Teaching Math in the Intermediate Grades

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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The value of x is ____.

sin 2100 is equal to -1/2

• True
• False

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

-900 is equivalent to - π/2 radians.

• True
• False

Which of the following is considered as an exponential function?

The ratio of cot θ is ____.

The graph below shows

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

π is equivalent to 1800.

• 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 following are equal to 1, except

What is the value of cos – 300?

The reference angle of the given figure below is:

• 1180
• 620
• 280
• 1520

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

• f/g
• g/e
• g/f
• f/e

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

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

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

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

• 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?

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

• + x4
• +10
• -3x7
• -6x5

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

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

The following measurements can be found in Quadrant III, except

• -2400
• 120
• (-2π)/3
• (-5π)/6

The following are the fundamental identities except

A polynomial function is defined as the product of monomials.

• True
• False

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

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

• True
• False

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

• True
• False

1.7 is a rational number

• True
• False

The following are all coterminal of 1350, except

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

• True
• False

What is (-3π)/11 in degree measures?

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

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

• 4
• 3
• 7
• 5

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

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

• True
• False

The name of the Greek letter ξ is _______.

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

• True
• False

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

• 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

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

• 2x = -4
• x = - 2
• x = 2
• x = -4

In what quadrant does 5π/9 belong?

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

In what quadrant does -2100, can be found?

What is the cofunction of cotangent?

• tangent
• sine
• cosine
• secant

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

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

Convert 9000 to radian measure.

• 5π
• -5π
• 2π
• 4π

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

Initial side of an angle is the one that rotates.

• True
• False

The maximum point is the highest point a graph reach.

• True
• False

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

• True
• False

K is the capital letter for kappa.

• True
• False

Hypotenuse is the longest side of a right triangle.

• True
• False

Identify ¾ as irrational or rational.

The reciprocal of sine is

Which of the following is coterminal of 900?

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

• True
• False

- 4π/3 is equivalent

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

The exponential function of the graph below is:

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

• 3
• 6
• -4
• 12

cos θ is equal to 1/sec⁡θ .

• True
• False

Solve: 2 csc x(3 – 2csc x + csc2 x)

Which of the following is the ordered pair for 3600?

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

• 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 34 = d in logarithmic form.

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

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

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

The exponential form of log b d2 = e is

The following are all exponential function except

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

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

• True
• False

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

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

The following are in standard position, except

The following are all exponential functions, except

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

Zero and positive integers are the __________.

• Whole Numbers

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

• 1
• √3/2
• √3/4
• 1/2

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

• True
• False

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

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

Oblique triangles are solved using the Pythagorean Theorem.

• True
• False

The trigonometric function of the ratio 7/25 is

The parts of the right triangle are

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

Convert 53 = y to logarithmic form.

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

10000 belong to what quadrant?

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

• -2
• 7
• -6
• 10

(-3π)/2 belongs to quadrant?

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

Which of the following is the cofunction of secant?

• cosecant
• cotangent
• cosine
• tangent

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

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 unknown measurement of the side of the right triangle below?

π radian is equivalent to 1800

• True
• False

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

• cosine
• tangent
• sine
• secant

Is csc2 θ = 1 – cot2 θ?

• True
• False

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

1800 is equivalent to p radians.

• True
• False

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

If sin α= 2/7, then cos α = 7/2.

• True
• False

Coterminal angles are the same degrees.

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

The Pythagorean Theorem was formulated by Pythagoras of Italy.

• True
• False

Using the triangle below, which is the hypotenuse?

Degree is a unit measure for angles.

• True
• False

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

• True
• False

Is tanθ/cotθ = 1?

• True
• False

Evaluate cos(900 + 900)

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.

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

• Natural Numbers

What is the function to be use to solve x?

In what quadrant do -1000 lies?

Convert -3150 to radian measure.

All angles has a reference angle of 300, except

What is the trigonometric function with a ratio adjacent/opposite

• cosecant
• cosine
• tangent
• cotangent

The value of sin 300 is

The ratio for cosecant is

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

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

- 3π/4 is equal to how many degrees?

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

• True
• False

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

• True
• False

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

Identify √5 as irrational or rational.

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

• True
• False

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

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

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

• 9
• 54
• -36
• -27

What is the ratio of sin β?

A clockwise direction is a positive measurement.

• True
• False

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

• Irrational Numbers

– 3120 can be found at Quadrant IV.

• True
• False

Which of the following polynomials has 3 terms?

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

• True
• False

Express the sum and difference of cos 300.

The cofunction of cosecant is cosine.

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

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

• -26/9
• -58/12
• -29/6
• -15/4

What is the exponential form of log 12 d = k

Which of the following is the symbol for eta?

• ε
• β
• θ
• H

2π is equals to 3600.

• True
• False

When do graph of exponential function goes down?

36250 can be found at quadrant?

-3000 is equal to _____ radians.

• (-5π)/3
• (-4π)/3
• π/4
• (-3π)/2

The answer: for -73 = ___ is?

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

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

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

• True
• False

Subtract:

The reciprocal of tangent

• secant
• cosecant
• cosine
• cotangent

What is the quadrant of -1800?

What is the reference angle of 1600?

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

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

• True
• False

A polynomial function is defined as the sum of monomials.

• True
• False

What is the coterminal of -700 ?

The following degree measurements are found in Quadrant I, except

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

• 1/2
• -1
• 2
• (-1)/2

All angles belongs to Quadrant III, which is not

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

• Integers

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

Identify √2 as s irrational or rational.

The reciprocal of cosine is sine.

• True
• False

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

• True
• False

Which of the following is equal to tan x?

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

• True
• False

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

The ratio for cosine is

Given the triangle below, the legs are

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

What is the exponential function of the table below?

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

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

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

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

A rational function is the quotient of two polynomials

• True
• False

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

• True
• False

The following angles belong to quadrant IV, except

Simplify sin x sec x/tanx .

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

The sin value of 1800 is

What is the equivalent of -3.5π in degrees?

• 6800
• 5800
• 6300
• 6500

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

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

• True
• False

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

Simplify: log 7 49 = x – 4.

cosine – 600 is equal to - √3/2.

• True
• False

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

The unknown measurement of the side of the triangle below is

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

• True
• False

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

Radian uses the symbol π .

• True
• False

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

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

• True
• False

The value of the unknown side 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

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

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

cosine 900 is equal to 1.

• True
• False

The following are coterminal of 900, except

• -2700
• 2700
• -6300
• 4500

The symbol i is called ________.

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

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

The unit circle is similar with coordinate plane.

• True
• False

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

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

What is the length of side y?

A rational function is the product of two polynomials.

The following may be seen in a right triangle, EXCEPT

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 first three trigonometric functions are sine, cosine and tangent.

• True
• False

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

• True
• False

What is the coterminal of 00?

A counterclockwise direction makes a negative degree measurement.

• True
• False

The Greek name for σ is rho.

• True
• False

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

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

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

The cofunction of cotangent is tangent.

• True
• False

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

• True
• False

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

• True
• False

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

• Rational Numbers

Which of the following angle is in standard position?

Is sin2θ cos2θ = 1?

• True
• False

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

The graph of the cosine functions always passes through the origin

• True
• False

Solve for y