Teaching Math in the Intermediate Grades

The reciprocal of tangent

• secant
• cosecant
• cosine
• cotangent

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

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

• True
• False

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

• True
• False

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

The following are all coterminal of 1350, except

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

Which of the following polynomials has 3 terms?

Coterminal angles are the same degrees.

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

1800 is equivalent to p radians.

• True
• False

The ratio for cosecant is

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

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

• True
• False

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

• Less Effective Instructional Decisions

The Greek name for σ is rho.

• True
• False

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

• True
• False

The following angles belong to quadrant IV, except

The following degree measurements are found in Quadrant I, except

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

1.7 is a rational number

• True
• False

cosine – 600 is equal to - √3/2.

• True
• False

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

• True
• False

cosine 900 is equal to 1.

• True
• False

Simplify: log 7 49 = x – 4.

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

The exponential function of the graph below is:

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

• Rational Numbers

Which of the following is considered as an exponential function?

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

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

• 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.

• More Effective Instructional Decisions

What is the cofunction of cotangent?

• tangent
• sine
• cosine
• secant

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

• True
• False

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

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

• Less Effective Instructional Decisions

When do graph of exponential function goes down?

36250 can be found at quadrant?

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

• More Effective Instructional Decisions

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

• 6
• 5
• 7
• 1

Is csc2 θ = 1 – cot2 θ?

• 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

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

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

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

What is the value of cos – 300?

Hypotenuse is the longest side of a right triangle.

• True
• False

Using the triangle below, which is the hypotenuse?

In what quadrant does -2100, can be found?

sin 2100 is equal to -1/2

• True
• False

The ratio of cot θ is ____.

2π is equals to 3600.

• True
• False

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

Convert 34 = d in logarithmic form.

-3000 is equal to _____ radians.

• (-5π)/3
• (-4π)/3
• π/4
• (-3π)/2

Convert 9000 to radian measure.

• 5π
• -5π
• 2π
• 4π

The trigonometric function of the ratio 7/25 is

What is the length of side y?

-900 is equivalent to - π/2 radians.

• True
• False

The value of the unknown side is ____.

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

• True
• False

What is the reference angle of 1600?

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

Solve for y

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

• True
• False

What is the trigonometric function with a ratio adjacent/opposite

• cosecant
• cosine
• tangent
• cotangent

Identify √2 as s irrational or rational.

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

Is tanθ/cotθ = 1?

• True
• False

Which of the following is the ordered pair for 3600?

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

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

10000 belong to what quadrant?

The name of the Greek letter ξ is _______.

What is the coterminal of -700 ?

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

• 1/2
• -1
• 2
• (-1)/2

The ratio for cosine 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

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

• True
• False

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

• True
• False

If sin α= 2/7, then cos α = 7/2.

• True
• False

Which of the following is equal to tan x?

What is (-3π)/11 in degree measures?

A rational function is the quotient of two polynomials

• True
• False

What is the coterminal of 00?

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

All angles belongs to Quadrant III, which is not

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

• True
• False

– 3120 can be found at Quadrant IV.

• True
• False

A rational function is the product of two polynomials.

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

• Integers

What is the function to be use to solve x?

In what quadrant does 5π/9 belong?

Evaluate cos(900 + 900)

The following are equal to 1, except

Subtract:

Identify √5 as irrational or rational.

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

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

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

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

• 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:
• Less Effective Instructional Decisions

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

Is sin2θ cos2θ = 1?

• True
• False

Base is where the exponent affixes

• True
• False

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

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

• Irrational Numbers

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

Zero and positive integers are the __________.

• Whole Numbers

The reciprocal of sine is

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

• 1
• √3/2
• √3/4
• 1/2

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

• -26/9
• -58/12
• -29/6
• -15/4

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

• + x4
• +10
• -3x7
• -6x5

The Pythagorean Theorem was formulated by Pythagoras of Italy.

• True
• False

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

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

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

What is the exponential function of the table below?

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

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

Degree is a unit measure for angles.

• True
• False

A clockwise direction is a positive measurement.

