Teaching Math in the Intermediate Grades

Simplify: log 7 49 = x – 4.

The following are all exponential functions, except

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

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

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

The ratio of cot θ is ____.

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 the exponential function 3q = 243 is 5.

• True
• False

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

In what quadrant does 5π/9 belong?

Express the sum and difference of cos 300.

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

• True
• False

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

• True
• False

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

• 1/2
• -1
• 2
• (-1)/2

A rational function is the product of two polynomials.

Which of the following is considered as an exponential function?

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

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

• True
• False

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

Which of the following is the cofunction of secant?

• cosecant
• cotangent
• cosine
• tangent

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

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

• Natural Numbers

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

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All angles belongs to Quadrant III, which is not

All angles has a reference angle of 300, except

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

• True
• False

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

• Irrational Numbers

Which of the following is the ordered pair for 3600?

The following are all coterminal of 1350, except

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

• True
• False

Convert 53 = y to logarithmic form.

Given the triangle below, the legs are

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

Radian uses the symbol π .

• True
• False

The reciprocal of sine is

The graph of the cosine functions always passes through the origin

• True
• False

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

Coterminal angles are the same degrees.

In what quadrant do -1000 lies?

What is the exponential function of the table below?

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

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

• True
• False

The unknown measurement of the side of the triangle below is

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

• 2x = -4
• x = - 2
• x = 2
• x = -4

The cofunction of cotangent is tangent.

• True
• False

The reference angle of the given figure below is:

• 1180
• 620
• 280
• 1520

-3000 is equal to _____ radians.

• (-5π)/3
• (-4π)/3
• π/4
• (-3π)/2

- 3π/4 is equal to how many degrees?

What is the trigonometric function with a ratio adjacent/opposite

• cosecant
• cosine
• tangent
• cotangent

The value of x is ____.

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

Mr. Swanson believes that all students should get the same instruction at the same time. To accomplish this he only uses whole group instruction.

• Less Effective Instructional Decisions

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

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

The ratio for cosecant is

A rational function is the quotient of two polynomials

• True
• False

The following degree measurements are found in Quadrant I, except

The following angles belong to quadrant IV, except

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

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

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

The maximum point is the highest point a graph reach.

• 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?

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

• 6
• 5
• 7
• 1

Solve: 2 csc x(3 – 2csc x + csc2 x)

Is csc2 θ = 1 – cot2 θ?

• True
• False

Convert 9000 to radian measure.

• 5π
• -5π
• 2π
• 4π

The cofunction of cosecant is cosine.

The parts of the right triangle are

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

- 4π/3 is equivalent

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

The following may be seen in a right triangle, EXCEPT

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

The symbol i is called ________.

The Greek name for σ is rho.

• True
• False

Zero and positive integers are the __________.

• Whole Numbers

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

• 4
• 3
• 7
• 5

1800 is equivalent to p radians.

• True
• False

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

• 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

Is sin2θ cos2θ = 1?

• True
• False

The following are in standard position, except

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

• -2
• 7
• -6
• 10

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

2π is equals to 3600.

• True
• False

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

• True
• False

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

• True
• False

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

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

• Integers

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

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

• f/g
• g/e
• g/f
• f/e

A counterclockwise direction makes a negative degree measurement.

• True
• False

Which of the following angle is in standard position?

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

What is the coterminal of 00?

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

The following are equal to 1, except

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

• 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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Identify √2 as s irrational or rational.

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

• True
• False

Simplify sin x sec x/tanx .

A polynomial function is defined as the sum of monomials.

• True
• False

The reciprocal of tangent

• secant
• cosecant
• cosine
• cotangent

The value of the unknown side is ____.

What is (-3π)/11 in degree measures?

Which of the following is the symbol for eta?

• ε
• β
• θ
• H

Is tanθ/cotθ = 1?

• True
• False

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

Simplify: log 3 92x = x + 12

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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Base is where the exponent affixes

• True
• False

The graph below shows

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

• True
• False

π radian is equivalent to 1800

• True
• False

The reciprocal of cosine is sine.

• True
• False

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

• True
• False

In what quadrant does -2100, can be found?

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

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

Solve for y

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

The answer: for -73 = ___ is?

Initial side of an angle is the one that rotates.

• True
• False

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

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

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

• 3
• 6
• -4
• 12

The value of sin 300 is

The unit circle is similar with coordinate plane.

• True
• False

Which of the following polynomials has 3 terms?

What is the value of cos – 300?

The exponential form of log b d2 = e is

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

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?

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

• True
• False

Convert -3150 to radian measure.

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

1.7 is a rational number

• True
• False

What is the value of x?

• 12.35
• 11.67
• 13.78
• 10.2

What is the logarithmic form of dr = ba ?

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

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

• True
• False

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

cos θ is equal to 1/sec⁡θ .

• True
• False

The sin value of 1800 is

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

• True
• False

What is the cofunction of cotangent?

• tangent
• sine
• cosine
• secant

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

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

• True
• False

What is the coterminal of -700 ?

Hypotenuse is the longest side of a right triangle.

• True
• False

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

• True
• False

The following are coterminal of 900, except

• -2700
• 2700
• -6300
• 4500

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 following measurements can be found in Quadrant III, except

• -2400
• 120
• (-2π)/3
• (-5π)/6

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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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

A clockwise direction is a positive measurement.

• True
• False

sin 2100 is equal to -1/2

• True
• False

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

Degree is a unit measure for angles.

• True
• False

The exponential function of the graph below is:

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

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

-900 is equivalent to - π/2 radians.

• True
• False

Which of the following is equal to tan x?

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

• True
• False

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

Evaluate cos(900 + 900)

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

What is the length of side y?

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.

When do graph of exponential function goes down?

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

• Rational Numbers

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

• True
• False

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

• True
• False

– 3120 can be found at Quadrant IV.

• True
• False

The following are the fundamental identities except

Subtract:

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

Using the triangle below, which is the hypotenuse?

What is the exponential form of log 12 d = k

10000 belong to what quadrant?

(-3π)/2 belongs to quadrant?

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

If sin α= 2/7, then cos α = 7/2.

• True
• False

Identify ¾ as irrational or rational.

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

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

• True
• False

Which of the following is coterminal of 900?

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

• -26/9
• -58/12
• -29/6
• -15/4

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

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

• True
• False

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

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

• True
• False

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

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

• 9
• 54
• -36
• -27

Oblique triangles are solved using the Pythagorean Theorem.

• True
• False

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

• True
• False

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

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

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

• True
• False

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

• cosine
• tangent
• sine
• secant

The trigonometric function of the ratio 7/25 is

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

cosine – 600 is equal to - √3/2.

• True
• False

Convert 34 = d in logarithmic form.

What is the function to be use to solve x?

cosine 900 is equal to 1.

• True
• False

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

• True
• False

π is equivalent to 1800.

• True
• False

Identify √5 as irrational or rational.

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

• True
• False

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

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

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

• True
• False

K is the capital letter for kappa.

• True
• False

The name of the Greek letter ξ is _______.

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

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

• 1
• √3/2
• √3/4
• 1/2

The ratio for cosine is

A polynomial function is defined as the product of monomials.

• 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

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

The following are all exponential function except

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

36250 can be found at quadrant?

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

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

• 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

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

• True
• False

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

What is the quadrant of -1800?

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

• True
• False

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

• 5
• 9
• 1
• 3