MCR3U Jeopardy

Trig

100

Find the Sin(30)

0.5

200

A ladder is 10m long and leans against a wall. the angle with the ground is 60 degrees. How high up the wall does it reach?

10Sin(60)

= 8.66m

300

A ladder reaches 8m up a wall and is 10m long. What angle does it make with ground?

sin-1 (8/10)

=53.1 Degrees

400

In a triangle, A= 40 degrees, a= 8, and b= 12. Find angle B.

Use the Sine Law.

(sinB/12) = (sin40/8)

=sin-1 (0.9642)

B= 74.8 Degrees

500

A triangle has sides 7cm, 9cm, and 12cm. Find the largest angle.

Use Cosine Law.

cosC= (7^2)+(9^2)-(12^2)/(2x7x9)

C=96.4 degrees

Finance

100

What does the "P" represent in A=P(1+rt)? 

Principal

200

You invest $500 at 4% simple interest for three years.

How much interest is earned?

I=Prt

I=(500)(0.04)(3)

=$60

300

an investment of $1000 earns 5% simple interest for 4 years .What is the final amount?

A=P(1+rt)

A=1000(1+0.05x4)

A=$1200

400

an investment of $2000 earns 5% interest compounded annually for 4 years.

What is the value of the investment at the end of the 4 years? (round to the nearest dollar)

A=P(1+r)^t 

A=2000(1.05)^4

A=2000(1.21551)

A=$2431

500

J-Fawce deposits $200 at the end of every month into an account earning 4.8% interest compounded monthly.

How much will J-Fawce have after 5 years?

A=200((1+0.048/12)^(5)(12)-1

Divided by 0.048/12

A=200(1.004)^60-1

Divided by 0.004

A=$13,512

Quadratics

100

Find the axis of symmetry of:

y=x² -6x +5

x= -b/2a

=-(-6)/2(1)

x=3

200

Factor completely:

x² +7x +12

FIND: 2 #s that multiply to 12, add to 7

3x4=12,    3+4=7

(x+3)(x+4)

300

Solve:

x² -9x +20=0

FIND: 2 #s that multiply to 20,    add to -9

-4(-5)= 20,   -4 + (-5) = -9

(x-4)(x-5)=0     Set each factor to 0

x-4=0 x=4       x-5=0   x=5

400

Find the vertex of:

y=x² -8x +7

x= -b/2a = -(-8)/2(1) = 4 Substitute into equation.

y= (4)² -8(4) +7

y= -9

Vertex: (4,-9)

500

Solve using the quadratic formula:

2x² +3x -2 =0

x+=1/2

x-= -2

Exponents

100

Simplify:

x³x⁴

Add 3 and 4

=x⁷

200

Simplify:

7⁵÷ 7²

=7³

or

343

300

Simplify:

4⁵×4²÷4³

= 4⁴

or

256

400

Simplify:

(2³)⁴÷2⁵

=2⁷

or

128

500

Simplify:

2⁸X2^-3÷ (2²)²

=2¹

or

2

Forms of Quadratics

100

this form instantly tells you the y intercept

standard form

200

this form tells you the zeros/X intercepts right away

factored form

300

Rewrite y=x²+6x+8 into factored form

y= (x+4)(x+2)

400

For y= -3(x+1)² +12, what way does this parabola open, and what is its maximum value?

Porabola opens down, and has a max value of 12

500

Complete the square to convert y=x² -10x+21 to vertex form.

y=(x-5)² -4