1. Math 20-1 Formula Sheet Exponent...

ID: A Name: __________________

2

1. Math 20-1 Formula Sheet

Sequences and Series

tn = t 1 + n − 1( )d

S n =n

22t 1 + n − 1( )dÈÎÍÍÍÍ

˘˚˙̇˙̇

S n =n

2t 1 + t nÊËÁÁ ˆ

¯˜̃

tn = t 1 rn − 1

S n =

t 1 rn

− 1Ê

Ë

ÁÁÁÁˆ

¯

˜̃˜̃

r − 1, r ≠ 1

S n =

rtn − t 1

r − 1, r ≠ 1

S∞

=

t 1

1 − r, r ≠ 1

Trigonometry

sin A

a=

sin Bb

=sin C

c

a

sin A=

bsin B

=c

sin C

c2= a

2+ b

2− 2ab ⋅ cos C

cos C =a

2+ b

2− c

2

2ab

Quadratic Functions

y = a x − pÊËÁÁ ˆ

¯˜̃

2+ q

y = ax2

+ bx + c

Quadratic Equations

Given ax2

+ bx + c = 0, a ≠ 0 then

x =−b ± b

2− 4ac

2a

Exponent Laws

a m⋅ a

n= a

m + n

a m÷ a

n= a

m − n, a ≠ 0

amÊ

Ë

ÁÁÁÁˆ

¯

˜̃˜̃

n

= amn

ab( )m= a

mb

m

ab

Ê

Ë

ÁÁÁÁÁˆ

¯

˜̃˜̃̃

m

=a

m

bm

, b ≠ 0

a −n=

1

an

, a ≠ 0

a

1

n= a

n

a

m

n= a

mnor a

nÊ

Ë

ÁÁÁÁˆ

¯

˜̃̃˜

m

Radicals

m akÊ

Ë

ÁÁÁÁˆ

¯

˜̃˜̃ n b

kÊ

Ë

ÁÁÁÁˆ

¯

˜̃˜̃ = mn ab

k

m a

k

n bk

=mn

ab

k

Fractions

ab

+cd

=ad + bc

bd

ab

⋅cd

=acbd

a

b

c

d

=ab

⋅dc

ID: A Name: __________________

3

Multiple Choice

1. The common difference in the arithmetic sequence 4

5,

13

10,

9

5,

23

10,

14

5, . . . is

A.1

2B.

26

25C. 4 D. 2

2. Determine the next three terms on the following sequence? 39, 27, 15, …

F. 3, –8, –19 G. 3, –10, –22 H. 3, –9, –22 J. 3, –9, –21

3. Find the first five terms for the following arithmetic sequence tn = 43 − 13n

A. 30, 17, 4, 17, 30 C. 43, 30, 17, 4, –9

B. 30, 29, 28, 27, 26 D. 30, 17, 4, –9, –22

4. Determine the number of terms in the sequence 48, 35, 22, …, − 1343

F. 3 G. 109 H. 108 J. 110

5. Complete the following arithmetic sequence. 83, , ,8,

A. 58; 33; –17 B. 57; 33; –43 C. 58; 33; –16 D. 57; 32; –43

6. Which term of the arithmetic sequence −6, 6, 18, … has a value of 1410?

F. t120 G. t119 H. t121 J. t1410

7. Determine the general term of the sequence 3, –2, –7, –12, –17, . . .

A. tn = −5n + 8 B. tn = 5n + 2 C. tn = 5n + 8 D. tn = −5n + 2

8. What is the 130th term of the sequence –23, –23.6, –24.2, –24.8, –25.4, …?

F. –100.4 G. –0.6 H. –101.6 J. 54.4

9. The sum of an arithmetic series where t1 =1

2, d = 2, and n = 49 is

A.4851

2B. 4753 C. 97 D.

4753

2

10. Determine the sum of the arithmetic series. 5 + 3 + 1 +ë + −107

F. –2856 G. –2805 H. –2881.5 J. –2907

11. The common ratio for the geometric sequence –7, −7

3, −

7

9, −

7

27, . . . is

A. −1

3B.