• True
• False

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

• 9
• 54
• -36
• -27

- 3π/4 is equal to how many degrees?

Students have done their work on chart paper and are holding the chart paper while explaining to the class how their reached their conclusions.

• More Effective Instructional Decisions

The following are all exponential function except

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

What is the exponential form of log 12 d = k

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

• 3
• 6
• -4
• 12

Express the sum and difference of cos 300.

The parts of the right triangle are

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

A counterclockwise direction makes a negative degree measurement.

• True
• False

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

• True
• False

Which of the following is coterminal of 900?

The exponential form of log b d2 = e is

The graph below shows

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

Which of the following angle is in standard position?

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

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

The following are all exponential functions, except

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

• f/g
• g/e
• g/f
• f/e

The following are in standard position, except

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

Oblique triangles are solved using the Pythagorean Theorem.

• True
• False

Simplify sin x sec x/tanx .

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

• Natural Numbers

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

• True
• False

The following are the fundamental identities except

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

• cosine
• tangent
• sine
• secant

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

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

π radian is equivalent to 1800

• True
• False

What is the quadrant of -1800?

Radian uses the symbol π .

• True
• False

Convert -3150 to radian measure.

All angles has a reference angle of 300, except

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

• True
• False

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

• True
• False

The value of sin 300 is

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

• True
• False

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

• 5
• 9
• 1
• 3

The unknown measurement of the side of the triangle below is

The maximum point is the highest point a graph reach.

• True
• False

The reciprocal of cosine is sine.

• True
• False

The unit circle is similar with coordinate plane.

• True
• False

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

• True
• False

What is the value of x?

• 12.35
• 11.67
• 13.78
• 10.2

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

In what quadrant do -1000 lies?

Identify ¾ as irrational or rational.

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

• 4
• 3
• 7
• 5

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

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

• True
• False

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

• True
• False

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

• True
• False

The value of x is ____.

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

• True
• False

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

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

• Less Effective Instructional Decisions

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

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

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 polynomial function is defined as the sum of monomials.

• True
• False

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

• 2x = -4
• x = - 2
• x = 2
• x = -4

Simplify: log 3 92x = x + 12

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

Students are acting out a problem in front of the class. Others in the class participate in a discussion of the problem.

• More Effective Instructional Decisions

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

• True
• False

Mr. Roberts stimulates students' curiosity and encourages them to investigate further by asking them questions that begin with, "What would happen if..?"

• More Effective Instructional Decisions

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

cos θ is equal to 1/sec⁡θ .

• True
• False

The following measurements can be found in Quadrant III, except

• -2400
• 120
• (-2π)/3
• (-5π)/6

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

• True
• False

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

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

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

• -2
• 7
• -6
• 10

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

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

• True
• False

The symbol i is called ________.

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

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

• True
• False

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

• True
• False

The sin value of 1800 is

K is the capital letter for kappa.

• True
• False

π is equivalent to 1800.

• True
• False

Which of the following is the symbol for eta?

• ε
• β
• θ
• H

The reference angle of the given figure below is:

• 1180
• 620
• 280
• 1520

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

The graph of the cosine functions always passes through the origin

• True
• False

Which of the following is the cofunction of secant?

• cosecant
• cotangent
• cosine
• tangent

The following are coterminal of 900, except

• -2700
• 2700
• -6300
• 4500

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

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

What is the equivalent of -3.5π in degrees?

• 6800
• 5800
• 6300
• 6500

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

(-3π)/2 belongs to quadrant?

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

- 4π/3 is equivalent

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

The following may be seen in a right triangle, EXCEPT

The cofunction of cosecant is cosine.

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

• True
• False

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

Convert 53 = y to logarithmic form.

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

• True
• False

The cofunction of cotangent is tangent.

• 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?

A polynomial function is defined as the product of monomials.

• True
• False

The unknown value of m in m7 = 2187 is 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

Initial side of an angle is the one that rotates.

• True
• False

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

• True
• False

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

Given the triangle below, the legs are

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

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

What is the ratio of sin β?

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