12th grade algebra

Question 1

2000 is invested at 3% interest compounded continuously, A = Pe^(rt). Find A after 15 years, to 2 decimal places.

Answer 

Question 2

Solve: x + y + z = 7, x − y + 2z = −2, 2x + y − z = 13. What is z?

Answer 

Question 3

Evaluate Σ (from r = 1 to 18) of (−4r + 2).

Answer 

Question 4

Solve: log_5(4x + 2) = 1. Give x as a number (fractions allowed).

Answer (as a fraction)

Question 5

Solve ln x = 0.7. Give x to 2 decimal places.

Answer 

Question 6

A ball is dropped from 12 m. Each bounce reaches 1/2 of the previous height. In theory it bounces for ever. What total distance does it travel?

Answer 

Question 7

What are the vertical asymptotes of f(x) = (4x² + 1)/(2x² − 72)?

• A. x = 36 and x = −36
• B. x = 6 and x = −6
• C. y = 2
• D. There are none

Question 8

Evaluate Σ (from k = 1 to 8) of (k − 1).

Answer 

Question 9

Find the sum to infinity of the geometric series with first term 5 and common ratio 1/5. Give a fraction if needed.

Answer (as a fraction)

Question 10

Without a calculator, log₂ 68 lies between two consecutive whole numbers. What is the smaller one?

Answer 

Question 11

Evaluate Σ (from r = 1 to 8) of r².

Answer 

Question 12

Find the term independent of x in (x + 1/x)⁴.

Answer 

Question 13

Describe the end behaviour of f(x) = −x³ + 3x − 1.

• A. Up on the left, up on the right
• B. Down on the left, down on the right
• C. Down on the left, up on the right
• D. Up on the left, down on the right

Question 14

At 3% a year, which compounding gives the most money after 5 years?

• A. Yearly
• B. Monthly
• C. Continuously
• D. They all give the same

Question 15

Solve: |x − 1| = 3. Give both solutions, separated by a comma.

x = 

Question 16

Find the determinant of the matrix [[2, −3], [6, −4]].

Answer