Teaching Math in the Intermediate Grades

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

• True
• False

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

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In what quadrant do -1000 lies?

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

The Pythagorean Theorem was formulated by Pythagoras of Italy.

• True
• False

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

• True
• False

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

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

Zero and positive integers are the __________.

• Whole Numbers

Convert 34 = d in logarithmic form.

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

• True
• False

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

• Irrational Numbers

1.7 is a rational number

• True
• False

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

• True
• False

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

• 3
• 6
• -4
• 12

What is the value of x?

• 12.35
• 11.67
• 13.78
• 10.2

What is the equivalent of -3.5π in degrees?

• 6800
• 5800
• 6300
• 6500

cos θ is equal to 1/sec⁡θ .

• True
• False

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

In what quadrant does -2100, can be found?

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

• cosine
• tangent
• sine
• secant

Evaluate cos(900 + 900)

What is the coterminal of 00?

The value of x is ____.

What is the exponential form of log 12 d = k

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

• True
• False

Which of the following is the symbol for eta?

• ε
• β
• θ
• H

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

• f/g
• g/e
• g/f
• f/e

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

• True
• False

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

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

• True
• False

K is the capital letter for kappa.

• True
• False

The reference angle of the given figure below is:

• 1180
• 620
• 280
• 1520

A rational function is the product of two polynomials.

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

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Identify ¾ as irrational or rational.

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

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

The unknown measurement of the side of the triangle below is

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

If sin α= 2/7, then cos α = 7/2.

• True
• False

A counterclockwise direction makes a negative degree measurement.

• True
• False

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

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

Oblique triangles are solved using the Pythagorean Theorem.

• True
• False

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

Degree is a unit measure for angles.

• True
• False

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

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

The reciprocal of cosine is sine.

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

• 2x = -4
• x = - 2
• x = 2
• x = -4

Subtract:

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

Hypotenuse is the longest side of a right triangle.

• True
• False

Which of the following is coterminal of 900?

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

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

• True
• False

The following are all exponential function except

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

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

• True
• False

What is (-3π)/11 in degree measures?

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

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

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

2π is equals to 3600.

• True
• False

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

• Integers

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

Which of the following is the ordered pair for 3600?

Is csc2 θ = 1 – cot2 θ?

• True
• False

Which of the following polynomials has 3 terms?

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

• True
• False

The name of the Greek letter ξ is _______.

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

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

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.

Convert 9000 to radian measure.

• 5π
• -5π
• 2π
• 4π

What is the trigonometric function with a ratio adjacent/opposite

• cosecant
• cosine
• tangent
• cotangent

The following are the fundamental identities except

– 3120 can be found at Quadrant IV.

• True
• False

Identify √2 as s irrational or rational.

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

A polynomial function is defined as the product of monomials.

• True
• False

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

• True
• False

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

What is the coterminal of -700 ?

The following are all coterminal of 1350, except

Convert 53 = y to logarithmic form.

What is the value of cos – 300?

Given the triangle below, the legs are

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

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

• 5
• 9
• 1
• 3

What is the ratio of sin β?

In what quadrant does 5π/9 belong?

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

• True
• False

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

• True
• False

Radian uses the symbol π .

• True
• False

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

Express the sum and difference of cos 300.

The reciprocal of tangent

• secant
• cosecant
• cosine
• cotangent

The Greek name for σ is rho.

• True
• False

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

• -26/9
• -58/12
• -29/6
• -15/4

-3000 is equal to _____ radians.

• (-5π)/3
• (-4π)/3
• π/4
• (-3π)/2

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

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

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

Simplify sin x sec x/tanx .

The following are coterminal of 900, except

• -2700
• 2700
• -6300
• 4500

The following degree measurements are found in Quadrant I, except

cosine – 600 is equal to - √3/2.

• True
• False

Initial side of an angle is the one that rotates.

• True
• False

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

• True
• False

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?

Identify √5 as irrational or rational.

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

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

• True
• False

The following are equal to 1, except

What is the length of side y?

The trigonometric function of the ratio 7/25 is

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

• 9
• 54
• -36
• -27

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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Which of the following is equal to tan x?

Using the triangle below, which is the hypotenuse?

The following measurements can be found in Quadrant III, except

• -2400
• 120
• (-2π)/3
• (-5π)/6

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

• True
• False

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

• True
• False

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

• True
• False

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

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

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

• Rational Numbers

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

• -2
• 7
• -6
• 10

Convert -3150 to radian measure.

The graph of the cosine functions always passes through the origin

• True
• False

The value of the unknown side is ____.

The following angles belong to quadrant IV, except

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

• 1
• √3/2
• √3/4
• 1/2

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

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

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

The cofunction of cosecant is cosine.

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

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

• 1/2
• -1
• 2
• (-1)/2

The maximum point is the highest point a graph reach.

• True
• False

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

What is the function to be use to solve x?

The following may be seen in a right triangle, EXCEPT

The graph below shows

10000 belong to what quadrant?

What is the logarithmic form of dr = ba ?

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

The exponential function of the graph below is:

Is tanθ/cotθ = 1?

• True
• False

A clockwise direction is a positive measurement.

• True
• False

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

• True
• False

The value of sin 300 is

π radian is equivalent to 1800

• True
• False

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

The following are in standard position, except

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

• True
• False

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

• 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

- 3π/4 is equal to how many degrees?

The symbol i is called ________.

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

The answer: for -73 = ___ is?

Simplify: log 3 92x = x + 12

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

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

All angles belongs to Quadrant III, which is not

What is the reference angle of 1600?

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

• Natural Numbers

Which of the following angle is in standard position?

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

• True
• False

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

• True
• False

The exponential form of log b d2 = e is

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

• 6
• 5
• 7
• 1

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

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

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

• + x4
• +10
• -3x7
• -6x5

Solve: 2 csc x(3 – 2csc x + csc2 x)

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

• True
• False

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

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

• True
• False

The parts of the right triangle are

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

Which of the following is considered as an exponential function?

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

What is the quadrant of -1800?

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

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Simplify: log 7 49 = x – 4.

The ratio for cosecant is

The unit circle is similar with coordinate plane.

• True
• False

Base is where the exponent affixes

• True
• False

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

All angles has a reference angle of 300, except

(-3π)/2 belongs to quadrant?

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

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

• True
• False

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

• True
• False

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

sin 2100 is equal to -1/2

• True
• False

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

1800 is equivalent to p radians.

• True
• False

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

• True
• False

π is equivalent to 1800.

• True
• False

Solve for y

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

The cofunction of cotangent is tangent.

• True
• False

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

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

The ratio for cosine is

Is sin2θ cos2θ = 1?

• True
• False

What is the cofunction of cotangent?

• tangent
• sine
• cosine
• secant

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

• True
• False

-900 is equivalent to - π/2 radians.

• True
• False

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

• 4
• 3
• 7
• 5

Which of the following is the cofunction of secant?

• cosecant
• cotangent
• cosine
• tangent

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

• True
• False

Coterminal angles are the same degrees.

36250 can be found at quadrant?

cosine 900 is equal to 1.

• True
• False

The following are all exponential functions, except

The sin value of 1800 is

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

When do graph of exponential function goes down?

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

A polynomial function is defined as the sum of monomials.

• True
• False

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

• True
• False

The reciprocal of sine is

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

• 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 ratio of cot θ is ____.

What is the exponential function of the table below?

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

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

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

- 4π/3 is equivalent

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

• True
• False

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

• True
• False