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SAT Math

Subjects : sat, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. Finding a Term in a Geometric Sequence
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.
Put each number in the original ratio over the sum of the numbers.

2. If r#t=t(r)-r(t) - then what is 4#3?
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

3. Converting from an Improper Fraction to a Mixed Number
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

4. Finding the Volume of a Cylinder
Two relatively prime numbers are integers that have no common factor other than 1.
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.
The value that falls in the middle of the set.
VofaC: (pie)r(2)h

5. Finding the Missing Number in a Series When You are Given the Average
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Cross multiply.
Combine like terms.
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.

6. Simplifying a Fraction to Lowest Terms
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Factor out and cancel all factors the numerator and denominator have in common.

7. Average Rate and How Do You Find It
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
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

8. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
Two relatively prime numbers are integers that have no common factor other than 1.
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 the units to keep things straight - Snowfall inches/hours

9. What value of x is not in the domain of the function f(x)=x-2/x-3?
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
Switch the numerator and denominator.
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
Probability: Number of Favorable Outcomes/Total Possible Outcomes

10. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Cross multiply.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
The whole number left over after division.

11. If (Square Root: x-1)+5=12 - what is the value of x/2?
Subtract the smallest from the largest and add 1
Multiply the numerators and multiply the denominators.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

12. Dividing 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
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
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

13. Simplifying an Algebraic Equation
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Cancel factors common to the numerator and denominator.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Use the distributive property then combine the like terms.

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

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15. Multiplying Binomials
Put each number in the original ratio over the sum of the numbers.
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms

16. Characteristics of a Square
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
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Average: Sum of the Terms/Number of the Terms
Cross multiply.

17. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

18. Setting Up a Ratio
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.
A(2)+b(2)=c(2)
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

19. How do you know if an integer is a multiple of 3 or 9?
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
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.
Multiply the numerators and multiply the denominators.
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.

20. Finding the Rate of Speed
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.
Factor out and cancel all factors the numerator and denominator have in common.
Use the formula distance=rate*time and its variations to help in this question.
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

21. What is the Pythagorean Theorem?
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
A(2)+b(2)=c(2)
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

22. Adding and Subtracting Fractions
Two relatively prime numbers are integers that have no common factor other than 1.
Put each number in the original ratio over the sum of the numbers.
The value that appears the most often.
Find a common denominator - then add or subtract the numerators.

23. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
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
Express them with a common denominator.
Use simple numbers like 1 and 2 and see what happens.
Use the units to keep things straight - Snowfall inches/hours

24. Counting Consecutive Integers
A(2)+b(2)=c(2)
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Subtract the smallest from the largest and add 1

25. Knowing if an Integer is a Multiple of 2 or 4
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
-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.

26. Finding the Mode of a Set of Numbers
The value that appears the most often.
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.
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 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

27. Definition of an Integer
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
The value that appears the most often.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.

28. Properties of a 30-60-90 Triangle
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
(x1+x2)/2 -(y1+y2)/2
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

29. Finding the GCF of Two or More Numbers
Use the formula distance=rate*time and its variations to help in this question.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
The value that falls in the middle of the set.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

30. If x(2)=7x+18 - what is the positive value of x?
Express them with a common denominator.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

31. Solving a System of Equations
-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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Use the formula distance=rate*time and its variations to help in this question.
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.

32. Factoring the Difference of Two Squares
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Use simple numbers like 1 and 2 and see what happens.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

33. What types of angles are formed when two lines intersect?
Adjacent angles are supplementary - Vertical angles are equal
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
A(2)+b(2)=c(2)
VofaRS=lwh

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

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35. 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
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.
VofaC: (pie)r(2)h
Use simple numbers like 1 and 2 and see what happens.

36. Finding the Length of an Arc in a Circle

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37. 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
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.

38. Definition of an Irrational Number
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Use the formula distance=rate*time and its variations to help in this question.

39. Adding and Subtracting Roots
Cross multiply.
Part=Percent x Whole
Just add or subtract the coefficients in front of the radicals.
Sum: Average x Number of Terms

40. An Important Property of a Line Tangent to a Circle
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.
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.
Get the absolute value equation by itself. Solve.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

41. Difference Between a Factor and a Multiple
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
-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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

42. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
-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.

43. Solving a Problem Involving Rates
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Use the units to keep things straight - Snowfall inches/hours
Factor out and cancel all factors the numerator and denominator have in common.
A(2)+b(2)=c(2)

44. What types of angles are formed when a transversal cross parallel lines?
Just add or subtract the coefficients in front of the radicals.
Four equal acute angles and four equal obtuse angles.
Multiply the numerators and multiply the denominators.
Part=Percent x Whole

45. Finding the Midpoint Between Two Points
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.
-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.
(x1+x2)/2 -(y1+y2)/2
Cancel factors common to the numerator and denominator.

46. Formula to Find Average
Put each number in the original ratio over the sum of the numbers.
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Average: Sum of the Terms/Number of the Terms

47. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
-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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
-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.

48. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.

49. Characteristics of a Parallelogram
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.
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.
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.

50. Converting from part-to-part ratios to part-to-whole ratios
Put each number in the original ratio over the sum of the numbers.
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.
The value that appears the most often.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.