### AS Maths Core 1 video paper

A typical core 1 maths paper (72 marks).

Express 5x² – 20x + 6 in the form p (x + a)² + b  (4)

2. Sketch the graph of the following:
i) y = 1/x²  (2)

ii) What is the transformation that transforms the curve y = 1/x² to y = 3/x²  (2)

3. Simplify (2 and 3 marks)
i) (5x)2 × 3x2 / x2
ii) (27x–3)–⅓

4. Solve the simultaneous equations
y = 2( x – 3 )² and 11x + y = 39  (5)

5. Express
i) √500  –   √245
in the form a√5 where a is an integer (3)

ii) 18 + √8 / 6 in the form a√5 + b√3, a and b are integers (3)

6. Solve 4x – 15x + 9 = 0  (5)

7. Solve the inequalities
i) – 11 ≤ 7x + 3 ≤ 0  (3)

ii) 7x + 6 < x² + 3x – 15   (5)

8. i) Find the co-ordinates of the stationary point on the curve y=12x² – 3/x – 4  (5)

ii) Determine whether the stationary point is a maximum or a minimum (2)

9. Points P (3, 8) , Q(5,–2) and R (– 1, 2 ) are joined to form a triangle.
i) Show that the triangle is right angled and state whether the right angle is at R  (5)

ii) Points P, Q and R lie on the circumference of a circle.
Find the equation of the circle in the form
x² + y² + ax + by + c = 0  (7)

10. y = (x – 2 )( x – 3)(x + 2) is a curve.
i) Sketch the curve indicating the co-ordinates of all point of intersection with the axis.  (3)
ii) Show that the gradient of the curve at A (3 , 0) is 5  (6)
iii) The line L is parallel to the tangent to the curve at point A. The curve meets L at a point where x = –1 .
Find the equation of L giving your answer in the form y = mx + c  (4)
iv) Determine whether L is a tangent to the curve at the point where x = –1  (3)