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P5 8.4: Solving combination inequalities

RulesEach team gets 3 lifelines: take away two

answers, ask Mr. Sampson, and use your phone/internet device. Using a lifeline will result in a deduction of $10, 000 from the question value

Note: For the ‘List The Steps…’ questions, no choices will be given. Instead of taking away two answers, we will tell you the first step

Each question is worth $40, 000, and groups will rotate answering questions. You get one chance to answer the question, and guessing a wrong answer will lose you $40, 000

F(x)=log(6x+1)G(x)=sin2x+7Solve for when f(x)>g(x)0≤x≤2pi Use the difference function

A.) ≈(1.5628, 3.3037)U(4.4816,2pi]B.) ≈(1.5627, 3.3036)∩(4.4816, 2pi)C.) (1.5628, 3.3037)U(4.4816, 2pi]D.) ≈[0, 1.5628)U(3.3037, 4.4816]

A.) ≈(1.5628, 3.3037)U(4.4816,2pi]

G(x)=log₂x+5F(x)=log₅(x+1)+7Solve for when G(x)≤F(x) using the difference functionA.) ≈(12.1212, ∞]B.) (-∞, 12.1211)C.) ≈(0,12.1212]D.) (-∞, 12.2121]

C.) ≈(0,12.1212]

G(x)=5sinx+cos2x-7F(x)=7x-9Solve for when G(x)≥F(x) using the quotient function0≤x≤2pi

A.) (0.7922, 9/7]B.) ≈[0.7923, 9/7)C.) ≈[0.7923, 7/9)D.) [-∞, 0.7923]

B.) ≈[0.7923, 9/7)

F(x)=sin2(x+pi)G(x)=cos2(x+(5pi/4))Solve for when G(x)>F(x) using the difference function 0≤x≤2piA.) ≈(0, 6.2832]B.) (0, 2.8956)C.) ≈[0, 3.1416]D.) None of the above

D.) None of the above

What is the quadratic formula?A.) x=-b±(2b+4ac)1/2/(2a)B.)x=-b±(b2-4ac)1/2/2a

C.) x=(b±((-b)2-4ac)-2)/2aD.) x=(-b±(b²-4ac)1/2)(2a)-1

D.) x=(-b±(b²-4ac)1/2)(2a)-1

F(x)=x3+10x2-8x-1G(x)=4x2-15x-3Solve when f(x)<g(x) using pencil and paperA.) ≈(-∞, (-5-(17)1/2)(2)-1 )U(-1, (-5+(17)1/2)(2)-1)B.) ((-5-(17)1/2)(2)-1, -1)U[(-5+(17)1/2)(2)-1, ∞)C.) (-∞, (-5-(17)1/2)(2)-1 )U(-1, (-5+(17)1/2)(2)-1)D.) ≈ ((-5-(17)1/2)(2)-1, -1)U[(-5+(17)1/2)(2)-1, ∞)

C.) (-∞, (-5-(17)1/2)(2)-1 )U(-1, (-5+(17)1/2)(2)-1)

List the steps to solve…F(x)=log25x

G(x)=x/5-6f(x)>g(x)Using the quotient function and the graphing calculator

1.) Insert f(x)/g(x) into y1, and y=1 into y2

2.) 2nd trace intersection3.) Approximate intersection on both

functions, and click enter4.) Anywhere f(x)/g(x) is greater than 1,

f(x)>g(x) will be true

f(x)=log25x+7G(x)=x2+5x-3Solve for when g(x)≥f(x) using the difference function

A.) ≈[1.9171, ∞)B.) [1.9171, ∞)C.) ≈(-∞, 1.9171]D.) ≈[0, 1.9171]

A.) ≈[1.9171, ∞)

G(x)=5x/(x+8)F(x)=5Solve for when g(x)=f(x) using the quotient functionA.) [2.7183, 3.1416]B.) (-∞, ∞)C.) (2.7183, 3.14159]D.) None of the above

