Maths4U Original · Short practice

Consider \(y=\left(- x - 1\right) \left(x - 3\right)\). The product form is given.

Find the smaller x-intercept.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Consider \(y=\left(x - 4\right) \left(x + 2\right)\). The product form is given.

Find the smaller x-intercept.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Consider \(y=\left(x - 4\right) \left(x + 2\right)\). The product form is given.

Find the larger x-intercept.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Consider \(y=\left(- x - 3\right) \left(x - 5\right)\). The product form is given.

Find the larger x-intercept.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Consider \(y=\left(- x - 3\right) \left(x - 5\right)\). The product form is given.

The symmetry line is \(\displaystyle x=k\). Find k.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Consider \(y=\left(x - 2\right) \left(x + 1\right)\). The product form is given.

The symmetry line is \(\displaystyle x=k\). Find k.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Consider \(y=\left(x - 6\right) \left(x + 4\right)\). The product form is given.

Find the y-intercept.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Consider \(y=\left(- x - 5\right) \left(x - 7\right)\). The product form is given.

Find the y-intercept.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle f(x)=3 + \frac{2}{x}\) on its full real domain.

The horizontal asymptote is \(\displaystyle y=k\). Find k.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle f(x)=4 + \frac{3}{x}\) on its full real domain.

The horizontal asymptote is \(\displaystyle y=k\). Find k.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle f(x)=4 + \frac{3}{x}\) on its full real domain.

Find f(1).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle f(x)=5 + \frac{4}{x}\) on its full real domain.

Find f(1).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle f(x)=5 + \frac{4}{x}\) on its full real domain.

Find the x-intercept.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle f(x)=6 + \frac{5}{x}\) on its full real domain.

Find the x-intercept.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle f(x)=6 + \frac{5}{x}\) on its full real domain.

For an allowed input x, find x(f(x)−6).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle f(x)=1 + \frac{6}{x}\) on its full real domain.

For an allowed input x, find x(f(x)−1).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=3\times 2^x+3\) for real x.

The horizontal asymptote is \(\displaystyle y=k\). Find k.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=4\times 3^x+4\) for real x.

The horizontal asymptote is \(\displaystyle y=k\). Find k.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=4\times 3^x+4\) for real x.

Find f(0).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=5\times 4^x+5\) for real x.

Find f(0).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=5\times 4^x+5\) for real x.

Find f(1).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=1\times 2^x+6\) for real x.

Find f(1).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=1\times 2^x+6\) for real x.

Solve \(\displaystyle f(x)=10\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=2\times 3^x+7\) for real x.

Solve \(\displaystyle f(x)=61\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(P(x)=3 x \left(x - 8\right) \left(x - 3\right)\).

Find the smaller positive root.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(P(x)=4 x \left(x - 10\right) \left(x - 4\right)\).

Find the smaller positive root.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(P(x)=4 x \left(x - 10\right) \left(x - 4\right)\).

Find the larger positive root.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(P(x)=x \left(x - 3\right) \left(x - 1\right)\).

Find the larger positive root.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(P(x)=x \left(x - 3\right) \left(x - 1\right)\).

Find the coefficient of x in the expansion.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(P(x)=2 x \left(x - 5\right) \left(x - 2\right)\).

Find the coefficient of x in the expansion.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(P(x)=2 x \left(x - 5\right) \left(x - 2\right)\).

Find P(−1).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(P(x)=3 x \left(x - 7\right) \left(x - 3\right)\).

Find P(−1).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=4 x^{5} - 5 x + 1\).

Find the coefficient of \(\displaystyle x^4\) in f′(x).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=x^{3} - 6 x + 2\).

Find the coefficient of \(\displaystyle x^2\) in f′(x).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=x^{3} - 6 x + 2\).

Find the constant term of f′(x).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=2 x^{4} - 7 x + 3\).

Find the constant term of f′(x).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=2 x^{4} - 7 x + 3\).

Find the gradient at \(\displaystyle x=2\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=3 x^{5} - 8 x + 4\).

Find the gradient at \(\displaystyle x=3\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=3 x^{5} - 8 x + 4\).

Find f″(1).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=4 x^{3} - 2 x - 4\).

Find f″(1).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=x^{3} - 3 x + 6\).

Find the smaller stationary x-coordinate.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=2 x^{3} - 24 x + 7\).

Find the smaller stationary x-coordinate.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=2 x^{3} - 24 x + 7\).

Find the larger stationary x-coordinate.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=3 x^{3} - 81 x + 8\).

Find the larger stationary x-coordinate.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=3 x^{3} - 81 x + 8\).

Find the local maximum value.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=4 x^{3} - 192 x + 9\).

Find the local maximum value.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=4 x^{3} - 192 x + 9\).

Find the local minimum value.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(f(x)=x^{3} - 75 x + 2\).

Find the local minimum value.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.