Teaching Math in the Intermediate Grades

What is the exponential form of log 12 d = k

Given the rational function (x+10)/2x = 5, what is the first step to simplify it?

• Multiply both sides to 2x
• Subtract 5 to both sides
• Divide the right side to 2x.
• Switch 5 and 2x.

The ascending order of a polynomial function is if the exponents are arranged from smallest to highest.

• True
• False

From the figure below, the trigonometric function to be use if the given ratio 37/35 is

• sec π
• sin ϕ
• csc π
• cos π

In what quadrant does -2100, can be found?

What is the first step in solving the exponential function -3x + 5 = 81?

sin 2100 is equal to -1/2

• True
• False

Oblique triangles are solved using the Pythagorean Theorem.

• True
• False

The unit circle is similar with coordinate plane.

• True
• False

Find y in the exponential function 7y - 8 = 49?

– 3120 can be found at Quadrant IV.

• True
• False

The maximum point is the highest point a graph reach.

• True
• False

The value of the unknown side is ____.

What is the trigonometric function with a ratio adjacent/opposite

• cosecant
• cosine
• tangent
• cotangent

A rational function is the quotient of two polynomials

• True
• False

A clockwise direction is a positive measurement.

• True
• False

You may apply the Law of Sines if two sides and an angle opposite one of these sides are given or the SSA.

• True
• False

What is the quadrant of -1800?

Which of the following angle is in standard position?

The Greek name for σ is rho.

• True
• False

If sin α= 2/7, then cos α = 7/2.

• True
• False

2π is equals to 3600.

• True
• False

What is the value of g in the logarithmic form log 4 1024 = g?

• 4
• 3
• 7
• 5

The following are the ordered pairs in a unit circle, which is NOT?

Given the polynomial function f(x) = (x + 5)(x - 7)(x + 3), what is the first step to graph it.

What is the other identity you can derived from 1 + cot2 x = csc2 x?

-3000 is equal to _____ radians.

• (-5π)/3
• (-4π)/3
• π/4
• (-3π)/2

Subtract 4 cot2 x – 3 cot x + 12 from -5 cot2 x – 3 cot x – 11.

What is the logarithmic form of dr = ba ?

• log r ba = d
• log d b= ra
• log d ba = r
• log r d= ba

10000 belong to what quadrant?

Degree is a unit measure for angles.

• True
• False

The unknown value of m in m7 = 2187 is 3.

• True
• False

(-3π)/2 belongs to quadrant?

• Quadrant II
• Quadrant I
• Quadrant III
• Quadrant IV

Using the triangle below, which is the hypotenuse?

Using trigonometric functions, it can find and solve the unknown angles.

• True
• False

Which of the following function is properly arranged in descending order?

• j(x) = x2 + 2x3 - 3x4 + 4x5
• f(x) = x7 + 5x4 – 4x3 – 3x2 + 2x - 1
• h(x) = x3 + x2 - x4 + 15
• g(x) = 10x3 - 8x4 + 6x5 - 4x6 + 2x

The simplified form of sec2 x – 1 + tan2 x is

Simplify: log 3 92x = x + 12

What is the unknown measurement of the side of the right triangle below?

What is the next step if you’re going to derived the identity 1 – cos2 x = sin2 x and to equated to 1?

The remainder theorem is used to find the remainder of two polynomials.

• True
• False

In arranging the polynomial function h(x) = 2x + 3x5 - 7x3 + 22, in ascending order, the first term is 3x5.

• True
• False

Simplify sin x sec x/tanx .

The parts of the right triangle are

• Angles and legs
• Two legs and hypotenuse
• Three legs
• Leg and hypotenuse

The ratio of cot θ is ____.

The ratio for cosine is

The exponential form of log b d2 = e is

Which of the following is the cofunction of secant?

• cosecant
• cotangent
• cosine
• tangent

From the exponential function g(x) = ax, either a or x cannot be negative integer.

A rational function is the product of two polynomials.

How many terms does the polynomial function g(x) = 7x2 + 3x3 - 12 + 24x6 - x4 has ?

• 6
• 5
• 7
• 1

Ms. Lopez ensures that her students do not get lost by requiring them to stop when they finish an assignment and wait for others to finish

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The value of x in the function k(x) = -x + 3 is -3.

• True
• False

What is the quotient when you divide cot3 x – sec3 x by cot x – sec x?

The graph of an exponential functions has 3 or more turning points

• True
• False

Which of the following polynomials has 3 terms?

