Ontario Secondary School Diploma (OSSD) · Mathematics (Grades 11 and 12)
Functions and Algebra
51 practice questions, each with the answer and an explanation.
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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.
All 51 questions
- If f(x) = 3x - 2, what is f(4)?
- What is the domain of f(x) = sqrt(x - 5) over the real numbers?
- Solve x^2 - 5x - 14 = 0.
- What is the vertex of y = (x - 3)^2 + 4?
- What is the discriminant of 2x^2 - 3x + 5, and what does it say about the roots?
- What is the inverse of f(x) = 2x + 6?
- Which describes y = -2(x - 4)^2 + 1 compared with y = x^2?
- Solve 2^(x + 1) = 32.
- What is log base 3 of 81 plus log base 3 of 9?
- A 80 g sample has a half-life of 5 days. About how much remains after 12 days?
- How much is $2000 worth after 3 years at 6% interest compounded annually?
- Factor 6x^2 + 7x - 3.
- Solve |2x - 3| = 7.
- Simplify (x^2 - 9)/(x^2 + x - 12) and state the restrictions.
- Solve the system 2x + y = 7 and x - y = 2.
- P(x) = x^3 + 2x^2 - 5x + 1 is divided by x - 2. What is the remainder?
- A ball's height is h = -5t^2 + 20t + 1.5 metres. What is its maximum height?
- For which values of k does x^2 + kx + 9 = 0 have exactly one real root?
- Solve 3/(x - 1) = 6/(x + 2).
- What is the y-intercept of y = 2x^2 - 8x + 5?
- A culture of 500 bacteria doubles every 3 hours. How many are there after 9 hours?
- What is the vertex of the parabola y = (x + 1)² - 5?
- What is the vertex of the parabola y = (x - 2)² - 6?
- What is the vertex of the parabola y = (x + 2)² - 6?
- Which single logarithm equals log 2 + log 3?
- If f(x) = 2x + 4 and g(x) = 2x + 4, what is f(g(2))?
- A sample of 640 g of a radioactive isotope has a half-life of 10 days. How much remains after 20 days?
- Solve for x: log base 2 of x = 3.
- How many real roots does 3x^2 - 4x + 1 = 0 have?
- What is the remainder when 3x^3 + 4x^2 + 3x - 8 is divided by (x - 3)?
- A sample of 240 g of a radioactive isotope has a half-life of 12 days. How much remains after 24 days?
- How many real roots does 2x^2 - 5x + 3 = 0 have?
- The first term of an arithmetic series is 3, the common difference is 5 and there are 10 terms. What is the sum?
- If f(x) = 3x + 0 and g(x) = 2x + 4, what is f(g(2))?
- For what value of c is (x - 3) a factor of x² + 1x + c?
- For what value of c is (x - 3) a factor of x² + c?
- For what value of c is (x + 1) a factor of x² + 3x + c?
- What is the vertex of the parabola y = (x - 1)² + 2?
- What is the vertex of the parabola y = (x - 5)² - 6?
- Solve for x: log base 2 of x = 2.
- A sample of 320 g of a radioactive isotope has a half-life of 5 days. How much remains after 20 days?
- The first term of an arithmetic series is 2, the common difference is 4 and there are 10 terms. What is the sum?
- If f(x) = 4x + 5 and g(x) = 2x - 1, what is f(g(3))?
- Solve for x: log base 3 of x = 3.
- Solve for x: log base 2 of x = 4.
- How many real roots does x^2 + 6x + 3 = 0 have?
- What is the remainder when 2x^3 - x^2 + 4x - 3 is divided by (x + 2)?
- A sample of 320 g of a radioactive isotope has a half-life of 12 days. How much remains after 36 days?
- How many real roots does 2x^2 - x - 4 = 0 have?
- For what value of c is (x - 2) a factor of x² + 4x + c?
- For what value of c is (x - 3) a factor of x² + 3x + c?
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