1

3C. –3 D. 3

ID: A Name: __________________

4

12. In the formula for the general term of a geometric sequence tn = 45

9

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

n − 1

, the common ratio is

F. 9 G.9

5H.

5

9J. 5

13. The sum of an infinite geometric series is 161

2 and its common ratio is

3

7. What is the first term of the series?

A.3

7B. 46 C.

1127

6D.

69

2

14. In an arithmetic sequence, t8 = 79 and t45 = 301. What is the value of t1?

F. 43 G. 49 H. 37 J. 30

15. Which of the following is a geometric sequence?

A. −9, 13.5, 20.25 B. −9, − 13.5, − 20.25 C. −9, − 12, − 15 D. −9, − 2, 5

16. State the common ratio of the geometric sequence. 288, 432, 648, …

F.2

3G. −

3

2H.

3

2J. 288

17. Complete the following geometric sequence. −2, , ,16,

A. 8; 8; 16 B. 4; –8; –32 C. 8; –8; –16 D. 4; 8; 32

18. Determine the sum (to 3 decimal places) of the first 7 terms of the geometric series: 12 + 36

7 +

108

49 + ë

F. 20.944 G. –20.944 H. 20.976 J. 20.990

19. Determine the sum of the infinite geometric series: 16 + 4 + 1 +1

4+ …

A. S∞

= 5.3 B. S∞

= 21.3 C. S∞

= 4 D. S∞

= 64

20. A geometric series has r = −3

5 and S

∞= 3.125. Determine t1.

F. t1 = −1 G. t1 = 5 H. t1 = −5 J. t1 = 3

ID: A

1

Sequences and Series RETest Worksheet

Answer Section

SHORT ANSWER

1. 1744

495

2. 82 678

OTHER

1. Math 20-1 Formulas

MULTIPLE CHOICE

1. A

2. J

3. D

4. H

5. A

6. G

7. A

8. F

9. D

10. J

11. B

12. H

13. B

14. H

15. B

16. H

17. B

18. F

19. B

20. G

Math 20-1ID: A Name: __________________

1

Trigonometry RE-test Worksheet

1. Given sinθ = 0.7547, where 0° ≤ θ < 360°,

determine the measure of θ , to the nearest degree.

2. Given cos θ = −0.9986, where 0° ≤ θ < 360°,


3. Given cos θ = −0.3420, where 0° ≤ θ < 360°,


4. Given tanθ = −0.1405, where 0° ≤ θ < 360°,


5. Given tanθ = −2.2460, where 0° ≤ θ < 360°,


6. Given the angle 279° is in standard postions.

Determine the reference angle.

7. Given the angle 266° is in standard postions.

Determine the reference angle.

8. Given that an angle has a reference angle of 54°,

determine the angle in standard position if the

angle is in quadrant one.

9. Given that an angle has a reference angle of 68°,

determine the angle in standard position if the

angle is in quadrant three.

10. Determine the exact value of sinθ if the terminal

arm of an angle in standard position passes through

the point 8, 8ÊËÁÁ ˆ

¯˜̃ .

11. Determine the exact value of cos θ if the terminal

arm of an angle in standard position passes through

the point −9, 4ÊËÁÁ ˆ

¯˜̃ .

12. Calculate the length of AC in ∆BAC to 1 decimal

place.

(The diagram is NOT drawn to scale)

13. Calculate the measure of ∠A in ∆CBA to the

nearest tenth of a degree.


14. Calculate the length of AB in ∆CAB to 1 decimal

place.


Name: ________________________ ID: A

2

15. Given that ∠B is obtuse, calculate the measurement

of ∠B in ∆BAC to 1 decimal place.


16. Given ∠C = 47, b = 16, c = 15 in ∆ABC, calculate

two possible measurements of ∠A to 1 decimal

place. [2 marks]

17. Given ∠C = 28, b = 15, c = 8 in ∆ABC, calculate

two possible measurements of ∠A to 1 decimal

place. [2 marks]

18. Sarah and Simone are walking in a walk-a-thon down a straight street that leads to the finish line. At the same

time, they both notice a tethered hot-air balloon directly over the finish line. Sarah sees that the angle from the

ground to the balloon as 20°, and Simone (who is 0.53 km closer to the finish line than Sarah) sees the angle from

the ground to the balloon as 56°.

