Teaching Math in the Intermediate Grades

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 trigonometric function of the ratio 7/25 is

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

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

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

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

• True
• False

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

• True
• False

Which of the following is considered as an exponential function?

Radian uses the symbol π .

• True
• False

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

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

• True
• False

Identify √2 as s irrational or rational.

The following are all exponential function except

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

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

• 4
• 3
• 7
• 5

(-3π)/2 belongs to quadrant?

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

What is the value of cos – 300?

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

• True
• False

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

• 3
• 6
• -4
• 12

What is (-3π)/11 in degree measures?

What is the function to be use to solve x?

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

• + x4
• +10
• -3x7
• -6x5

Zero and positive integers are the __________.

• Whole Numbers

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

• 5
• 9
• 1
• 3

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.

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

• True
• False

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

• 9
• 54
• -36
• -27

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

• True
• False

The following are in standard position, except

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

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

• True
• False

1800 is equivalent to p radians.

• True
• False

What is the trigonometric function with a ratio adjacent/opposite

• cosecant
• cosine
• tangent
• cotangent

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

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The reciprocal of sine is

The ratio for cosine is

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 graph of the cosine functions always passes through the origin

• True
• False

In what quadrant does -2100, can be found?

Convert 53 = y to logarithmic form.

10000 belong to what quadrant?

Which of the following is the symbol for eta?

• ε
• β
• θ
• H

The unit circle is similar with coordinate plane.

• True
• False

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

• True
• False

What is the length of side y?

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

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

The cofunction of cosecant is cosine.

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

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 value of b in 6b = 1/36?

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

The ratio for cosecant is

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

• 6
• 5
• 7
• 1

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

Given the triangle below, the legs are

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

Simplify: log 7 49 = x – 4.

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

• True
• False

2π is equals to 3600.

• True
• False

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

What is the reference angle of 1600?

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

• Integers

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

• 1
• √3/2
• √3/4
• 1/2

What is the coterminal of 00?

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?

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

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

• True
• False

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

• True
• False

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

π radian is equivalent to 1800

• True
• False

Evaluate cos(900 + 900)

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

The following degree measurements are found in Quadrant I, except

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

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

• True
• False

The exponential form of log b d2 = e is

If sin α= 2/7, then cos α = 7/2.

• 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

A polynomial function is defined as the sum of monomials.

• True
• False

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

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

What is the cofunction of cotangent?

• tangent
• sine
• cosine
• secant

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

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

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

• -26/9
• -58/12
• -29/6
• -15/4

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

• True
• False

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

• True
• False

1.7 is a rational number

• True
• False

What is the ratio of sin β?

Hypotenuse is the longest side of a right triangle.

• True
• False

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

• True
• False

Oblique triangles are solved using the Pythagorean Theorem.

• True
• False

-3000 is equal to _____ radians.

• (-5π)/3
• (-4π)/3
• π/4
• (-3π)/2

When do graph of exponential function goes down?

cosine 900 is equal to 1.

• True
• False

The exponential function of the graph below 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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Base is where the exponent affixes

• True
• False

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

• True
• False

All angles has a reference angle of 300, except

A counterclockwise direction makes a negative degree measurement.

• True
• False

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

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

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

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

• True
• False

Is tanθ/cotθ = 1?

• True
• False

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

What is the exponential function of the table below?

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

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

• True
• False

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

• True
• False

What is the coterminal of -700 ?

The following are coterminal of 900, except

• -2700
• 2700
• -6300
• 4500

sin 2100 is equal to -1/2

• 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

Express the sum and difference of cos 300.

The following may be seen in a right triangle, EXCEPT

The value of the unknown side is ____.

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

• True
• False

A polynomial function is defined as the product of monomials.

• True
• False

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

Convert 34 = d in logarithmic form.

The maximum point is the highest point a graph reach.

• True
• False

Which of the following is equal to tan x?

What is the quadrant of -1800?

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

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

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

The cofunction of cotangent is tangent.

• True
• False

The following are equal to 1, except

A rational function is the product of two polynomials.

Simplify sin x sec x/tanx .

The following measurements can be found in Quadrant III, except

• -2400
• 120
• (-2π)/3
• (-5π)/6

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

Is sin2θ cos2θ = 1?

• True
• False

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

• f/g
• g/e
• g/f
• f/e

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

The following are all coterminal of 1350, except

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

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

• 1/2
• -1
• 2
• (-1)/2

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

• True
• False

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

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

Is csc2 θ = 1 – cot2 θ?

• True
• False

Which of the following is the cofunction of secant?

• cosecant
• cotangent
• cosine
• tangent

Solve for y

– 3120 can be found at Quadrant IV.

• 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

Simplify: log 3 92x = x + 12

Which of the following angle is in standard position?

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

• 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

cosine – 600 is equal to - √3/2.

• True
• False

π is equivalent to 1800.

• True
• False

Convert 9000 to radian measure.

• 5π
• -5π
• 2π
• 4π

A rational function is the quotient of two polynomials

• True
• False

Which of the following polynomials has 3 terms?

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

• True
• False

The value of x is ____.

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

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

• -2
• 7
• -6
• 10

The graph below shows

The following are all exponential functions, except

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

• True
• False

Subtract:

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

The ratio of cot θ is ____.

36250 can be found at quadrant?

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

The reciprocal of cosine is sine.

• True
• False

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

• True
• False

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

• Irrational Numbers

The reciprocal of tangent

• secant
• cosecant
• cosine
• cotangent

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

In what quadrant do -1000 lies?

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

A clockwise direction is a positive measurement.

• True
• False

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

-900 is equivalent to - π/2 radians.

• True
• False

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

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

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- 3π/4 is equal to how many degrees?

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

• cosine
• tangent
• sine
• secant

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

• True
• False

The sin value of 1800 is

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

The value of sin 300 is

Solve: 2 csc x(3 – 2csc x + csc2 x)

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

• True
• False

Which of the following is the ordered pair for 3600?

Degree is a unit measure for angles.

• True
• False

Identify ¾ as irrational or rational.

The reference angle of the given figure below is:

• 1180
• 620
• 280
• 1520

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

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 exponential form of log 12 d = k

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

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

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

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

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

• Rational Numbers

- 4π/3 is equivalent

All angles belongs to Quadrant III, which is not

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

• Natural Numbers

The symbol i is called ________.

Coterminal angles are the same degrees.

Initial side of an angle is the one that rotates.

• 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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Convert -3150 to radian measure.

In what quadrant does 5π/9 belong?

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

• 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

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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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

cos θ is equal to 1/sec⁡θ .

• True
• False

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

The following are the fundamental identities except

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

• True
• False

What is the value of x?

• 12.35
• 11.67
• 13.78
• 10.2

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

• True
• False

The Greek name for σ is rho.

• True
• False

Which of the following is coterminal of 900?

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

• True
• False

The parts of the right triangle are

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

Using the triangle below, which is the hypotenuse?

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

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

• 2x = -4
• x = - 2
• x = 2
• x = -4

The Pythagorean Theorem was formulated by Pythagoras of Italy.

• True
• False

K is the capital letter for kappa.

• True
• False

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

• True
• False

The answer: for -73 = ___ is?

Identify √5 as irrational or rational.

What is the equivalent of -3.5π in degrees?

• 6800
• 5800
• 6300
• 6500

The name of the Greek letter ξ is _______.

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

• True
• False

The following angles belong to quadrant IV, except

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

The unknown measurement of the side of the triangle below is