Arithmetic and Algebra

Question 1

𝑛^𝑎 × 𝑛^𝑏 =

Answer 1

𝑛^𝑎+𝑏

Question 2

Answer 2

𝑛^𝑎−𝑏

Question 3

(𝑛^𝑎)^𝑏 =

Answer 3

𝑛^𝑎×𝑏

Question 4

𝑛^−𝑎 =

Answer 4

Question 5

Answer 5

Question 6

𝑛¹ =

Answer 6

𝑛

Question 7

𝑛⁰ =

Answer 7

1

Question 8

𝑉𝑎𝑙𝑢𝑒 =

use Principal, Rate %, and Time

Answer 8

𝑉𝑎𝑙𝑢𝑒 = 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 × (1 ± 𝑅𝑎𝑡𝑒)^{𝑇𝑖𝑚𝑒}

Question 9

𝑉𝑎𝑙𝑢𝑒 =

Use Principal, Rate, Period, and Time

Answer 9

𝑉𝑎𝑙𝑢𝑒 = 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 × (1 ± [𝑅𝑎𝑡𝑒/𝑃𝑒𝑟𝑖𝑜𝑑] )^{𝑇𝑖𝑚𝑒×𝑃𝑒𝑟𝑖𝑜𝑑}

Question 10

𝑟𝑎𝑡𝑒 =

Use Distance and Time

Answer 10

𝑟𝑎𝑡𝑒 = 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒/𝑡𝑖𝑚𝑒

Question 11

𝑃𝑒𝑟𝑐𝑒𝑛𝑡 =

Use Part and Whole

Answer 11

𝑃𝑒𝑟𝑐𝑒𝑛𝑡 = (𝑃𝑎𝑟𝑡/𝑊ℎ𝑜𝑙𝑒) × 100%

Question 12

𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐶ℎ𝑎𝑛𝑔𝑒 =

Use New and Old

Answer 12

𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐶ℎ𝑎𝑛𝑔𝑒 = (𝑁𝑒𝑤−𝑂𝑙𝑑)/𝑂𝑙𝑑

Question 13

𝑃(𝐴) =

Answer 13

Question 14

𝑃(𝐴 𝑎𝑛𝑑 𝐵) =

Answer 14

𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 𝑃(𝐴) × 𝑃(𝐵)

Question 15

𝑃(𝐴 𝑜𝑟 𝐵) =

Answer 15

𝑃(𝐴 𝑜𝑟 𝐵) = 𝑃(𝐴) + 𝑃(𝐵)

Question 16

𝑃(𝑛𝑜𝑡 𝐴) =

Answer 16

𝑃(𝑛𝑜𝑡 𝐴) = 1 − 𝑃(𝐴)

Question 17

𝑖 =

Answer 17

Question 18

𝑖² =

Answer 18

𝑖² = − 1

Question 19

𝑖³ =

Answer 19

Question 20

𝑖⁴ =

Answer 20

𝑖⁴ = 1

Question 21

Remove 𝑖 from denominator with conjugate:

Answer 21

Question 22

Answer 22

Question 23

Vert. Shift:

Answer 23

𝑓(𝑥) + 𝑐

Question 24

Horiz. Shift:

Answer 24

𝑓(𝑥 − 𝑐)

Question 25

Vert. Flip:

Answer 25

− 𝑓(𝑥)

Question 26

Horiz. Flip:

Answer 26

𝑓(− 𝑥)

Question 27

Slope-Intercept:

Answer 27

𝑦 = 𝑚𝑥 + 𝑏

𝑚 = slope and 𝑏 = y-intercept

Question 28

Point-Slope:

Answer 28

𝑦 − 𝑦₁ = 𝑚(𝑥 − 𝑥₁)

Question 29

Quadratic f(x) =

Answer 29

𝑎𝑥² + 𝑏𝑥 + 𝑐

Question 30

𝑉𝑒𝑟𝑡𝑒𝑥 =

Answer 30

Question 31

𝑦-intercept =

Answer 31

𝑐

Question 32

𝑥-intercepts =

Answer 32

Question 33

Discriminant =

Answer 33

𝑏² − 4𝑎𝑐

• negative: no solutions,
• positive: two solutions,
• zero: one solution

Question 34

Factored: 𝑓(𝑥) =

Answer 34

𝑓(𝑥) = (𝑥 − 𝑝)(𝑥 − 𝑞)

Question 35

Factored: 𝑥-intercepts are…

Answer 35

𝑥-intercepts are 𝑝 and 𝑞

Question 36

Factored: Vertex =

Answer 36

𝑎(𝑥 − ℎ)² + 𝑘

Vertex = (ℎ, 𝑘)

• If 𝑎 > 0, upward;
• if 𝑎 < 0, downward