Teaching Math in the Intermediate Grades

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

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

What is the coterminal of -700 ?

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

2π is equals to 3600.

• True
• False

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

• True
• False

The unknown measurement of the side of the triangle below is

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

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

• 6
• 5
• 7
• 1

What is (-3π)/11 in degree measures?

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

• Irrational Numbers

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

Identify ¾ as irrational or rational.

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

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

• -26/9
• -58/12
• -29/6
• -15/4

The cofunction of cosecant is cosine.

In what quadrant does 5π/9 belong?

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

Which of the following polynomials has 3 terms?

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

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 unknown value of m in m7 = 2187 is 3.

• True
• False

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 length of side y?

The following are equal to 1, except

Is sin2θ cos2θ = 1?

• 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

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

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

• True
• False

K is the capital letter for kappa.

• True
• False

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

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

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

• True
• False

Solve for y

Base is where the exponent affixes

• True
• False

Simplify: log 3 92x = x + 12

Which of the following angle is in standard position?

What is the value of x?

• 12.35
• 11.67
• 13.78
• 10.2

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

• 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

Subtract:

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

Zero and positive integers are the __________.

• Whole Numbers

The ratio of cot θ is ____.

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

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

• True
• False

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

• True
• False

(-3π)/2 belongs to quadrant?

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

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

Which of the following is the symbol for eta?

• ε
• β
• θ
• H

Which of the following is equal to tan x?

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

• True
• False

Which of the following is coterminal of 900?

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

What is the exponential function of the table below?

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

Which of the following is the cofunction of secant?

• cosecant
• cotangent
• cosine
• tangent

The maximum point is the highest point a graph reach.

• True
• False

1800 is equivalent to p radians.

• True
• False

Solve: 2 csc x(3 – 2csc x + csc2 x)

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

• True
• False

The following degree measurements are found in Quadrant I, except

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

cos θ is equal to 1/sec⁡θ .

• True
• False

Simplify: log 7 49 = x – 4.

The answer: for -73 = ___ is?

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

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

• True
• False

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

When do graph of exponential function goes down?

The ratio for cosecant is

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

What is the function to be use to solve x?

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.

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

The unit circle is similar with coordinate plane.

• True
• False

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

• 9
• 54
• -36
• -27

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

• 4
• 3
• 7
• 5

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

• True
• False

– 3120 can be found at Quadrant IV.

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

• True
• False

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

π radian is equivalent to 1800

• True
• False

The symbol i is called ________.

The value of the unknown side is ____.

A counterclockwise direction makes a negative degree measurement.

• True
• False

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

Identify √2 as s irrational or rational.

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

1.7 is a rational number

• True
• False

Convert 53 = y to logarithmic form.

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

The following may be seen in a right triangle, EXCEPT

The following are all exponential function except

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

The trigonometric function of the ratio 7/25 is

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

• 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?

- 4π/3 is equivalent

The reciprocal of sine 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

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

• 3
• 6
• -4
• 12

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

• True
• False

What is the exponential form of log 12 d = k

The name of the Greek letter ξ is _______.

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

• True
• False

All angles belongs to Quadrant III, which is not

A rational function is the product of two polynomials.

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

The cofunction of cotangent is tangent.

• True
• False

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

• True
• False

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

• Rational Numbers

The Greek name for σ is rho.

• True
• False

Hypotenuse is the longest side of a right triangle.

• True
• False

The reciprocal of cosine is sine.

• True
• False

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

• True
• False

Simplify sin x sec x/tanx .

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

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

Convert -3150 to radian measure.

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

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

The exponential form of log b d2 = e is

The reference angle of the given figure below is:

• 1180
• 620
• 280
• 1520

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

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

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

The following angles belong to quadrant IV, except

Is tanθ/cotθ = 1?

• True
• False

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

What is the cofunction of cotangent?

• tangent
• sine
• cosine
• secant

The graph below shows

sin 2100 is equal to -1/2

• True
• False

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

Convert 34 = d in logarithmic form.

10000 belong to what quadrant?

What is the equivalent of -3.5π in degrees?

• 6800
• 5800
• 6300
• 6500

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

What is the logarithmic form of dr = ba ?

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

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

• True
• False

Convert 9000 to radian measure.

• 5π
• -5π
• 2π
• 4π

The sin value of 1800 is

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

• -2
• 7
• -6
• 10

Using the triangle below, which is the hypotenuse?

What is the quadrant of -1800?

Identify √5 as irrational or rational.

The following are the fundamental identities except

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

• 2x = -4
• x = - 2
• x = 2
• x = -4

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

• True
• False

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

• 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

What is the coterminal of 00?

A clockwise direction is a positive measurement.

• True
• False

Which of the following is considered as an exponential function?

Coterminal angles are the same degrees.

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

• Natural Numbers

The ratio for cosine is

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

• cosine
• tangent
• sine
• secant

π is equivalent to 1800.

• True
• False

Given the triangle below, the legs are

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

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

• True
• False

Degree is a unit measure for angles.

• True
• False

The parts of the right triangle are

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

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

• 5
• 9
• 1
• 3

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

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

• 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?

Evaluate cos(900 + 900)

The following are in standard position, except

The value of sin 300 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

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

• True
• False

In what quadrant do -1000 lies?

Initial side of an angle is the one that rotates.

• True
• False

The following are all exponential functions, except

A polynomial function is defined as the sum of monomials.

• True
• False

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

All angles has a reference angle of 300, except

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

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

The following are all coterminal of 1350, except

Which of the following is the ordered pair for 3600?

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

• True
• False

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

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What is the trigonometric function with a ratio adjacent/opposite

• cosecant
• cosine
• tangent
• cotangent

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

• True
• False

What is the reference angle of 1600?

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

• True
• False

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

• Integers

The value of x is ____.

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

What is the value of cos – 300?

If sin α= 2/7, then cos α = 7/2.

• 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

The exponential function of the graph below is:

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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In what quadrant does -2100, can be found?

The Pythagorean Theorem was formulated by Pythagoras of Italy.

• True
• False

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

• True
• False

What is the ratio of sin β?

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

36250 can be found at quadrant?

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

• True
• False

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

• 1
• √3/2
• √3/4
• 1/2

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

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

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

• 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?

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

A rational function is the quotient of two polynomials

• True
• False

Radian uses the symbol π .

• True
• False

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

cosine – 600 is equal to - √3/2.

• True
• False

- 3π/4 is equal to how many degrees?

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

Oblique triangles are solved using the Pythagorean Theorem.

• True
• False

-900 is equivalent to - π/2 radians.

• True
• False

A polynomial function is defined as the product of monomials.

• True
• False

Is csc2 θ = 1 – cot2 θ?

• True
• False

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 coterminal of 900, except

• -2700
• 2700
• -6300
• 4500

The reciprocal of tangent

• secant
• cosecant
• cosine
• cotangent

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

• f/g
• g/e
• g/f
• f/e

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

Express the sum and difference of cos 300.

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

• True
• False

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

-3000 is equal to _____ radians.

• (-5π)/3
• (-4π)/3
• π/4
• (-3π)/2

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

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

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