Simplify the function k(-3) = 3y4 + 2y5 - 21 11. Simplify the function k(-3) = 3y4 + 2y5 - 21

If the length of the hypotenuse and one leg of a right triangle were known, the right triangle can be solve.

• True
• False

Any real number that cannot be expressed in fractional form is an __________.

• Irrational Numbers

The following are all coterminal of 1350, except

What is the value of x?

• 12.35
• 11.67
• 13.78
• 10.2

The trigonometric function to be use in order to solve x is ____.

• cosine
• tangent
• sine
• secant

The exponential function of the graph below is:

The trigonometric function of the ratio 7/25 is

A triangular parcel of land with points E, F, G was to be fenced. ∠E = 47° and ∠F = 78°. EG = 180m. What is the measurement of ∠G?

Is sin2θ cos2θ = 1?

• True
• False

If you convert -43 = -64 to logarithmic form, the answer: is log -4 -64 = 3

• True
• False

What is the value of x in the function g(x) = 2x - 1?

• 1/2
• -1
• 2
• (-1)/2

The following measurements can be found in Quadrant III, except

• -2400
• 120
• (-2π)/3
• (-5π)/6

cosine – 600 is equal to - √3/2.

• True
• False

The given polynomial function is h(x) = (x - 3)(x + 5) (x - 1)(2x - 1)(x + 7), what is the degree of the function?

The sin value of 1800 is

The symbol of omega in lower case and upper case are ω and Ω

• True
• False

if you’re going to sketch the graph of f(x) = 7sin Θ. 7 stands for

How many terms does the polynomial function n(z) = 4 + z5 – 5z2 – 0 + 12z7 has?

In what quadrant do -1000 lies?

Simplify: log 7 49 = x – 4.

The value of x is ____.

Which of the following is the inverse of d(x) = 3/x + 4?

Using the exponential function, e(x) = 4x, continue the value of f(x) from the table below.

Convert -3150 to radian measure.

When do graph of exponential function goes down?

Convert 9000 to radian measure.

• 5π
• -5π
• 2π
• 4π

What is the remainder when you divide x3 - 1 to x - 1?

What is the value of cos – 300?

1800 is equivalent to p radians.

• True
• False

π is equivalent to 1800.

• True
• False

Express the sum and difference of cos 300.

Students read about the history of the Pythagorean Theorem. After reading, they solve problems using the theorem. Students then write about what they did compared to original uses of the Pythagorean Theorem.

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All angles has a reference angle of 300, except

Given the triangle below, the legs are

• AB & BC
• BC & AC
• AC & CB
• AB & BA

π radian is equivalent to 1800

• True
• False

cosine 900 is equal to 1.

• True
• False

Using the exponential function g(x) = 22x + 3. Complete the table below.

What is (-3π)/11 in degree measures?

Is sin (α + β) = sin α cos β - cos α sin β?

• True
• False

36250 can be found at quadrant?

Which of the following is considered as an exponential function?

The log b 25 = 2 is equivalent to 2b = 25.

• True
• False

Simplify: f(-5) = 4b2 + 8b - 35

In what quadrant does 5π/9 belong?

What is the value of b in 6b = 1/36?

The following degree measurements are found in Quadrant I, except

The following are all exponential function except

• g(x) = x5
• g(x) = bx
• –g(x) = 2xx-1
• g(x) = -3x

The ratio for cosecant is

Students have done their work on chart paper and are holding the chart paper while explaining to the class how their reached their conclusions.

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The leading coefficient of the polynomial function b(x) = 8 + 5x3 - 7x8 + 12x5 - x is 8.

• True
• False

If the length of two legs were given, then the right triangle may be solve.

• True
• False

Given the rational function (x+3)/5 = (x-7)/(x+1), what is the first step to solve it?

• Subtract x + 7 on both sides
• Multiply both sides by (5)(x + 1)
• Add x + 1 on both sides
• Divide both sides by x + 3

Subtract:

The reference angle of the given figure below is:

• 1180
• 620
• 280
• 1520

It refers to the position of the terminal sides of different degrees and yet located at the same position.

The inverse of 2x + 5 is 2/x-5

The counting numbers (1, 2, 3, ...), and their counterparts (-1, -2, -3, ...), and zero are __________.

• Integers

K is the capital letter for kappa.

• True
• False

The symbol i is called ________.

The inverse of the function of f(x) = x -12 is g(x) = x + 12.

• True
• False

A counterclockwise direction makes a negative degree measurement.

