Teaching Math in the Intermediate Grades

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

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

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

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

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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

A rational function is the quotient of two polynomials

• True
• False

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

In what quadrant do -1000 lies?

The following are all coterminal of 1350, 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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1800 is equivalent to p radians.

• True
• False

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

• True
• False

A polynomial function is defined as the product of monomials.

• 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

Identify √2 as s irrational or rational.

The sum of the trigonometric functions 2 sin x + 5 and 4 - sin x 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 clockwise direction is same as the movements of the hands of a clock.

• True
• False

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

• True
• False

36250 can be found at quadrant?

A counterclockwise direction makes a negative degree measurement.

• True
• False

In what quadrant does 5π/9 belong?

Solve for y

The following are all exponential functions, except

Convert 34 = d in logarithmic form.

The unit circle is similar with coordinate plane.

• True
• False

Oblique triangles are solved using the Pythagorean Theorem.

• True
• False

Initial side of an angle is the one that rotates.

• True
• False

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

• 1
• √3/2
• √3/4
• 1/2

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

• 4
• 3
• 7
• 5

Simplify: log 3 92x = x + 12

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

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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

A clockwise direction is a positive measurement.

• True
• False

Evaluate cos(900 + 900)

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

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

• True
• False

The Greek name for σ is rho.

• True
• False

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

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

• cosine
• tangent
• sine
• secant

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

If sin α= 2/7, then cos α = 7/2.

• True
• False

The value of x is ____.

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

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

• True
• False

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

• -26/9
• -58/12
• -29/6
• -15/4

The name of the Greek letter ξ is _______.

The value of sin 300 is

Zero and positive integers are the __________.

• Whole Numbers

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

(-3π)/2 belongs to quadrant?

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

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

• True
• False

The graph below shows

Express the sum and difference of cos 300.

The trigonometric function of the ratio 7/25 is

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

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

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

• 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

sin 2100 is equal to -1/2

• True
• False

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

Which of the following is coterminal of 900?

What is the exponential function of the table below?

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

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

The following degree measurements are found in Quadrant I, except

The following may be seen in a right triangle, EXCEPT

Which of the following is equal to tan x?

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

• 3
• 6
• -4
• 12

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

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

• True
• False

The ratio for cosecant is

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

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

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

• True
• False

- 4π/3 is equivalent

Which of the following is considered as an exponential function?

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

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

• 2x = -4
• x = - 2
• x = 2
• x = -4

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

• True
• False

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

K is the capital letter for kappa.

• True
• False

The cofunction of cotangent is tangent.

• True
• False

The following are equal to 1, except

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

What is the value of cos – 300?

Identify ¾ as irrational or rational.

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

• True
• False

Is sin2θ cos2θ = 1?

• True
• False

Which of the following polynomials has 3 terms?

Base is where the exponent affixes

• True
• False

– 3120 can be found at Quadrant IV.

• True
• False

Given the triangle below, the legs are

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

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

• True
• False

2π is equals to 3600.

• True
• False

What is the length of side y?

The reciprocal of tangent

• secant
• cosecant
• cosine
• cotangent

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

• Natural Numbers

What is (-3π)/11 in degree measures?

Is tanθ/cotθ = 1?

• True
• False

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

Coterminal angles are the same degrees.

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

cosine 900 is equal to 1.

• True
• False

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

Which of the following is the ordered pair for 3600?

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

• True
• False

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

• True
• False

All angles has a reference angle of 300, except

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

The following are coterminal of 900, except

• -2700
• 2700
• -6300
• 4500

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

• + x4
• +10
• -3x7
• -6x5

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

• True
• False

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

• True
• False

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

• 6
• 5
• 7
• 1

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

What is the coterminal of -700 ?

1.7 is a rational number

• True
• False

Radian uses the symbol π .

• True
• False

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

• Integers

The Pythagorean Theorem was formulated by Pythagoras of Italy.

• True
• False

Convert 53 = y to logarithmic form.

What is the exponential form of log 12 d = k

- 3π/4 is equal to how many degrees?

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 value of the unknown side is ____.

The following angles belong to quadrant IV, except

Hypotenuse is the longest side of a right triangle.

• True
• False

The exponential function of the graph below is:

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

What is the equivalent of -3.5π in degrees?

• 6800
• 5800
• 6300
• 6500

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.

What is the coterminal of 00?

The reference angle of the given figure below is:

• 1180
• 620
• 280
• 1520

The graph of the cosine functions always passes through the origin

• True
• False

Solve: 2 csc x(3 – 2csc x + csc2 x)

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

• True
• False

The following measurements can be found in Quadrant III, except

• -2400
• 120
• (-2π)/3
• (-5π)/6

The following are all exponential function except

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

Simplify sin x sec x/tanx .

π is equivalent to 1800.

• True
• False

The exponential form of log b d2 = e is

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

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

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

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

• True
• False

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

• -2
• 7
• -6
• 10

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

• f/g
• g/e
• g/f
• f/e

What is the reference angle of 1600?

In what quadrant does -2100, can be found?

Which of the following angle is in standard position?

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

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

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

• True
• False

10000 belong to what quadrant?

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

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

• True
• False

Convert 9000 to radian measure.

• 5π
• -5π
• 2π
• 4π

When do graph of exponential function goes down?

The sin value of 1800 is

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

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

• Irrational Numbers

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

The parts of the right triangle are

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

The ratio for cosine is

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

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

• 9
• 54
• -36
• -27

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

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

• True
• False

What is the cofunction of cotangent?

• tangent
• sine
• cosine
• secant

Using the triangle below, which is the hypotenuse?

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

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

• 5
• 9
• 1
• 3

The symbol i is called ________.

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

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?

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

• True
• False

What is the function to be use to solve x?

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

Is csc2 θ = 1 – cot2 θ?

• True
• False

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

• 1/2
• -1
• 2
• (-1)/2

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

• True
• False

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

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

• True
• False

What is the value of x?

• 12.35
• 11.67
• 13.78
• 10.2

A rational function is the product of two polynomials.

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

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

• True
• False

The maximum point is the highest point a graph reach.

• True
• False

The cofunction of cosecant is cosine.

Subtract:

Simplify: log 7 49 = 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 graph of an exponential functions has 3 or more turning points

• True
• False

cos θ is equal to 1/sec⁡θ .

• True
• False

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

• Rational Numbers

The reciprocal of cosine is sine.

• 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 ratio of cot θ is ____.

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

Which of the following is the cofunction of secant?

• cosecant
• cotangent
• cosine
• tangent

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

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

What is the ratio of sin β?

The following are the fundamental identities except

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

• True
• False

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

• True
• False

What is the quadrant of -1800?

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

• True
• False

Which of the following is the symbol for eta?

• ε
• β
• θ
• H

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

• True
• False

-900 is equivalent to - π/2 radians.

• True
• False

The answer: for -73 = ___ is?

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

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

• True
• False

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

Degree is a unit measure for angles.

• True
• False

Convert -3150 to radian measure.

π radian is equivalent to 1800

• True
• False

The reciprocal of sine is

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

The following are in standard position, except

The unknown measurement of the side of the triangle below is

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

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

A polynomial function is defined as the sum of monomials.

• 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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All angles belongs to Quadrant III, which is not

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

-3000 is equal to _____ radians.

• (-5π)/3
• (-4π)/3
• π/4
• (-3π)/2

Identify √5 as irrational or rational.

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