Click here to do these on a digital whiteboard. Note that these are a repeat of the holiday questions.
Q1
Answer
Find the values of $k$ for which the line $y = kx-4$ is tangent to the curve $y = x^2 + x$.
$k = -3, 5$
Q2
Answer
A circle has centre $C(-2, 4)$ and radius $5$.
  1. Find the equation of the circle in the form $x^2 + y^2 + ax + by + c = 0$.
  2. Show that the tangent to the circle at the point $P(-5, 8)$ has equation $3x - 4x + 47 = 0$.
  3. Verify that the point $T(3, 14)$ lies on this tangent.
  4. Find the area of triangle $CPT$.
  1. $x^2 + y^2 + 4x - 8y - 5 = 0$
  2. Use gradient of radius and perpendicularity
  3. Substitute coordinates in
  4. $25$
Q3
Answer
  1. Solve $$5^{x-1} = 120$$ giving your answer to 3 significant figures.
  2. Solve $$\log_2 x + 2\log_2 3 = \log_2(x+5)$$
  1. $3.97$
  2. $\dfrac{5}{8}$