GCE Maths Core 1 online (OCR)
Revise with this OCR core 1 maths online test(1) with answers. (detail at end)
72 marks, A=80%, B=70% etc
Solve the inequality x2 – 9x – 22 ≥ 0
2. Complete the square
i) Express 5x2 + 30x + 36 in the form
5(x + a)2 + b
ii) Hence write down the equation of the line of symmetry of the curve 5x2 + 30x + 36
3. Graph transformations
Sketch the curve of the following:
The curve is stretched by a scale factor of ½ parallel to the x-axis.
ii) What is the equation of the curve after it has been transformed.
iiii) What is the transformation that transforms the curve y = x3 to y = (- x)3
4. Solve Quadratic equation
Solve the equation
7. Roots, discriminant
i) State the number of real roots of the equation
5x2 + 30x –3 = 0
ii) Calculate the discriminant of
4x2 – 4x + 7
iii) Sketch the curve 4x2 – 4x + 7
Label the points where it crosses the axes and the
iv) State the number of real roots of the equation
4x2 – 4x + 7
8. Simultaneous equation
a) Describe the curve (x – 5 )2 + y2 = 36
b) Find the co-ordinates of the points of intersection of the curve and line given below.
x2 + y2 = 4
y – 2x – 1 = 0
Leave your answer in surd form.
i) What is the gradient of a line l1 which has the equation
5x –2y + 3 = 0
ii) Find the equation of a line l2 which passes through the point (2, 3) which is perpendicular to the line l1.
Give your answer in the form ax + by + c = 0
Line l1 crosses the x-axis at A and line l2 crosses the y-axis at B
iii) What are the co-ordinates of the mid-point of AB
iv) Calculate the length of AB.
Give your answer in the form
10. Stationary points
Detailed answer paper at core-1-ocr-ans-paper-1 dot pdf
NB this is not a link, type the address in after the .co.uk/