Determine the height of the balloon, to the nearest hundredth of a kilometre.

19. Two airplanes leave the Hay River airport in the Northwest Territories at the same time. One airplane travels at

370 km/h. The other airplane travels at 520 km/h. About 2 h later, they are 930 km apart. Determine the angle

between their paths, to the nearest degree.

ID: A

1

Trigonometry RE-test Worksheet

Answer Section

1. θ1 = 49°, θ2 = 131°

2. θ1 = 177°, θ2 = 183°

3. θ1 = 110°, θ2 = 250°

4. θ1 = 172° , θ2 =352°

5. θ1 = 114° , θ2 =294°

6. 81°

7. 86°

8. 54°

9. 248°

10. sinθ = 1

2

11. cos θ = −9

97

12. b = 19.4

13. ∠A = 22.6°

14. c = 32.5

15. angle B = 133.0°

16. ∠A = 81.7, or 4.3

17. ∠A = 90.3, or 33.7

18. The height of the balloon is 0.26 km.

19. 60°

Math 20-1ID: A Name: __________________

1

Quadratic Functions: Retest Worksheet

Short Answer

1. Given the equation y = x2

+ 4x + 3,

determine the following:

a) y-intercept: ___________

b) x-intercept(s): ___________

c) vertex: ___________

d) axis of symmetry: ___________

e) domain: ___________

e) range: ___________

2. Given the equation y = x2

− 6x + 8,

determine the following:

a) y-intercept: ___________

b) x-intercept(s): ___________

c) vertex: ___________

d) axis of symmetry: ___________

e) domain: ___________

e) range: ___________

3. The graph of a quadratic function is shown below.

Determine its equation:

4. The graph of a quadratic function is shown below.

Determine its equation:

Name: ________________________ ID: A

2

5. Change the equation y = 6x2

− 72x + 212 to the

form y = a x − pÊËÁÁ ˆ

¯˜̃

2+ q by completing the square.

.


− 4x + 6 to the form


¯˜̃


.


− 16x + 19 to the form


¯˜̃


.


+ 30x + 79 to the form


¯˜̃


.

Name: ________________________ ID: A

3

9. Given the vertex is 1, − 3ÊËÁÁ ˆ

¯˜̃and a point on the

graph is 4,24ÊËÁÁ ˆ

¯˜̃ . Determine the equation of the

parabola in the form y = a x − pÊËÁÁ ˆ

¯˜̃

2+ q

.

10. Given the vertex is −1, 6ÊËÁÁ ˆ

¯˜̃and a point on the graph

is 1,− 2ÊËÁÁ ˆ

¯˜̃ . Determine the equation of the parabola

in the form y = a x − pÊËÁÁ ˆ

¯˜̃

2+ q

.

11. A store sells energy bars for $2.25. At this price,

the store sold an average of 120 bars per month last

year. The manager has been told that for every 5¢

decrease in price, he can expect the store to sell

eight more bars monthly.

a) Write a quadratic function you can use to model

this situation?

b) Determine the maximum revenue the manager

can expect the store to achieve.

c) What price will give that maximum?

12. A dinner theatre has 600 season ticket holders. The

owners of the theatre have decided to raise the

price of a season ticket from the current price of

$400. According to a recent survey of season ticket

holders, for every $50 increase in the price, 30

season ticket holders will not renew their seats.

a) Write a quadratic function you can use to model

this situation?

b) Determine the maximum revenue the concert

could achieve.

c) What should the owners charge for each season

ticket in order to maximize their revenue?

Name: ________________________ ID: A

4

13. A hospital sells raffle tickets to raise funds for new

medical equipment. Last year, 2000 tickets were

sold for $20 each. The fund-raising coordinator

estimates that for every $1 decrease in price, 200

more tickets will be sold.

a) What decrease in price will maximize the

revenue?

b) What is the price of a ticket that will maximize

the revenue?

c) What is the maximum revenue? Show and

explain your work.

