11th grade algebra

Question 1

Solve x³ + 4x² − 5x = 0. Give all the solutions, separated by commas.

x = 

Question 2

Solve 3^(x + 2) = 27.

x = 

Question 3

Which transformation maps y = f(x) onto y = −f(x)?

• A. Vertical stretch, scale factor 5
• B. Translation 5 units right
• C. Translation 5 units up
• D. Reflection in the x-axis

Question 4

Which rule generates 1, 3, 7, 15, …?

• A. uₙ₊₁ = 2uₙ + 1
• B. uₙ₊₁ = 2uₙ − 1
• C. uₙ₊₁ = 3uₙ + 0
• D. uₙ₊₁ = uₙ + 2

Question 5

What is the x-coordinate of the vertex of y = 2x² + 8x + 11?

Answer 

Question 6

Find the sum of the first 16 terms of the arithmetic series −4 + 3 + 10 + …

Answer 

Question 7

A loan of $1700 grows by 1.5% interest each month, then a payment of $400 is made. So Bₙ₊₁ = 1.015Bₙ − 400. What is the balance after 3 months? Round to 2 decimal places.

Answer 

Question 8

Solve: |4x| ≤ 4

• A. −1 ≤ x ≤ 1
• B. −4 ≤ x ≤ 4
• C. x ≤ −1 or x ≥ 1

Question 9

u₁ = 1 and uₙ₊₁ = 3uₙ + 4. Find u₄.

Answer 

Question 10

Solve 6 × 1.2^x = 18. Give x to 3 decimal places.

Answer 

Question 11

The point (0, −4) lies on y = f(x). Where does it move to on y = 4f(x)? Type it like (2, −1).

Answer 

Question 12

When x³ + 5x² + kx − 14 is divided by (x + 2), the remainder is 0. Find k.

Answer 

Question 13

Factorise: x³ + 64

• A. (x + 4)(x² − 8x + 16)
• B. (x + 4)(x² + 4x + 16)
• C. (x + 4)³
• D. (x + 4)(x² − 4x + 16)

Question 14

The series 2 + 7 + 12 + … has a sum of 1199. How many terms are there?

Answer 

Question 15

Daniel is revising the power law of logarithms. Which statement is true?

• A. log(a/b) = log a ÷ log b
• B. log(aⁿ) = n log a
• C. log(ab) = log a × log b
• D. log(a + b) = log a + log b

Question 16

Without solving, find the product of the roots of 2x² − 11x − 7 = 0. Give a fraction if needed.

Answer (as a fraction)