10th grade algebra

Question 1

Solve x² − 8x − 4 = 0 with the quadratic formula. Simplify fully.

• A. x = 4 ± 4√5
• B. x = 8 ± 2√5
• C. x = −4 ± 2√5
• D. x = 4 ± 2√5

Question 2

Which is equal to 1/∛x?

• A. x^(3/1)
• B. −x^(1/3)
• C. x^(−3)
• D. x^(−1/3)

Question 3

Solve x² + 3x − 3 = 0 using the quadratic formula. Give the larger solution to 2 decimal places.

Answer 

Question 4

Work out the discriminant of 4x² + 9x − 3 = 0.

Answer 

Question 5

f(x) = −x + 3 and g(x) = 3x + 1. Find f(g(x)) and simplify.

Answer 

Question 6

Solve the system y = x² + 5x − 12 and y = 3x + 3. Give the x-values, separated by a comma.

x = 

Question 7

f(x) = x² − 1 and g(x) = 3x − 1. Find f(g(x)) and simplify.

Answer 

Question 8

Simplify: (x² − 9)/(x + 3)

• A. (x − 3)
• B. (x² − 3)
• C. (x + 3)
• D. 1/(x − 3)

Question 9

x² + 6x + k = 0 has exactly one (repeated) root. Find k.

Answer 

Question 10

Solve: x² − 5x − 24 < 0

• A. x < −3 or x > 8
• B. x < −8 or x > 3
• C. −3 < x < 8
• D. −8 < x < 3

Question 11

Write x² − 6x + 8 in the form (x + p)² + q. What is q?

Answer 

Question 12

Write ∛(x²) as a power of x.

• A. x^(3/2)
• B. x^(-1)
• C. x^(2/3)
• D. x^(−2/3)

Question 13

Simplify: (x² − 4)/(x + 2) × (x + 2)/(x − 2)

• A. (x + 2)
• B. 1
• C. (x − 2)
• D. x² − 4

Question 14

What is the domain of f(x) = √(−7 − x) (real numbers only)?

• A. x > −7
• B. x ≤ −7
• C. x ≥ −7
• D. x ≠ −7

Question 15

How many real solutions does 2x² + 10x + 3 = 0 have?

• A. Two
• B. One (repeated)
• C. None

Question 16

Factorise: 5x² + x − 6

• A. (5x − 6)(x + 1)
• B. (5x + 6)(x − 1)
• C. (x + 6)(5x − 1)
• D. (5x − 1)(x + 6)