14. Three rectangular areas are being enclosed along

the side of a building, as shown. There is 64 m of

fencing material. Assume that all the material is

used.

a) Write the function that represents the total area

in terms of the distance from the wall.

b) Determine the maximum area.

c) Determine the length and width of the overall

enclosure.

15. A rectangular dog pen is to be fenced with 28 m of

fencing. Determine the maximum area and the

width of this rectangle.

16. A rectangular lot is bordered on one side by a

building and the other 3 sides by 600 m of fencing.

Determine the area of the largest lot possible.

17. A science museum wants to build an outdoor patio.

The patio will be bordered on one side by a wall of

the museum and the other 3 sides by 40 m of

fencing. Determine the area of the largest patio

possible.

18. Two numbers have a difference of 6 and their

product is a minimum. Determine the numbers.

19. Two numbers have a difference of 8. The sum of

their squares is a minimum. Determine the

numbers.

20. The sum of two numbers is –12. Their product is a

maximum. Determine the numbers.

ID: A

1

Quadratic Functions: Retest Worksheet

Answer Section

SHORT ANSWER

1. a) 3

b) –1, –3

c) −2,−1ÊËÁÁ ˆ

¯˜̃

d) x = −2

e) y ≥ −1

2. a) 8

b) 2, 4

c) 3,−1ÊËÁÁ ˆ

¯˜̃

d) x = 3

e) y ≥ −1

3. y = x2

− 1

4. y = −0.5x2

+ 2x

5. y = 6 x − 6( )2

− 4

6. y = 2 x − 1( )2

+ 4

7. y = 4 x − 2( )2

+ 3

8. y = 3 x + 5( )2

+ 4

9. y = 3 x − 1( )2

− 3

10. y = −2 x + 1( )2

+ 6

11. a) R = (2.25 − 0.05x)(120 + 8x)

b) $360

c) $1.50 (x is 15)

12. a) R = (400 + 50x)(600 − 30x)

b) $294 000

c) $700 (x is 6)

ID: A

2

13. Determine an equation to represent the situation.

For each $1 decrease in price, 200 more tickets will be sold. Let x represent the number of $1 decreases in the

price of a ticket.

When the price decreases by $1 x times:

• the price, in dollars, of a ticket is 20 − x.

• the number of tickets sold is 2000 + 200x.

• the revenue, in dollars, is (20 − x)(2000 + 200x).

Let the revenue be R dollars.

An equation is: R = (20 − x)(2000 + 200x)

Use a graphing calculator.

Graph: R = (20 − x)(2000 + 200x)

Use the CALC function to determine the coordinates of the vertex.

a) From the graph, the maximum revenue occurs when the number of $1 decreases is 5. So, the decrease in price

that will maximize the revenue is $5.

b) The price of a ticket that will maximize the revenue is: $20 − $5 = $15

c) Substitute x = 5 in R = (20 − x)(2000 + 200x) to determine the maximum revenue.

R = (20 − 5)(2000 + 200(5))

R = 45 000

The maximum revenue is $45 000.

14. a) A = 3 64 − 4d( )d or A = 192d − 12d2

b) 768 m²

c) 8 m × 32 m

15. A = 49 m2; w = 7 m

16. 45 000 m2

17. 200 m2

18. –3 and 3

19. –4 and 4

20. –6 and –6

Math 20-1ID: A Name: __________________

1

Absolute Value and Reciprocal Functions RE-Test workheet

1. Evaluate 2 + 72|

||| − 8 − −3( )|| || + −2 − 8| | + −5| | .

.

2. Draw the graph of y = 2x − 3| |

3. Given f(x) = x 2 + 5x + 4, sketch a graph of the

reciprocal function y =1

f(x) and identify the

vertical asymptotes, if they exist.

4. Write an equation for the absolute value function.

Show your work.

.

5. Determine the equation of the following graph.

Show your work.

Name: ________________________ ID: A

2

6. Solve this equation: | 7

8x −

3

2 | = 2

.

7. Solve this equation: x 2 − 12x − 65| | = 20

.

