Average: Sum of the Terms/Number of the Terms
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.
VofaRS=lwh

13. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
(pie)r(squared)
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

14. What is the Pythagorean Theorem?
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Factor out and cancel all factors the numerator and denominator have in common.
A(2)+b(2)=c(2)
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.

15. Converting From a Mixed Number to an Improper Fraction
VofaC: (pie)r(2)h
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

16. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Use the formula distance=rate*time and its variations to help in this question.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
FOIL: First - Outer - Inner - Last... Combine Like Terms

17. Simplifying a Fraction to Lowest Terms
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Factor out and cancel all factors the numerator and denominator have in common.
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

18. 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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

19. 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.
Part=Percent x Whole
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Slope=change in y/change in x

20. Definition of a Rational Number
Adjacent angles are supplementary - Vertical angles are equal
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

21. 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?
Slope=change in y/change in x
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.
Part=Percent x Whole
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.

22. Finding the Surface Area of a Rectangular Solid
Use simple numbers like 1 and 2 and see what happens.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The whole number left over after division.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

23. Finding the Mode of a Set of Numbers
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
The value that appears the most often.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

24. 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.
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

25. PEMDAS
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Part=Percent x Whole
The value that appears the most often.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

26. Finding the Reciprocal of a Fraction
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.
Switch the numerator and denominator.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.

27. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
The value that appears the most often.
Subtract the smallest from the largest and add 1
Use the formula distance=rate*time and its variations to help in this question.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

28. Prime Factorization of a Number
Express them with a common denominator.
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
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

29. What types of angles are formed when a transversal cross parallel lines?
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
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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Four equal acute angles and four equal obtuse angles.

30. Multiplying Monomials
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Cross multiply.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.

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

32. Counting the Total Number of Possibilities for Several Events to Occur
Combine like terms.
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
(x1+x2)/2 -(y1+y2)/2

33. Properties of a 45-45-90 Triangle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
Use the units to keep things straight - Snowfall inches/hours
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

34. Properties of a 30-60-90 Triangle
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.
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. Finding the LCM of Two or More Numbers

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36. Finding the Circumference of a Circle
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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
2(pie)r
Subtract the smallest from the largest and add 1

37. Finding the Slope When Given an Equation of a Line
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Switch the numerator and denominator.

38. Expressing the Union and Intersection of Sets
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 and cancel all factors the numerator and denominator have in common.
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
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. Definition of Remainder
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
The whole number left over after division.

40. What types of angles are formed when two lines intersect?
Use the units to keep things straight - Snowfall inches/hours
Adjacent angles are supplementary - Vertical angles are equal
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

41. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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

42. Finding the Slope of a Line When Given Two Points on the Line
Just add or subtract the coefficients in front of the radicals.
Slope=change in y/change in x
Isolate the radical expression and use the standard rules of algebra.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

43. Convert From a Fraction to a Decimal - Vice Versa
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.
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.

44. What are Two Special Pythagorean Triples?

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45. How do you know if an integer is a multiple of 3 or 9?
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.
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
Isolate the radical expression and use the standard rules of algebra.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

46. Factoring a Polynomial ('FOIL in Reverse')
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
-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.
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

47. If x(2)=7x+18 - what is the positive value of x?
Part=Percent x Whole
Use the units to keep things straight - Snowfall inches/hours
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

48. Characteristics of a Square
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

49. Raising a Power to a Power
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 variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Cancel factors common to the numerator and denominator.
Multiply the exponents - (x^3)^4=x^3*4=x^12

50. Finding the Sum of the Average of a Series of Numbers
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Sum: Average x Number of Terms
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides