Teaching Math in the Intermediate Grades

Evaluate cos(900 + 900)

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

When do graph of exponential function goes down?

Coterminal angles are the same degrees.

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

• True
• False

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

• True
• False

What is the exponential function of the table below?

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

36250 can be found at quadrant?

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

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

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

• 3
• 6
• -4
• 12

The symbol i is called ________.

The reciprocal of tangent

• secant
• cosecant
• cosine
• cotangent

The answer: for -73 = ___ 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

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

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

• True
• False

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

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

• 2x = -4
• x = - 2
• x = 2
• x = -4

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

• Natural Numbers

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

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

Is tanθ/cotθ = 1?

• True
• False

Identify √2 as s irrational or rational.

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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The maximum point is the highest point a graph reach.

• True
• False

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

• True
• False

The value of the unknown side is ____.

Which of the following is the symbol for eta?

• ε
• β
• θ
• H

What is the length of side y?

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

cosine 900 is equal to 1.

• True
• False

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

• True
• False

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

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

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

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

• 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?

What is the equivalent of -3.5π in degrees?

• 6800
• 5800
• 6300
• 6500

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

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The following are the fundamental identities except

The reciprocal of cosine is sine.

• True
• False

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

• 5
• 9
• 1
• 3

The exponential function of the graph below is:

Express the sum and difference of cos 300.

The ratio for cosine is

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

• Rational Numbers

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

All angles has a reference angle of 300, except

Which of the following is the ordered pair for 3600?

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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Which of the following is considered as an exponential function?

A rational function is the quotient of two polynomials

• 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?

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

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

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

• True
• False

If sin α= 2/7, then cos α = 7/2.

• True
• False

What is the coterminal of -700 ?

Is csc2 θ = 1 – cot2 θ?

• True
• False

A rational function is the product of two polynomials.

Radian uses the symbol π .

• True
• False

π is equivalent to 1800.

• True
• False

Base is where the exponent affixes

• True
• False

The graph of the cosine functions always passes through the origin

• True
• False

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

The following angles belong to quadrant IV, except

What is the exponential form of log 12 d = k

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

• -26/9
• -58/12
• -29/6
• -15/4

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

• True
• False

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

• True
• False

Solve: 2 csc x(3 – 2csc x + csc2 x)

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

What is the coterminal of 00?

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

Which of the following is equal to tan x?

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

• 4
• 3
• 7
• 5

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

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

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

• True
• False

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

• 1
• √3/2
• √3/4
• 1/2

The following may be seen in a right triangle, EXCEPT

The value of x is ____.

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

cos θ is equal to 1/sec⁡θ .

• True
• False

The value of sin 300 is

The reciprocal of sine 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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What is the logarithmic form of dr = ba ?

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

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

A polynomial function is defined as the product of monomials.

• 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

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

• True
• False

The exponential form of log b d2 = e is

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

• True
• False

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

• 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

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

What is the reference angle of 1600?

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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What is the cofunction of cotangent?

• tangent
• sine
• cosine
• secant

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

• True
• False

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

• True
• False

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

1800 is equivalent to p radians.

• True
• False

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

What is the quadrant of -1800?

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

• True
• False

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

The reference angle of the given figure below is:

• 1180
• 620
• 280
• 1520

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

• 9
• 54
• -36
• -27

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

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

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

• True
• False

sin 2100 is equal to -1/2

• True
• False

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

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

The Greek name for σ is rho.

• True
• False

Identify ¾ as irrational or rational.

-900 is equivalent to - π/2 radians.

• True
• False

Oblique triangles are solved using the Pythagorean Theorem.

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

• True
• False

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

Simplify: log 3 92x = x + 12

The following are coterminal of 900, except

• -2700
• 2700
• -6300
• 4500

What is the ratio of sin β?

A clockwise direction is a positive measurement.

• True
• False

Using the triangle below, which is the hypotenuse?

Zero and positive integers are the __________.

• Whole Numbers

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

• cosine
• tangent
• sine
• secant

Solve for y

- 4π/3 is equivalent

Given the triangle below, the legs are

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

In what quadrant does 5π/9 belong?

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

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

Convert 34 = d in logarithmic form.

Which of the following is the cofunction of secant?

• cosecant
• cotangent
• cosine
• tangent

In what quadrant do -1000 lies?

Convert -3150 to radian measure.

Which of the following is coterminal of 900?

10000 belong to what quadrant?

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

The name of the Greek letter ξ is _______.

The following are all exponential function except

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

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

What is (-3π)/11 in degree measures?

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

Hypotenuse is the longest side of a right triangle.

• True
• False

– 3120 can be found at Quadrant IV.

• True
• False

K is the capital letter for kappa.

• True
• False

What is the value of cos – 300?

The following are all exponential functions, except

Simplify: log 7 49 = x – 4.

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

• True
• False

The following are equal to 1, except

In what quadrant does -2100, can be found?

A counterclockwise direction makes a negative degree measurement.

• True
• False

The graph below shows

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

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

• True
• False

Which of the following angle is in standard position?

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

• True
• False

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

• Irrational Numbers

All angles belongs to Quadrant III, which is not

The following are in standard position, except

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

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

The trigonometric function of the ratio 7/25 is

Subtract:

The sin value of 1800 is

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

• True
• False

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

• True
• False

Convert 9000 to radian measure.

• 5π
• -5π
• 2π
• 4π

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

• True
• False

π radian is equivalent to 1800

• True
• False

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

• f/g
• g/e
• g/f
• f/e

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

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

• True
• False

A polynomial function is defined as the sum of monomials.

• True
• False

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

• True
• False

Identify √5 as irrational or rational.

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 following degree measurements are found in Quadrant I, except

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

• -2
• 7
• -6
• 10

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

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

• True
• False

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

• True
• False

The following are all coterminal of 1350, except

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

Which of the following polynomials has 3 terms?

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

• Integers

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.

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

- 3π/4 is equal to how many degrees?

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

• True
• False

What is the value of x?

• 12.35
• 11.67
• 13.78
• 10.2

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

1.7 is a rational number

• True
• False

What is the trigonometric function with a ratio adjacent/opposite

• cosecant
• cosine
• tangent
• cotangent

The unknown measurement of the side of the triangle below is

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

The cofunction of cosecant is cosine.

Simplify sin x sec x/tanx .

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

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

The Pythagorean Theorem was formulated by Pythagoras of Italy.

• True
• False

Convert 53 = y to logarithmic form.

cosine – 600 is equal to - √3/2.

• True
• False

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

• True
• False

The following measurements can be found in Quadrant III, except

• -2400
• 120
• (-2π)/3
• (-5π)/6

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

• 6
• 5
• 7
• 1

(-3π)/2 belongs to quadrant?

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

The parts of the right triangle are

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

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

Degree is a unit measure for angles.

• True
• False

What is the function to be use to solve x?

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

The cofunction of cotangent is tangent.

• True
• False

The ratio of cot θ is ____.

2π is equals to 3600.

• True
• False

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

• True
• False

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

• True
• False

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

• True
• False

Is sin2θ cos2θ = 1?

• True
• False

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

• 1/2
• -1
• 2
• (-1)/2

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

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

• True
• False

The unit circle is similar with coordinate plane.

• True
• False

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

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Initial side of an angle is the one that rotates.

• True
• False