Teaching Math in the Intermediate Grades

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

The following may be seen in a right triangle, EXCEPT

What is the trigonometric function with a ratio adjacent/opposite

• cosecant
• cosine
• tangent
• cotangent

-900 is equivalent to - π/2 radians.

• True
• False

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

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 trigonometric function to be use to solve for y?

The trigonometric function of the ratio 7/25 is

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

The following are coterminal of 900, except

• -2700
• 2700
• -6300
• 4500

The value of the unknown side is ____.

All angles has a reference angle of 300, except

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

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

Hypotenuse is the longest side of a right triangle.

• True
• False

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

The simplified form of sec2 x – 1 + tan2 x 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

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

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

• 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

• Less Effective Instructional Decisions

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

• True
• False

What is the exponential function of the table below?

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

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

• True
• False

A polynomial function is defined as the sum of monomials.

• True
• False

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

• True
• False

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

• 3
• 6
• -4
• 12

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

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 first three trigonometric functions are sine, cosine and tangent.

• True
• False

The following are equal to 1, except

cos θ is equal to 1/sec⁡θ .

• 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.

• Less Effective Instructional Decisions

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

Which of the following is the ordered pair for 3600?

Is tanθ/cotθ = 1?

• True
• False

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

• 9
• 54
• -36
• -27

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

• True
• False

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

• True
• False

The answer: for -73 = ___ is?

The reference angle of the given figure below is:

• 1180
• 620
• 280
• 1520

Which of the following polynomials has 3 terms?

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

• Less Effective Instructional Decisions

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

• f/g
• g/e
• g/f
• f/e

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

The Pythagorean Theorem was formulated by Pythagoras of Italy.

• True
• False

The reciprocal of sine is

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

K is the capital letter for kappa.

• True
• False

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

• True
• False

Convert 34 = d in logarithmic form.

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

• True
• False

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

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 graph of an exponential functions has 3 or more turning points

• True
• False

The sin value of 1800 is

What is the length of side y?

cosine 900 is equal to 1.

• True
• False

cosine – 600 is equal to - √3/2.

• True
• False

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

• True
• False

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

The unknown measurement of the side of the triangle below is

-3000 is equal to _____ radians.

• (-5π)/3
• (-4π)/3
• π/4
• (-3π)/2

What is the value of x?

• 12.35
• 11.67
• 13.78
• 10.2

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

• Rational Numbers

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

- 4π/3 is equivalent

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

• True
• False

The ratio for cosecant is

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

• True
• False

A rational function is the quotient of two polynomials

• True
• False

What is the equivalent of -3.5π in degrees?

• 6800
• 5800
• 6300
• 6500

The unit circle is similar with coordinate plane.

• 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?

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

• 2x = -4
• x = - 2
• x = 2
• x = -4

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

The reciprocal of cosine is sine.

• True
• False

What is the quadrant of -1800?

Is csc2 θ = 1 – cot2 θ?

• True
• False

1800 is equivalent to p radians.

• True
• False

Subtract:

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

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 value of cos – 300?

10000 belong to what quadrant?

Radian uses the symbol π .

• True
• False

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

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

Evaluate cos(900 + 900)

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

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

• Integers

The ratio of cot θ is ____.

Solve: 2 csc x(3 – 2csc x + csc2 x)

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 ratio of sin β?

The following are in standard position, except

The value of sin 300 is

Convert -3150 to radian measure.

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

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

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

• True
• False

Identify √2 as s irrational or rational.

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

Express the sum and difference of cos 300.

sin 2100 is equal to -1/2

• True
• False

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

Degree is a unit measure for angles.

• 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

π radian is equivalent to 1800

• True
• False

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

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

• True
• False

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

• True
• False

The parts of the right triangle are

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

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

The reciprocal of tangent

• secant
• cosecant
• cosine
• cotangent

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

• True
• False

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

• -2
• 7
• -6
• 10

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

• True
• False

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

• 4
• 3
• 7
• 5

The graph below shows

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

• True
• False

If sin α= 2/7, then cos α = 7/2.

