Teaching Math in the Intermediate Grades

The answer: for -73 = ___ is?

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

The ratio of cot θ is ____.

Simplify: log 7 49 = x – 4.

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.

K is the capital letter for kappa.

• 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?

2π is equals to 3600.

• True
• False

1800 is equivalent to p radians.

• True
• False

Degree is a unit measure for angles.

• True
• False

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

• True
• False

The following are the fundamental identities except

A polynomial function is defined as the sum of monomials.

• True
• False

Simplify: log 3 92x = x + 12

A counterclockwise direction makes a negative degree measurement.

• True
• False

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

Convert -3150 to radian measure.

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

The reciprocal of cosine is sine.

• 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

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

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

• True
• False

The following are in standard position, except

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

• Rational Numbers

Which of the following angle is in standard position?

Which of the following is coterminal of 900?

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

• 5
• 9
• 1
• 3

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

Initial side of an angle is the one that rotates.

• True
• False

The value of sin 300 is

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

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

• Less Effective Instructional Decisions

What is (-3π)/11 in degree measures?

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

• True
• False

The following are equal to 1, except

Convert 53 = y to logarithmic form.

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

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

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

• True
• False

– 3120 can be found at Quadrant IV.

• True
• False

If sin α= 2/7, then cos α = 7/2.

• True
• False

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

• True
• False

The exponential form of log b d2 = e 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

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

Zero and positive integers are the __________.

• Whole Numbers

The following are all exponential function except

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

The name of the Greek letter ξ 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 function to be use to solve 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?

Which of the following polynomials has 3 terms?

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

What is the length of side y?

10000 belong to what quadrant?

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

• True
• False

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

• f/g
• g/e
• g/f
• f/e

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

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.

What is the coterminal of -700 ?

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

• True
• False

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

All angles has a reference angle of 300, except

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

• True
• False

Solve: 2 csc x(3 – 2csc x + csc2 x)

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

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

• True
• False

What is the exponential form of log 12 d = k

What is the ratio of sin β?

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

• True
• False

cos θ is equal to 1/sec⁡θ .

• True
• False

Given the triangle below, the legs are

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

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

1.7 is a rational number

• True
• False

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

• True
• False

A polynomial function is defined as the product of monomials.

• True
• False

Coterminal angles are the same degrees.

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 following degree measurements are found in Quadrant I, except

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

The reciprocal of tangent

• secant
• cosecant
• cosine
• cotangent

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

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

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

• -2
• 7
• -6
• 10

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

• 6
• 5
• 7
• 1

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

• True
• False

What is the reference angle of 1600?

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

• True
• False

-3000 is equal to _____ radians.

• (-5π)/3
• (-4π)/3
• π/4
• (-3π)/2

Using the triangle below, which is the hypotenuse?

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

• 1/2
• -1
• 2
• (-1)/2

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 the symbol for eta?

• ε
• β
• θ
• H

Identify √2 as s irrational or rational.

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

• 4
• 3
• 7
• 5

Identify ¾ as irrational or rational.

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

Solve for y

Base is where the exponent affixes

• True
• False

A rational function is the product of two polynomials.

What is the equivalent of -3.5π in degrees?

• 6800
• 5800
• 6300
• 6500

The following are coterminal of 900, except

• -2700
• 2700
• -6300
• 4500

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

• True
• False

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

In what quadrant does -2100, can be found?

The exponential function of the graph below is:

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

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

Subtract:

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

• cosine
• tangent
• sine
• secant

The value of the unknown side is ____.

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

• + x4
• +10
• -3x7
• -6x5

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

Evaluate cos(900 + 900)

What is the cofunction of cotangent?

• tangent
• sine
• cosine
• secant

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

Hypotenuse is the longest side of a right triangle.

• True
• False

Which of the following is considered as an exponential function?

The following are all coterminal of 1350, except

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

• True
• False

What is the coterminal of 00?

What is the exponential function of the table below?

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

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

• True
• False

What is the trigonometric function with a ratio adjacent/opposite

• cosecant
• cosine
• tangent
• cotangent

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

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

• True
• False

The cofunction of cotangent is tangent.

• True
• False

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

Convert 34 = d in logarithmic form.

The following angles belong to quadrant IV, except

The Pythagorean Theorem was formulated by Pythagoras of Italy.

• True
• False

cosine 900 is equal to 1.

• True
• False

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

• True
• False

π is equivalent to 1800.

• True
• False

Is tanθ/cotθ = 1?

• True
• False

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

• True
• False

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

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A rational function is the quotient of two polynomials

• True
• False

- 4π/3 is equivalent

The cofunction of cosecant is cosine.

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

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

• Integers

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

• True
• False

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

π radian is equivalent to 1800

• True
• False

Which of the following is the ordered pair for 3600?

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

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

• True
• False

The sin value of 1800 is

Is sin2θ cos2θ = 1?

• True
• False

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

Convert 9000 to radian measure.

• 5π
• -5π
• 2π
• 4π

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

• -26/9
• -58/12
• -29/6
• -15/4

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

In what quadrant does 5π/9 belong?

The maximum point is the highest point a graph reach.

• True
• False

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

• True
• False

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

• True
• False

The following measurements can be found in Quadrant III, except

• -2400
• 120
• (-2π)/3
• (-5π)/6

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

• True
• False

Which of the following is equal to tan x?

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

- 3π/4 is equal to how many degrees?

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

• True
• False

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

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sin 2100 is equal to -1/2

• True
• False

36250 can be found at quadrant?

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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(-3π)/2 belongs to quadrant?

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

The value of x is ____.

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

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

• True
• False

-900 is equivalent to - π/2 radians.

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

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 following are all exponential functions, except

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

• 2x = -4
• x = - 2
• x = 2
• x = -4

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

The unknown measurement of the side of the triangle below is

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

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

• 3
• 6
• -4
• 12

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

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

• 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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Radian uses the symbol π .

• True
• False

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

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

• True
• False

A clockwise direction is a positive measurement.

• True
• False

Which of the following is the cofunction of secant?

• cosecant
• cotangent
• cosine
• tangent

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

The following may be seen in a right triangle, EXCEPT

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

• 1
• √3/2
• √3/4
• 1/2

The reciprocal of sine is

Express the sum and difference of cos 300.

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

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

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

• True
• False

The Greek name for σ is rho.

• True
• False

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

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

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

• True
• False

All angles belongs to Quadrant III, which is not

The reference angle of the given figure below is:

• 1180
• 620
• 280
• 1520

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

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

• Natural Numbers

What is the value of x?

• 12.35
• 11.67
• 13.78
• 10.2

Oblique triangles are solved using the Pythagorean Theorem.

• True
• False

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

Identify √5 as irrational or rational.

The graph of the cosine functions always passes through the origin

• True
• False

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

• True
• False

In what quadrant do -1000 lies?

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

• True
• False

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

• 9
• 54
• -36
• -27

The ratio for cosine is

When do graph of exponential function goes down?

The trigonometric function of the ratio 7/25 is

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

• True
• False

The graph below shows

Is csc2 θ = 1 – cot2 θ?

• True
• False

cosine – 600 is equal to - √3/2.

• True
• False

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

The parts of the right triangle are

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

What is the value of cos – 300?

The unit circle is similar with coordinate plane.

• True
• False

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

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

• Irrational Numbers

The symbol i is called ________.

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

What is the quadrant of -1800?

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

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

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

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

• True
• False

Simplify sin x sec x/tanx .