Given that $3x^2 + bx + 10 \equiv a(x + 3)^2 + c$, find the constants $a$, $b$ and $c$.
$a = 3$, $b = 18$, $c = -17$
Q2
Answer
Find the coordinates of the points of intersection of the curve $y = 12 - x - x^2$ and the line $3x + y = 4$.
$(4, -8)$ and $(-2, 10)$
Q3
Answer
Solve $12 - x - x^2 > 0$.
$-4 < x < 3$
Q4
Answer
Express $\dfrac{4}{3-\sqrt{7}}$ in the form $a + b\sqrt{7}$ where $a$ and $b$ are integers.
$7\sqrt{5}$
Q5
Answer
Find the gradient of the curve $y = 2x^2$ at the point where $x = 3$
Find the coordinates of the point on the curve $y = 2x^2$ where the gradient of the normal is $\dfrac{1}{8}$.
The points $A(1, y_1)$, $B(1.01, y_2)$ and $C(1.1,y_3)$ lie on the curve $y = kx^2$. The gradient of the chord $AC$ is $6.3$ and the gradient of the chord $AB$ is $6.03$. Write down the gradient of the curve at $A$ and deduce the value of $k$.
$12$
$(-2,8)$
Gradient $6$, $k = 3$
Q6
Answer
A circle has equation $x^2 + y^2 - 6x - 10y - 30 = 0$. Find the centre and radius of the circle.