• True
• False

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

• 1/2
• -1
• 2
• (-1)/2

What is the reference angle of 1600?

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

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

• True
• False

– 3120 can be found at Quadrant IV.

• True
• False

Base is where the exponent affixes

• True
• False

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

In what quadrant do -1000 lies?

The value of x is ____.

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

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

• -26/9
• -58/12
• -29/6
• -15/4

2π is equals to 3600.

• True
• False

Simplify: log 3 92x = x + 12

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

• More Effective Instructional Decisions

The ratio for cosine is

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

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

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

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

Oblique triangles are solved using the Pythagorean Theorem.

• True
• False

The following are all coterminal of 1350, except

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

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

The cofunction of cotangent is tangent.

• 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?

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.

Initial side of an angle is the one that rotates.

• True
• False

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

• True
• False

The following are all exponential function except

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

A clockwise direction is a positive measurement.

• True
• False

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

Which of the following angle is in standard position?

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

• 1
• √3/2
• √3/4
• 1/2

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

• True
• False

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

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

• Less Effective Instructional Decisions

Simplify: log 7 49 = x – 4.

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

When do graph of exponential function goes down?

The exponential function of the graph below is:

Solve for y

The exponential form of log b d2 = e is

Simplify sin x sec x/tanx .

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

• True
• False

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

• True
• False

A counterclockwise direction makes a negative degree measurement.

• True
• False

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

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

36250 can be found at quadrant?

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

• True
• False

Identify ¾ as irrational or rational.

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

• Natural Numbers

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

Identify √5 as irrational or rational.

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

• True
• False

All angles belongs to Quadrant III, which is not

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

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?

The name of the Greek letter ξ is _______.

The following measurements can be found in Quadrant III, except

• -2400
• 120
• (-2π)/3
• (-5π)/6

Which of the following is coterminal of 900?

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

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

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

• 6
• 5
• 7
• 1

The maximum point is the highest point a graph reach.

• True
• False

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

• 5
• 9
• 1
• 3

The cofunction of cosecant is cosine.

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

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

• True
• False

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

• True
• False

What is the function to be use to solve x?

- 3π/4 is equal to how many degrees?

What is the coterminal of -700 ?

In what quadrant does -2100, can be found?

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

• Irrational Numbers

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

• True
• False

Using the triangle below, which is the hypotenuse?

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

• True
• False

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

• True
• False

What is the exponential form of log 12 d = k

The following are all exponential functions, except

Convert 53 = y to logarithmic form.

What is (-3π)/11 in degree measures?

Given the triangle below, the legs are

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

Which of the following is the symbol for eta?

• ε
• β
• θ
• H

A polynomial function is defined as the product of monomials.

• True
• False

What is the cofunction of cotangent?

• tangent
• sine
• cosine
• secant

Coterminal angles are the same degrees.

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

Is sin2θ cos2θ = 1?

• True
• False

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

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 Greek name for σ is rho.

• True
• False

Zero and positive integers are the __________.

• Whole Numbers

Which of the following is the cofunction of secant?

• cosecant
• cotangent
• cosine
• tangent

(-3π)/2 belongs to quadrant?

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

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

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

A rational function is the product of two polynomials.

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

• True
• False

In what quadrant does 5π/9 belong?

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

• True
• False

Convert 9000 to radian measure.

• 5π
• -5π
• 2π
• 4π

What is the coterminal of 00?

The following are the fundamental identities except

The graph of the cosine functions always passes through the origin

• True
• False

The symbol i is called ________.

The following angles belong to quadrant IV, except

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

• True
• False

Which of the following is equal to 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:
• Less Effective Instructional Decisions

The following degree measurements are found in Quadrant I, except

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

• cosine
• tangent
• sine
• secant

Which of the following is considered as an exponential function?

1.7 is a rational number

• True
• False