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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. Multiplying Fractions
Cross multiply.
Multiply the numerators and multiply the denominators.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.

2. An Important Property of a Line Tangent to a Circle
Average: Sum of the Terms/Number of 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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.

3. Evaluating an Algebraic Expression
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.

4. If 4(x(2)-10x+25) - then what is the value of x?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.
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 numerators and multiply the denominators.

5. Finding the Distance Between Two Points on a Coordinate Graph
Part=Percent x Whole
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

6. Multiplying Binomials
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.

7. Finding the Reciprocal of a Fraction
Four equal acute angles and four equal obtuse angles.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Switch the numerator and denominator.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

8. Finding the Circumference of a Circle
2(pie)r
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 variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
A(2)+b(2)=c(2)

9. Solving a Problem Involving Rates
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Two relatively prime numbers are integers that have no common factor other than 1.
Use the units to keep things straight - Snowfall inches/hours

10. PEMDAS
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Put the equation into y=mx+b-- in which case b is the y-intercept.
Find a common denominator - then add or subtract the numerators.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

11. Finding the Surface Area of a Rectangular Solid
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Multiply the exponents - (x^3)^4=x^3*4=x^12

12. Converting from part-to-part ratios to part-to-whole ratios
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Sum: Average x Number of Terms

13. 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?
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.
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.

14. Calculating Negative Exponents and Radical Exponents
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Part=Percent x Whole

15. Finding the Volume of a Cylinder
Average: Sum of the Terms/Number of the Terms
Factor out and cancel all factors the numerator and denominator have in common.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
VofaC: (pie)r(2)h

16. Finding the y-intercept When Given an Equation of a Line
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
Switch the numerator and denominator.

17. What are Two Special Pythagorean Triples?

18. Solving a Radical Equation
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.
Isolate the radical expression and use the standard rules of algebra.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

19. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.

20. Direct Variation and Inverse Variation
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
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

21. What Does Solving In Terms of Mean?
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Part=Percent x Whole
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
-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.

22. Simplifying a Fraction to Lowest Terms
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
Factor out and cancel all factors the numerator and denominator have in common.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Express them with a common denominator.

23. If (Square Root: x-1)+5=12 - what is the value of x/2?
Plug in the given values for the unknowns and calculate according to PEMDAS.
The value that appears the most often.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

24. Simplifying Square Roots
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
Use the distributive property then combine the like terms.

25. Converting From a Mixed Number to an Improper Fraction
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Sum: Average x Number of Terms

26. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Get the absolute value equation by itself. 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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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.

27. Characteristics of a Rectangle
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

28. Finding a Term in a Geometric Sequence
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

29. 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
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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 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

30. Factoring a Polynomial ('FOIL in Reverse')
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Average: Sum of the Terms/Number of the Terms
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

31. Number of Groups - +1 Each Time
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.

32. Finding the Midpoint Between Two Points
Put each number in the original ratio over the sum of the numbers.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
(x1+x2)/2 -(y1+y2)/2
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

33. Characteristics of a Parallelogram
Put each number in the original ratio over the sum of the numbers.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

34. 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
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.
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

35. Finding the Area of a Sector

36. 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?
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.
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

37. Definition of an Integer
Cross multiply.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Slope=change in y/change in x
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.

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

39. Difference Between a Factor and a Multiple
Cross multiply.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
-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.

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

41. Adding and Subtracting Monomials
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Use the distributive property then combine the like terms.

42. Properties of Similar Triangles
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Combine like terms.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.

43. Solving a Linear Equation
Do whatever is necessary to both sides to isolate the variable.
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

44. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
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.

45. Scalene - Isosceles - and Equilateral Triangles
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
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.

46. Finding the Slope of a Line When Given Two Points on the Line
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Slope=change in y/change in 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.

47. 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?
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
-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.
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

48. Definition of Remainder
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.
The whole number left over after division.
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

49. Dividing Expressions with Exponents that Have a Common Base
Put the equation into y=mx+b-- in which case b is the y-intercept.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

50. Finding the Mode of a Set of Numbers
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
The value that appears the most often.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.