Quantitative Reasoning

Sequences

100

Identify the type of sequence for each and explain:

   x,  2x,  4x,  8x, ...

  x,  x+7,  x+14,  x+21, ...

1. Geometric

2. Arithmetic

200

Identify all key features of the following sequences

6,  12,  24,  48, ...

7, 13, 19, 25, ...

1) a₀ = 6    and      r = 2

2) a₀ = 7    and      d = 6

300

Write an equation for the following sequence,

12,  19,  26,  33, ...

Sequence   a_n = 7n + 12

Function   f(x) = 7x + 12

400

Write an equation for the following sequence,

3,  21,  147,  1029, ...

Sequence   a_n = 3(7)ⁿ

Function   f(x) = 3(7)^x

500

Write an equation for the following sequence,

2000,  400,  80,  16, ...

and determine the 6^th term of the sequence?

a_n = 2000(.2)ⁿ

f(x) = 2000(.2)^x

a₅ = .64

Polynomials Vocabulary

100

Write 6x⁵ + 8x - 3x³ + 7x⁷ 

in standard form.

7x⁷ + 6x⁵  - 3x³ + 8x

Because it needs to be written in descending order by degree

200

When 3x² + 7x - 6 + 2x³ is written in standard form, the leading coefficient is 

1) 7

2) 2 

3) 3 

4) -6

The answer is 2 because it is in front of the highest degree variable.

300

Which polynomial has a leading coefficient of 4 and a degree of 3? 

1) 3x⁴ - 2x² + 4x - 7 

2) 4 + x - 4x² + 5x³ 

3) 4x⁴ - 3x³ + 2x² 

4) 2x + x² + 4x³

the answer is 4 because the leading term has 4 in front (coefficient) and is multiplying x³ (degree)

400

Which statement is correct about the polynomial 

3x² +5x - 2? 

1) It is a third-degree polynomial with a constant term of -2. 

2) It is a third-degree polynomial with a leading coefficient of 3. 

3) It is a second-degree polynomial with a constant term of 2. 

4) It is a second-degree polynomial with a leading coefficient of 3.

4 because it is not third degree (x³) and the constant is +2 not -2

500

Write 2 expressions 

- in standard form

-leading coefficient of 3

- degree of 2

- constant of 4

3x² + ____x + 4

Adding/ Subtracting Polynomials

100

Find the sum of (7x + 8) and (9x - 4)

16x + 4

200

Find the sum of (x² + 11x + 28) and (x² + x + 4)

2x² + 12x +32

300

(x² + 11x + 28) - (x² + x + 4)

10x + 24

400

(5x² + 23x - 12) - (3x² + 15x + 9)

2x² + 8x - 21

500

Subtract (4x² + 4x + 7) 

From (3x² + 17x + 23)

-1x² + 13x +16

OR

-x² + 13x +16

Multiplying terms and Polynomials

100

(x + 4) (x + 7)

x² + 11x + 28

200

(2x + 3) (x + 7)

2x² + 17x + 21

300

( 5x³ ) ( 9x² ) 

45x⁵

400

(3x + 5) (x - 7)

3x² - 16x - 35

500

( 14x^³ ) divide ( 5x^² )

2.8x¹

2.8x

Factoring Polynomials

100

Factor x² + 8x +15

(1x + 3) (1x + 5)

(x + 3) (x + 5)

200

Factor x² - 7x - 30

(x + 3) (x - 10) 

300

Factor 2x² - x - 45

(2x + 9) (x - 5)

400

Factor completely

3x² + 42x + 72

3 (x + 12) (x + 2)

500

Factor Completely 

4x² - 2x - 30

2 (2x + 5) (x - 3)