• True
• False

The Law of Cosines may apply if the given are two angles and the included side.

• True
• False

the counting numbers, this set holds all of the whole numbers except zero (1, 2, 3, ....)

• Natural Numbers

The following are the fundamental identities except

In arranging the polynomial function b(x) = 8 + 5x3 - 7x8 + 12x5 - x in descending order, the last term is - x.

• True
• False

The first three trigonometric functions are sine, cosine and tangent.

• True
• False

Evaluate cos(900 + 900)

Solve: 2 csc x(3 – 2csc x + csc2 x)

Identify √2 as s irrational or rational.

Evaluate sin(900 + 300), using sum and difference formula.

• 1
• √3/2
• √3/4
• 1/2

What is the length of side y?

What must be the value of the unknown in the box to make it an exponential function?

Students are acting out a problem in front of the class. Others in the class participate in a discussion of the problem.

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The following are equal to 1, except

Solve for y

What is the direction of the graph of the exponential function f(x) = 5-x?

Which of the following is the graph of a polynomial function if the leading coefficient is positive and the degree is even?

A polynomial function is defined as the product of monomials.

• True
• False

Coterminal angles are the same degrees.

Which of the following is equal to tan x?

The unknown measurement of the side of the triangle below is

The graph of f(x) = 7x and f(x) = 7x – 3 swift to the right and going down.

• True
• False

The following may be seen in a right triangle, EXCEPT

Radian uses the symbol π .

• True
• False

What is the remainder if 2x5 - 2x4 + 12 is divided by x - 2?

In 900 position of the terminal side in a unit circle, the value of cosine is

When arrange in ascending order, the last term of the polynomial function m(x) = -6x5 + x4 – 3x7 + 10 must be?

• + x4
• +10
• -3x7
• -6x5

The sum of the trigonometric functions 2 sin x + 5 and 4 - sin x is

Base is where the exponent affixes

• True
• False

The reciprocal of sine is

The following are in standard position, except

The students in Mr. McCollum's class are talking to each other about math problems.

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The name of the Greek letter ξ is _______.

Convert 53 = y to logarithmic form.

When you substitute -3 in the polynomial function a(x) = 7x3 + 8x2 + 20, the value of x is 135.

• True
• False

In simplifying the exponential function 32x + 7 = 27, the value of x is

• 2x = -4
• x = - 2
• x = 2
• x = -4

What is the coterminal of 00?

Mr. Roberts stimulates students' curiosity and encourages them to investigate further by asking them questions that begin with, "What would happen if..?"

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3 sin x + 2 sin2x cannot be added because they don’t have similar terms

• True
• False

n degrees, what is the equivalent value of 7π/8 ?

What is the ratio of sin β?

To verify if k(x) = x/2 - 7 and j(x) = 2x + 7 are inverses of each other, the first step is:

Which of the following table of values shows an example of exponential function?

Identify √5 as irrational or rational.

Which of the following polynomial function has a degree of 3?

What is the measurement of the other leg if the hypotenuse is 12 and the shortest leg is 3?

In Pythagorean identity, The following are equal to 1, except

Using the polynomial function f(x) = 5x2 + 21, what is the value of the unfilled box in the table of values below.

The unknown value of q in 4q = 4096 is 7.

• True
• False

The Pythagorean Theorem was formulated by Pythagoras of Italy.

• True
• False

What is the exponential function of the table below?

• g(x) = 2x
• g(x) = -2x
• g(x) = -3x
• g(x) = -2x- 1

If we solve f(x) = x - 7, the value of x is 7.

• True
• False

cos θ is equal to 1/sec⁡θ .

• True
• False

Cos 1150 is equal to cos( 300 + 600 + 150)

John Napier is the one who first used the term logarithm.

• True
• False

The graph below shows

Students are in groups. One student in the group works out the problem while the others closely observe.

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Which of the following is the symbol for eta?

• ε
• β
• θ
• H

What is the leading coefficient of the polynomial function h(x) = x3 + 2x4 - x7 + 12 -13x?

From the unit circle, the ordered pair (0, 1) can be found along x-axis at the left.

The reciprocal of tangent

• secant
• cosecant
• cosine
• cotangent

What is the value of x in the function h(x) = -2x + 12?

• 3
• 6
• -4
• 12

is any number which can be written in a fractional form.

• Rational Numbers

What is the cofunction of cotangent?

• tangent
• sine
• cosine
• secant

The following angles belong to quadrant IV, except

The unknown value of q in the exponential function 3q = 243 is 5.

