Teaching Math in the Intermediate Grades

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

The graph below shows

A clockwise direction is a positive measurement.

• True
• False

Is sin2θ cos2θ = 1?

• True
• False

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

• True
• False

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

• True
• False

Which of the following is considered as an exponential function?

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

• True
• False

What is the coterminal of -700 ?

What is the value of x?

• 12.35
• 11.67
• 13.78
• 10.2

Solve: 2 csc x(3 – 2csc x + csc2 x)

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

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

• -2
• 7
• -6
• 10

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

Which of the following angle is in standard position?

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

• 1
• √3/2
• √3/4
• 1/2

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

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

• True
• False

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

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The following may be seen in a right triangle, EXCEPT

– 3120 can be found at Quadrant IV.

• True
• False

What is the logarithmic form of dr = ba ?

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

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

• True
• False

The symbol i is called ________.

The answer: for -73 = ___ is?

What is the function to be use to solve x?

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

• True
• False

The value of sin 300 is

The reciprocal of cosine is sine.

• True
• False

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

Which of the following is the symbol for eta?

• ε
• β
• θ
• H

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

π radian is equivalent to 1800

• True
• False

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

• True
• False

What is (-3π)/11 in degree measures?

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

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

• True
• False

Convert -3150 to radian measure.

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

In what quadrant does 5π/9 belong?

A rational function is the product of two polynomials.

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

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

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

• True
• False

- 3π/4 is equal to how many degrees?

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

1.7 is a rational number

• True
• False

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

• cosine
• tangent
• sine
• secant

Degree is a unit measure for angles.

• True
• False

Identify √5 as irrational or rational.

Convert 9000 to radian measure.

• 5π
• -5π
• 2π
• 4π

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

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

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

Zero and positive integers are the __________.

• Whole Numbers

-900 is equivalent to - π/2 radians.

• True
• False

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

• True
• False

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

• True
• False

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

• True
• False

What is the length of side y?

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

• True
• False

What is the quadrant of -1800?

Is csc2 θ = 1 – cot2 θ?

• True
• False

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

• Integers

The cofunction of cotangent is tangent.

• True
• False

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

• True
• False

What is the trigonometric function with a ratio adjacent/opposite

• cosecant
• cosine
• tangent
• cotangent

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

Hypotenuse is the longest side of a right triangle.

• True
• False

The exponential form of log b d2 = e is

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

• Rational Numbers

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

sin 2100 is equal to -1/2

• True
• False

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

• True
• False

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

• True
• False

All angles belongs to Quadrant III, which is not

Which of the following polynomials has 3 terms?

2π is equals to 3600.

• True
• False

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

• + x4
• +10
• -3x7
• -6x5

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

Simplify: log 7 49 = x – 4.

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

• 3
• 6
• -4
• 12

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

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The reciprocal of tangent

• secant
• cosecant
• cosine
• cotangent

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

• True
• False

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

• 5
• 9
• 1
• 3

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

• 1/2
• -1
• 2
• (-1)/2

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

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

Initial side of an angle is the one that rotates.

• True
• False

Given the triangle below, the legs are

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

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

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

In what quadrant do -1000 lies?

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

Convert 53 = y to logarithmic form.

1800 is equivalent to p radians.

• True
• False

-3000 is equal to _____ radians.

• (-5π)/3
• (-4π)/3
• π/4
• (-3π)/2

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

The following are in standard position, except

Identify ¾ as irrational or rational.

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

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

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

• 9
• 54
• -36
• -27

π is equivalent to 1800.

• True
• False

What is the coterminal of 00?

Coterminal angles are the same degrees.

What is the exponential form of log 12 d = k

- 4π/3 is equivalent

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

The Greek name for σ is rho.

• True
• False

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

Which of the following is coterminal of 900?

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

• True
• False

The Pythagorean Theorem was formulated by Pythagoras of Italy.

• True
• False

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

• True
• False

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

Two students are working problems on the board while the rest of the class watches.

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Which of the following is the ordered pair for 3600?

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

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

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

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

• Irrational Numbers

When do graph of exponential function goes down?

cos θ is equal to 1/sec⁡θ .

• True
• False

Oblique triangles are solved using the Pythagorean Theorem.

• True
• False

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 cofunction of cosecant is cosine.

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

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

• 6
• 5
• 7
• 1

The following are all exponential functions, except

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

• True
• False

The following are coterminal of 900, except

• -2700
• 2700
• -6300
• 4500

Evaluate cos(900 + 900)

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

Identify √2 as s irrational or rational.

The value of the unknown side is ____.

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

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

• 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 ratio of sin β?

A polynomial function is defined as the sum of monomials.

• True
• False

The reciprocal of sine is

K is the capital letter for kappa.

• True
• False

(-3π)/2 belongs to quadrant?

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

What is the cofunction of cotangent?

• tangent
• sine
• cosine
• secant

Simplify: log 3 92x = x + 12

What is the reference angle of 1600?

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.

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

The unit circle is similar with coordinate plane.

• True
• False

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

The following are all exponential function except

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

The reference angle of the given figure below is:

• 1180
• 620
• 280
• 1520

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

The maximum point is the highest point a graph reach.

• 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

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

• True
• False

cosine – 600 is equal to - √3/2.

• True
• False

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

• True
• False

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

• True
• False

The parts of the right triangle are

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

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

• True
• False

What is the value of cos – 300?

The graph of the cosine functions always passes through the origin

• True
• False

The following angles belong to quadrant IV, except

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

• True
• False

Using the triangle below, which is the hypotenuse?

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

• 2x = -4
• x = - 2
• x = 2
• x = -4

Convert 34 = d in logarithmic form.

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

• True
• False

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

A polynomial function is defined as the product of monomials.

• True
• False

Express the sum and difference of cos 300.

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

• 4
• 3
• 7
• 5

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

• f/g
• g/e
• g/f
• f/e

The following are equal to 1, except

Base is where the exponent affixes

• True
• False

The value of x is ____.

Which of the following is equal to tan x?

The following degree measurements are found in Quadrant I, except

Simplify sin x sec x/tanx .

The exponential function of the graph below is:

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

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?

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

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

• -26/9
• -58/12
• -29/6
• -15/4

cosine 900 is equal to 1.

• True
• False

The name of the Greek letter ξ is _______.

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

• True
• False

A counterclockwise direction makes a negative degree measurement.

• True
• False

Subtract:

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

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

• True
• False

If sin α= 2/7, then cos α = 7/2.

• True
• False

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

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

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

• True
• False

Solve for y

The unknown measurement of the side of the triangle below is

The sin value of 1800 is

Is tanθ/cotθ = 1?

• True
• False

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

All angles has a reference angle of 300, except

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

The trigonometric function of the ratio 7/25 is

The following are the fundamental identities except

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

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

• Natural Numbers

36250 can be found at quadrant?

The ratio for cosecant is

What is the equivalent of -3.5π in degrees?

• 6800
• 5800
• 6300
• 6500

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

• True
• False

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

The following measurements can be found in Quadrant III, except

• -2400
• 120
• (-2π)/3
• (-5π)/6

In what quadrant does -2100, can be found?

The ratio for cosine is

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

Which of the following is the cofunction of secant?

• cosecant
• cotangent
• cosine
• tangent

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

• True
• False

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

A rational function is the quotient of two polynomials

• True
• False

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

• True
• False

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

Radian uses the symbol π .

• True
• False

10000 belong to what quadrant?

The following are all coterminal of 1350, except

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

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 ratio of cot θ is ____.

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