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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Subjects
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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. Notation: f(x) read: 'f of x' evaluation: if you want to evaluate the function for f(4) - replace x with 4 everywhere in the equation
Function - Notation - and Evaulation
Identifying the Parts and the Whole
Number Categories
Solving a Proportion
2. Use units to keep things straight (make sure you use 1 unit for each thing) Example: use just inches in your cross multiplication - not inches and feet
Greatest Common Factor
Rate
Comparing Fractions
Counting the Possibilities
3. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Direct and Inverse Variation
Adding and Subtracting monomials
Tangency
Mixed Numbers and Improper Fractions
4. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Even/Odd
Percent Formula
Multiplying and Dividing Powers
Volume of a Rectangular Solid
5. If a right triangle's leg-to-leg ratio is 5:12 - or if the leg-to-hypotenuse ratio is 5:13 or 12:13 - it's a 5-12-13 triangle
Circumference of a Circle
Mixed Numbers and Improper Fractions
Factor/Multiple
The 5-12-13 Triangle
6. To find the y-intercept: put the equation into slope-intercept form (b is the y-intercept): y=mx+b or plug x=0 and solve for y - To find the x-intercept: plug y=0 and solve for x
Area of a Circle
Using an Equation to Find an Intercept
Exponential Growth
Intersecting Lines
7. Direct variation: equation: y=kx - where k is a nonzero constant trick: y changes directly as x does inverse variation: equation: xy=k trick: y doubles as x halves and vice-versa
Direct and Inverse Variation
Identifying the Parts and the Whole
Average Formula -
Volume of a Rectangular Solid
8. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Characteristics of a Parallelogram
PEMDAS
Finding the Distance Between Two Points
Pythagorean Theorem
9. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
Domain and Range of a Function
Interior Angles of a Polygon
Tangency
10. To multiply or divide integers - firstly ignore the sign and compute the problem - given 2 negatives make a positive - 2 positives make a positive - and one negative - and one positive make a negative attach the correct sign
Multiplying/Dividing Signed Numbers
Finding the Original Whole
Direct and Inverse Variation
Volume of a Cylinder
11. For all right triangles: a^2+b^2=c^2
Pythagorean Theorem
Mixed Numbers and Improper Fractions
Negative Exponent and Rational Exponent
Characteristics of a Rectangle
12. To add a positive and negative integer first ignore the signs and find the positive difference between the two integers - attatch the sign of the original with higher absolute value - to subtract negative integers simply change it into an addition pr
Adding/Subtracting Signed Numbers
Function - Notation - and Evaulation
Number Categories
Area of a Triangle
13. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Area of a Circle
Relative Primes
Intersecting Lines
Union of Sets
14. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
PEMDAS
Adding and Subtraction Polynomials
Using an Equation to Find the Slope
Reducing Fractions
15. The smallest multiple (other than zero) that two or more numbers have in common.
Direct and Inverse Variation
Rate
Setting up a Ratio
(Least) Common Multiple
16. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Multiplying and Dividing Roots
Interior and Exterior Angles of a Triangle
Average Rate
Using the Average to Find the Sum
17. Use this example: Example: after a 5% increase - the population was 59 -346. What was the population before the increase? Work: 1.05x=59 -346 Answer: 56 -520
Median and Mode
Comparing Fractions
Finding the Original Whole
Tangency
18. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Multiplying Monomials
Multiplying/Dividing Signed Numbers
Parallel Lines and Transversals
Even/Odd
19. 1. Re-express them with common denominators 2. Convert them to decimals
Finding the Original Whole
The 5-12-13 Triangle
Circumference of a Circle
Comparing Fractions
20. Integers are whole numbers; they include negtavie whole numbers and zero - Rational numbers can be expressed as a ratio of two integers - irration numbers are real numbers that cant be expressed precisely as a fraction or decimal.
