Test your basic knowledge |

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 the y-intercept When Given an Equation of a Line
Just add or subtract the coefficients in front of the radicals.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Put the equation into y=mx+b-- in which case b is the y-intercept.
Put each number in the original ratio over the sum of the numbers.

2. PEMDAS
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

3. Finding the Area of a Circle
(pie)r(squared)
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.

4. How do you know if an integer is a multiple of 3 or 9?
Use the distributive property then combine the like terms.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
-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.

5. Finding the Slope When Given an Equation of a Line
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Cancel factors common to the numerator and denominator.

6. What is the Pythagorean Theorem?
A(2)+b(2)=c(2)
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.
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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

7. Formula Used to Find Percent
Part=Percent x Whole
Factor out and cancel all factors the numerator and denominator 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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

8. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

9. Finding the Domain and Range of a Function
Multiply the numerators and multiply the denominators.
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.
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
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.

10. Finding the Area of a Triangle

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

11. Number of Groups - +1 Each Time
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.
2(pie)r
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Express them with a common denominator.

12. Simplifying Square Roots
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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 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.

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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183

14. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
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
Factor out and cancel all factors the numerator and denominator have in common.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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

15. Properties of a 45-45-90 Triangle
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.
Use simple numbers like 1 and 2 and see what happens.
A(2)+b(2)=c(2)
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

16. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

17. Properties of Similar Triangles
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.

18. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
Four equal acute angles and four equal obtuse angles.
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.
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

19. Solving a Radical Equation
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Isolate the radical expression and use the standard rules of algebra.
-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.
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. Simplifying a Fraction to Lowest Terms
VofaC: (pie)r(2)h
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Sum: Average x Number of Terms
Factor out and cancel all factors the numerator and denominator have in common.

21. 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
Find a common denominator - then add or subtract the numerators.
Adjacent angles are supplementary - Vertical angles are equal
Plug in the given values for the unknowns and calculate according to PEMDAS.

22. Finding a Term in a Geometric Sequence
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.
Slope=change in y/change in x
Multiply the numerators and multiply the denominators.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

23. Calculating Negative Exponents and Radical Exponents
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Combine like terms.

24. An Important Property of a Line Tangent to a Circle
Use the formula distance=rate*time and its variations to help in this question.
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.
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 the equation into y=mx+b-- in which case b is the y-intercept.

25. Multiply and Divide Positive and Negative Numbers
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.
Cancel factors common to the numerator and denominator.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

26. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

27. What Does Solving In Terms of Mean?
Cross multiply.
-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.
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
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

28. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
The whole number left over after division.
Put the equation into y=mx+b-- in which case b is the y-intercept.

29. 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?
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^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.
(x1+x2)/2 -(y1+y2)/2
Cross multiply.

30. Definition of Remainder
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.
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
Find a common denominator - then add or subtract the numerators.
The whole number left over after division.

31. Properties of the Interior and Exterior Angles of a Triangle
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.
Find a common denominator - then add or subtract the numerators.
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

32. Raising a Power to a Power
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
Multiply the exponents - (x^3)^4=x^3*4=x^12
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

33. 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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
VofaC: (pie)r(2)h
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

34. 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.
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)
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.

35. Multiplying Fractions
Multiply the numerators and multiply the denominators.
2(pie)r
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes

36. Convert From a Fraction to a Decimal - Vice Versa
-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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

37. Evaluating an Algebraic Expression
Plug in the given values for the unknowns and calculate according to PEMDAS.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

38. Knowing if an Integer is a Multiple of 5 or 10
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
-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.
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.
The value that falls in the middle of the set.

39. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24

40. Properties of a 30-60-90 Triangle
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Sum: Average x Number of Terms
Cancel factors common to the numerator and denominator.

41. Finding the Distance Between Two Points on a Coordinate Graph
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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

42. Finding the Reciprocal of a Fraction
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.
Switch the numerator and denominator.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

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

44. Finding the Circumference of a Circle
Factor out and cancel all factors the numerator and denominator have in common.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
2(pie)r
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. Dividing Expressions with Exponents that Have a Common Base
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.
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.
Subtract the smallest from the largest and add 1
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

46. If the average of a - b - and 48 is 48 - what is the value of a + b?
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Find a common denominator - then add or subtract the numerators.
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
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

47. Direct Variation and Inverse Variation
Average the smallest and largest number
Use the formula distance=rate*time and its variations to help in this question.
Part=Percent x Whole
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

48. Average Rate and How Do You Find It
Get the absolute value equation by itself. Solve.
Cancel factors common to the numerator and denominator.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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

49. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Multiply the numerators and multiply the denominators.
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.

50. Finding the Mode of a Set of Numbers
Switch the numerator and denominator.
The value that appears the most often.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.