8. Write this absolute value function in piecewise

notation.

y = (x + 3)2 − 9|| ||

9. Given the quadratic function y = f x( )below, sketch

the graph of y =1

f x( ). Use the same coordinate

plane shown.

10. The cross-section of the sloping roof of a house is

represented on a coordinate grid so that the points

representing the bottom of the roof lie on the

x-axis. The equation of the function describing the

cross-section is h x( ) = −2

3 x|

||

|

||+ 4, where h is the

height of the roof, in metres, and x is the horizontal

distance from the centre of the roof, in metres.

What is the width of the bottom of the roof?

ID: A

1

Absolute Value and Reciprocal Functions RE-Test workheet

Answer Section

1. 55

2.

3.

The graph of y = f(x) opens up and has

x-intercepts –1 and –4.

So, the graph of the reciprocal function has

vertical asymptotes x = −1 and x = −4.

Plot points where the lines y = 1 and y = −1

intersect the graph of y = f(x) . These points

are common to both graphs. Using these

points and the asymptotes, draw smooth

curves that approach the asymptotes but

never touch them.The graph of the

reciprocal function has Shape 3.

ID: A

2

4.

Choose two points on the line to determine the

slope of the linear function:

(–4, 5) and (–2, 1)

m =

y 2 − y 2

x 2 − x 1

m =1 − (5)

−2 − (−4)

m = −2

y-intercept: –3

An equation for the absolute value function is:

y = − 2x − 3| |

5. y = 2x2 − 8| |

6. x = 4 and x = −4

7

7. The solutions are: x = −5, x = 17, x = 15, and x = −3

8. y =(x + 3)2 − 9, if x ≤ −6 or x ≥ 0

−(x + 3)2 + 9, if − 6 < x < 0

ÏÌÓ

ÔÔÔÔÔÔ

9.

10. Therefore, the distance between the two points is 12 m. The width of the bottom of the roof is 12 m.

Radicals Review

1. Write this entire radical as a mixed radical:



4. For which values of the variable, x, is this radical defined?

5. Simplify by adding or subtracting like terms:

6. Simplify by adding or subtracting like terms:

7. Expand and simplify this expression:




11. Simplify this expression:

12. Solve this equation:

13. Solve this equation:

14. Determine the root of each equation.

a)

b)

c)

d)

Answer Section (Radicals)

SHORT ANSWER

1. ANS:

2. ANS:

3. ANS:

4. ANS:

5. ANS:

6. ANS:

7. ANS:

8. ANS:

9. ANS:

10. ANS:

11. ANS:

12. ANS:

13. ANS:

14. ANS:

a)

b)

c) The equation has no real root.

d)

Math 20-1ID: A Name: _________________ Class: _______

1

Quadratic Equations RE-Test Worksheet

1. Factor this polynomial expression: 16 x − 4( )2

− 9 4y + 3ÊËÁÁ ˆ

¯˜̃

2 [2 marks]

.

2. Factor this polynomial expression: 4 x + 4( )2

+ 72 x + 4( ) + 224 [2 marks]

.

3. Determine the discriminant of x2

+ 18x + 81 = 0 [1 mark]

Name: ________________________ ID: A

2

4. Describe the nature of the roots of x2

− 2x + 1 = 0 (Do not solve) [1 mark]

5. Solve 12x2

+ x − 3 = 0 to the nearest hundredth. [2 marks]

6. Determine the exact solution(s) for (2x − 5)2 = 6 [2 marks]

7. Solve 6x2

− 6x = 0 by factoring. [2 marks]

8. Solve −x2

+ 7x − 10 = 0 by factoring. [2 marks]

9. Algebraically solve −4x2

+ x + 3 = 0 [2 marks]

Name: ________________________ ID: A

3

10. Determine the exact roots of 12x2

− x − 9 = 0 [2 marks]

11. Determine the exact roots of 9x2

+ x − 9 = 0 [2 marks]

Problem

1. A penny is dropped from the top of the High Level Bridge. It’s height, h meters, above the river t seconds after it

is released is modeled by the quadratic function: h t( ) = 101 − 4.8t2. To the nearest tenth of a second, how long

has the penny fallen for when it is 19 m above the river? [1 mark]

.