• True
• False

What is the ratio of tan λ, using the figure below

• f/g
• g/e
• g/f
• f/e

Which of the following is coterminal of 900?

The graph of the cosine functions always passes through the origin

• True
• False

The following are the steps in solving the x of the function 32x + 7 = 27. What is the correct step?

Is tanθ/cotθ = 1?

• True
• False

The cofunction of cotangent is tangent.

• True
• False

What is the trigonometric function to be use to solve for y?

Which of the following is the graph of a polynomial function?

Given the polynomial function: p(x) = 2x + 7x4 – x2 + 3x3 -13 + x5, which of the following is the correct arrangement in ascending order?

Evaluate the polynomial function f(3) = 2x3 + 3x2 - 7x - 51.

• 9
• 54
• -36
• -27

- 2π and 2π can be found at two opposite direction

• True
• False

Initial side of an angle is the one that rotates.

• True
• False

If the hypotenuse and one acute angle were given, all unknowns of the oblique triangle may be solve.

• True
• False

- 4π/3 is equivalent

What is the degree of the polynomial function m(x) = -6x5 + x4 – 3x7 + 10

• -2
• 7
• -6
• 10

What is the value of x in (x+8)/(2x-5) = -3?

Reference angles are angles that are less than 900 and always positive.

• True
• False

1.7 is a rational number

• True
• False

The value of sin 300 is

At the end of class Ms. Stark collects everyone's worksheet and grades them.

• At the end of class Ms. Stark collects everyone's worksheet and grades them.
• Answer:
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Two students are working problems on the board while the rest of the class watches.

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All angles belongs to Quadrant III, which is not

Is any number which can name a location on a number line Every location on a number line can be called in some way by a ___________.

• Real Numbers

What is the function to be use to solve x?

The degree of the polynomial function in one variable is the largest exponent of its variable.

• True
• False

Which of the following is the ordered pair for 3600?

Divide 12 tan4 x + 8 tan3 x – 10 tan2 x – 6 tan x by 2 tan x.

• 6 tan3 x + 4 tan2 x – 5 tan x + 3
• 6 tan3 x - 4 tan2 x + 5 tan x – 3 tan x
• 6 tan3 x + 4 tan2 x – 5 tan x - 3
• 6 tan4 x + 4 tan3 x – 5 tan2 x – 3 tan x

In △PAN, P = 27.5°, A = 90°, what is the angle measurement of N?

The expression log g k = w is read as "The logarithm of g base k is w."

• True
• False

Hypotenuse is the longest side of a right triangle.

• True
• False

The cofunction of cosecant is cosine.

The answer: for -73 = ___ is?

If the smallest leg of a right triangle measure 5cm and the other leg measure 12 cm, how long is the longest side?

A polynomial function is defined as the sum of monomials.

• True
• False

The initial side is found in either x or y - axis.

• True
• False

Identify ¾ as irrational or rational.

The following are coterminal of 900, except

• -2700
• 2700
• -6300
• 4500

A clockwise direction is same as the movements of the hands of a clock.

• True
• False

Mr. Swanson believes that all students should get the same instruction at the same time. To accomplish this he only uses whole group instruction.

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The following are all exponential functions, except

Is csc2 θ = 1 – cot2 θ?

• True
• False

If the polynomial functions leading coefficient is negative and the degree is odd, where do the graph starts?

What is the equivalent of -3.5π in degrees?

• 6800
• 5800
• 6300
• 6500

Zero and positive integers are the __________.

• Whole Numbers

-900 is equivalent to - π/2 radians.

• True
• False

Convert 34 = d in logarithmic form.

What is the coterminal of -700 ?

The reciprocal of cosine is sine.

• True
• False

- 3π/4 is equal to how many degrees?

Is cos (α + β) = cos α cos β - sin α sin β?

• True
• False

Find the value of z in 2/(z+5) = 12

• -26/9
• -58/12
• -29/6
• -15/4

What is the degree of the polynomial function m(x) = 5x3 + 3x7 - 2x4 + x9 - 18?

• 5
• 9
• 1
• 3

An exponential function is represented as g(x) = x3.

• True
• False

What is the reference angle of 1600?

Which of the following is the sum of 3 cos x + 12 and 5cos x - 8?

• 8 cos x + 4
• 2 cos x + 4
• 8 cos x - 4
• 2 cos x - 4

What is the value of the exponential function h(-3) = 3x – 2?