D.) None of the above

What is the definition of pi?A.) The ratio of the circumference of a circle

to its diameterB.) The space between two concentric circlesC.) Part of the circumference of a circleD.) A line which bisects a circle, passing

through its centre

A.) The ratio of the circumference of a circle to its diameter

1.) 5x+7-2y=02.) 8-4y+10x=0Solve for when eqn 1>eqn 2 using the difference functionA.) None of the belowB.) (3, 5]C.) [3, 5)D.) (3, 5)

A.) None of the below

F(x)=sin5x+6G(x)=2(5)x/2

Solve for when g(x)>f(x) using the difference formulaA.) (-∞, ∞)B.) [1.5564, ∞)C.) (1.5563, ∞)D.) ≈(-∞, 1.5563)

D.) ≈(-∞, 1.5563)

F(x)=5log(2x-5)+6G(x)=2/(x3+5x-1)Solve for when g(x)<f(x) using difference function, exact answer only

A.) (-∞, 2.8295]B.) (-∞, 2.8295)C.) (2.8259, ∞)D.) None of the above

D.) None of the above

What is an obtuse angle?A.) An angle less than 90◦B.) Exactly 90◦C.) More than 90◦, but less than 180 ◦D.) More than 180 ◦, but less than 360 ◦

C.) More than 90◦, but less than 180 ◦

List the steps to solve…F(x)=5x²+7x-8G(x)=6x³+4x²-9x+12Solve from when f(x)≤g(x) using a graphing

calculator, the quotient function, and another handy function

Insert f(x)/g(x) into y₁Insert h(x)=1 into y₂2nd trace, intersectionWhere ever f(x)/g(x) is less than one, f(x) will

be less than g(x)

F(x)=52x+1

G(x)=-6x⁵-x³+x²+5000Solve for when f(x)>g(x) using difference functionA.) None of the belowB.) (- ∞, 2.1629]C.) ≈(2.1629, ∞)D.) ≈[2.1628, ∞)

C.) ≈(2.1629, ∞)

List the steps to…F(x)=5x²+7x-8G(x)=5x³-7x²+9x-3Using the difference function, by handF(x)>g(x)

Set equations equal to each otherBring everything over to one sideUse factor theorem to factorUse either graphing or the interval method to

decide when f(x)>g(x)

Where did the use of decimals originate?A.) ChinaB.) IndiaC.) GreeceD.) Scotland

A.) China

F(x)=x³+5x²-7x+2g(x)=10x²-3x-18Solve for when g(x)>f(x) by paper and pencil

A.) (-∞,-2)∩(2,5)B.) None of theseC.) (- ∞, 5]D.) (-∞,-2)U(2,5)

D.) (-∞,-2)U(2,5)

What is the next number?0, 1, 1, 2, 3, 5, 8, 13…A.) 34B.) 20C.) 10D.) 21

D.) 21

F(x)=x⁴-5x³-31x²-7x-1g(x)=-5x³-16x²+3x-25Solve for when f(x)>g(x) using pencil and paperA.) [-3, -2]U[1,4]B.) (-∞, -3)U(-2, 1)U(4,∞)C.) (-∞, -3]U[-2, 1]U[4, ∞)D.) (-3, -2)U(1,4)

B.) (-∞, -3)U(-2, 1)U(4,∞)

List the steps to…F(x)=log₅xG(x)=x-3

Solve for when f(x)>g(x) using the difference formula and a graphing calculator

Insert f(x)-g(x) in to the calculator2nd trace zeroes, estimate both sides of x axis,

press enterWhen f(x)-g(x) is above the x axis, f(x) will be

greater than g(x)(Or, one could enter both equations

separately and use the intersect feature.)

F(x)=x³-5x²-2x-3g(x)=-9x²+5x+7Solve for when f(x)=g(x) using pencil and paperA.) 1, -5, 2B.) 2, -5, -1C.) -2, 5, 1D.) 5, 1, 2

B.) 2, -5, -1

F(x)=x(6x-1)(x-1)g(x)=2(5x²-5x+1)Solve using pencil and paper for when f(x)≥g(x)

A.) [0, 1/6]U[1/6, 1]B.) (-∞, 1/6]U[1, 0]U[1, ∞)C.) (-∞, 0]U(1, ∞)D.) [1/3, ½]U[2,∞)

D.) [1/3, ½]U[2,∞)

CONGRATULATIONS!You’ve passed!