2. Marc’s rectangular garden measures 9 m by 12 m. He wants to double the area of his garden by adding equal

lengths to both dimensions. Determine this length to the nearest tenth of a metre. Show your work. [2 marks]

ID: A

1

Quadratic Equations RE-Test Worksheet

Answer Section

SHORT ANSWER

1. 4x + 12y − 7ÊËÁÁ ˆ

¯˜̃ 4x − 12y − 25ÊËÁÁ ˆ

¯˜̃

2. 4(x + 18)(x + 8)

3. 0

4. Discriminant = 0 and therefore equal real roots

5. x =Ö− 0.54 or 0.46

6. x =5

2±

6

2

7. x = 0 or 1

8. x = 5 or 2

9. x = 1 or −3

4

10. x =1 ± 433

24

11. x =−1 ± 5 13

18

PROBLEM

1. 4.1 s

2. The length to be added is approximately 4.3 m.

Rational Expressions

Multiple Choice

____ 1. Which of the following are NOT rational expressions?

i) ii)

iii) iv)

A. iii and iv B. i, iii, and iv C. ii and iii D. ii and iv

____ 2. Which of the following rational expressions are defined for all real values of x?

i) ii) iii) iv)

A. i and ii B. iv C. i and iii D. i and iv

____ 3. Which of the following are the non-permissible values for this rational expression?

A. , , and

C. and

B. and D. , , and

____ 4. Simplify.

A.

C.

B.

D.

____ 5. Simplify.

A.

C.

B.

D.

____ 6. Simplify.

A.

C.

B.

D.

____ 7. Simplify this expression:

A. B.

C.

D.

____ 8. Solve.

A.

B.

C.

D.

____ 9. Solve.

A. C. B. D. no solution

____ 10. Simplify.

A. ,

C. ,

B. ,

D. ,

Short Answer


2. Simplify.

3. A plane travels from A to B and back, a distance of about 195 each way. On the journey out, the plane has a

25 km/h tailwind, and on the return trip, it has a 20 km/h headwind. Write a simplified rational expression for

the total flying time in terms of the plane’s average speed in still air, .

4. Simplify.

5. Solve.


7. Write the least common multiple of the expressions in each pair.

a)

b)

c)

8. Simplify this expression and state the non-permissible values. Show your work.

Rational Expressions

Answer Section

MULTIPLE CHOICE

1. B

2. D

3. D

4. A

5. B

6. B

7. D

8. D

9. C

10. C

SHORT ANSWER

1. ,

2.

3.

4.

5.

6. 1, 5, 5

2, 2

7. a)

b)

c)

8.

So,

Math 20-1ID: A Name: __________________

1

Quadratic Systems of Equations RE-Test worksheet

1. (1 point)

Solve by graphing:

y =3

4x − 4( )

2− 2

3x + 2y − 8 = 0

2. (1 point)

Solve by graphing:

x2

+ 6x + 4y − 7 = 0

2x + y − 1 = 0

3. (2 points)

Algebraically solve:y =8x−29

4x2− 24x−y +35 = 0

.

ID: A

2

4. (2 points)

Algebraically solve::

x2

+ 8x − y + 12 = 0

3x + y + 16 = 0

.

5. (1 point)

Algebraically solve:

A line with slope = −2 and y-intercept of +1

intersects a parabola with vertex (1, –2) and a point

3, − 6ÊËÁÁ ˆ

¯˜̃

.

ID: A

3

Problems: (Show all work). Graphical solutions require equations, sketch, and window settings.

1. (6 points)

After a football is kicked, it reaches a maximum height of 13 m and it hits the ground

26 m from where it was kicked. After a soccer ball is kicked, it reaches a maximum

height of 9 m and it hits the ground 40 m from where it was kicked. The paths of both

balls are parabolas.

a) Consider both balls to be kicked from the same starting point and place this at the origin of a coordinate grid. Draw a

diagram to model the given information for the two kicked balls. (1 point)

b) Determine a quadratic equation in the form of: y = a(x − p)2

+ q to model the football height compared to the horizontal

distance it travelled and a quadratic equation in the form of: y = a(x − p)2

+ q to model the soccer ball height compared to

the horizontal distance it travelled.