Even/Odd
Number Categories
Circumference of a Circle
Dividing Fractions
21. Start with 100 as a starting value - Example: A price rises by 10% one year and by 20% the next. What's the combined percent increase? - Say the original price is $100. Year one: $100 + (10% of 100) = 100 + 10 = 110 Year two: 110 + (20% of 110) = 110
Length of an Arc
Multiplying and Dividing Powers
Combined Percent Increase and Decrease
Number Categories
22. A sector is a piece of the area of a circle. If n is the degree measure of the sector's central angle then the formula is: Area of a Sector = (n/360) (pr^2)
Setting up a Ratio
Percent Increase and Decrease
Identifying the Parts and the Whole
Area of a Sector
23. Part = Percent x Whole
Average Rate
Volume of a Rectangular Solid
Exponential Growth
Percent Formula
24. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
(Least) Common Multiple
Relative Primes
Similar Triangles
25. Example: If the ratio of males to females is 1 to 2 - then what is the ratio of males to people? - work: 1/(1+2) answer: 1/3
Using an Equation to Find an Intercept
Part-to-Part Ratios and Part-to-Whole Ratios
Surface Area of a Rectangular Solid
Intersecting Lines
26. An arc is a piece of the circumference. If n is the degree measure of the arc's central angle - then the formula is: Length of an Arc = 1 (n/360) (2pr)
Prime Factorization
Length of an Arc
Determining Absolute Value
Area of a Sector
27. An isosceles triangle has 2 equal sides and the angles opposite the equal sides (base angles) are also equal - an equaliteral is a triangle where all 3 sides are equal - thus the angles are equal - regardless of side length the angle is always 60 deg
Percent Formula
Average Formula -
Isosceles and Equilateral triangles
Multiplying Fractions
28. Sum=(Average) x (Number of Terms)
Triangle Inequality Theorem
Function - Notation - and Evaulation
Using the Average to Find the Sum
Adding and Subtracting monomials
29. Integers that have no common factor other than 1 - to determine whether two integers are relative primes break them both down to their prime factorizations
Interior and Exterior Angles of a Triangle
Multiplying and Dividing Powers
Counting the Possibilities
Relative Primes
30. A square is a rectangle with four equal sides; Area of Square = side*side
Multiplying and Dividing Roots
Characteristics of a Square
Pythagorean Theorem
Using the Average to Find the Sum
31. The 3 angles of any triangle add up to 180 degrees - an exterior angles of a triangle is equal to the sum of the remote interior angles - the 3 exterior angles add up to 360 degrees
Interior and Exterior Angles of a Triangle
Multiples of 2 and 4
Characteristics of a Rectangle
Factor/Multiple
32. Negative exponent: put number under 1 in a fraction and work out the exponent Rational exponent: square root it- 1. make the root of the problem whatever the denominator of the exponent is 2. the exponent under your root sign is the numerator of the
Adding and Subtraction Polynomials
Reducing Fractions
Number Categories
Negative Exponent and Rational Exponent
33. To multiply fractions - multiply the numerators and multiply the denominators
Identifying the Parts and the Whole
Multiplying Fractions
Union of Sets
Evaluating an Expression
34. The length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides
Triangle Inequality Theorem
Multiplying/Dividing Signed Numbers
Using an Equation to Find an Intercept
Average Rate
35. Subtract the smallest from the largest and add 1
Average of Evenly Spaced Numbers
Solving a System of Equations
Counting Consecutive Integers
Interior and Exterior Angles of a Triangle
36. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Reciprocal
Dividing Fractions
Similar Triangles
Adding/Subtracting Signed Numbers
37. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Finding the Original Whole
Prime Factorization
Triangle Inequality Theorem
Evaluating an Expression
38. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Tangency
Characteristics of a Rectangle
Area of a Circle
Multiplying and Dividing Roots
39. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Using the Average to Find the Sum
Mixed Numbers and Improper Fractions
Adding and Subtracting monomials
Using an Equation to Find the Slope
40. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them
Adding and Subtracting Roots
Multiples of 3 and 9
Adding and Subtracting monomials
Even/Odd
41. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Surface Area of a Rectangular Solid
Adding and Subtracting monomials
Adding/Subtracting Fractions
Function - Notation - and Evaulation
42. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Counting Consecutive Integers
Multiples of 3 and 9
Finding the Original Whole
Setting up a Ratio
43. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Interior and Exterior Angles of a Triangle
Length of an Arc
Isosceles and Equilateral triangles
Average Formula -
44. Factor out the perfect squares
Average Formula -
Using the Average to Find the Sum
Simplifying Square Roots
Repeating Decimal
45. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Isosceles and Equilateral triangles
Multiplying/Dividing Signed Numbers
Similar Triangles
Characteristics of a Rectangle
46. Use the sum - Example: if the average of 4 #s is 7 - and the #s are 3 - 5 - 8 - and ____ - what is the fourth #? Work: sum= 4*7 =28 3+5+8=16 28-16=? Answer: 12
Multiplying and Dividing Roots
The 3-4-5 Triangle
Finding the Missing Number
Intersection of sets
47. To increase: add decimal version of percent to one and times that # to the # you want to increase. Example: increase 40 by 25% Work: 1.25*40=? Answer: 50
Raising Powers to Powers
Counting the Possibilities
Percent Increase and Decrease
Finding the Distance Between Two Points
48. A parallelogram has two pairs of parallel sides - opposite sides are equal - opposite angles are equal - consecutive angles add up to 180 degrees; Area of Parallelogram = base x height
Using an Equation to Find an Intercept
Intersecting Lines
Characteristics of a Parallelogram
Tangency
49. you can add/subtract when the part under the radical is the same
PEMDAS
Simplifying Square Roots
Adding and Subtracting Roots
Using Two Points to Find the Slope
50. To divide fractions - invert the second one and multiply
Setting up a Ratio
Dividing Fractions
Multiples of 2 and 4
Relative Primes