(2 point)

c) Solve the system of two equations. If you are using a graphical approach, make sure you include all relevant information -

including the window settings and equations you used to solve the problem for full marks. Round your answer to the nearest

centimeter (2 points)

d) What is occuring at the intersection point, in the context of this problem? (1 point)

ID: A

4

2. (5 points)

The perimeter of the right triangle is 510 m. The area of the triangle is 30y square metres.

a) Write a simplified expression for the triangle’s perimeter in terms of x and y. (1 point)

b) Write a simplified expression for the triangle’s area in terms of x and y. (1 point)

c) Write a system of equations and explain how it relates to this problem. (1 point)

d) Solve the system for x and y. What are the dimensions of the triangle? (2 points)

ID: A

5

Other

1. (0 points)

Math 20-1 Formula Sheet

Sequences and Series

tn = t 1 + n − 1( )d

S n =n

22t 1 + n − 1( )dÈÎÍÍÍÍ

˘˚˙̇˙̇

S n =n

2t 1 + t nÊËÁÁ ˆ

¯˜̃

tn = t 1 rn − 1

S n =

t 1 rn

− 1Ê

Ë

ÁÁÁÁˆ

¯

˜̃˜̃

r − 1, r ≠ 1

S n =

rtn − t 1

r − 1, r ≠ 1

S∞

=

t 1

1 − r, r ≠ 1

Trigonometry

sin A

a=

sin Bb

=sin C

c

a

sin A=

bsin B

=c

sin C

c2= a

2+ b

2− 2ab ⋅ cos C

cos C =a

2+ b

2− c

2

2ab

Quadratic Functions


¯˜̃

2+ q

y = ax2

+ bx + c

Quadratic Equations

Given ax2

+ bx + c = 0, a ≠ 0 then

x =−b ± b

2− 4ac

2a

Exponent Laws

a m⋅ a

n= a

m + n

a m÷ a

n= a

m − n, a ≠ 0

amÊ

Ë

ÁÁÁÁˆ

¯

˜̃˜̃

n

= amn

ab( )m= a

mb

m

ab

Ê

Ë

ÁÁÁÁÁˆ

¯

˜̃˜̃̃

m

=a

m

bm

, b ≠ 0

a −n=

1

an

, a ≠ 0

a

1

n= a

n

a

m

n= a

mnor a

nÊ

Ë

ÁÁÁÁˆ

¯

˜̃̃˜

m

Radicals

m akÊ

Ë

ÁÁÁÁˆ

¯

˜̃˜̃ n b

kÊ

Ë

ÁÁÁÁˆ

¯

˜̃˜̃ = mn ab

k

m a

k

n bk

=mn

ab

k

Fractions

ab

+cd

=ad + bc

bd

ab

⋅cd

=acbd

a

b

c

d

=ab

⋅dc

ID: A

1

Quadratic Systems of Equations RE-Test worksheet

Answer Section

SHORT ANSWER

1. P1(2,1)

P2(4,–2)

2. P1(3,–5)

P2(–1,3)

3. Solution: 4,3ÊËÁÁ ˆ

¯˜̃

4. P1(–7,5)

P2(–4,–4)

5. y =−2x+1

y =− x − 1( )2

− 2

Solution: 2,−3ÊËÁÁ ˆ

¯˜̃

ID: A

2

PROBLEM

1. a.

b.

football: y =−1

52x x − 26( )

soccerball: y =−9

1600x x − 40( )

c. (20.21, 9.00)

d. The intersection point is where the two balls are at the same height given the same horizontal distance

travelled.

2. a) 8x + y + 129

b) 15

2x

2+

363

2x

c)

y = − 8x + 381

y =1

4x

2+

121

20x

d) x = 20 and y = 221

base = 221, height = 60, hypotenuse = 229

OTHER

1. Math 20-1 Formulas

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