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

1. Inequalities  Menu

Solve the inequality x2 – 9x – 22 ≥ 0


2. Complete the square  Menu

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  Menu

Sketch the curve of the following:

i) transformation

The curve transforming graphs 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  Menu

Solve the equation solve quadratic equation


5. Surds  Menu

i) Express surds in the form surds 2

ii) Simplify surds 3

iii) Simplify


6. Differentiation  Menu

 i) Expand y = ( 4x + 3 )2( 2x – 4 )

ii) Find

iii) Find

iv) Find for y =


7. Roots, discriminant  Menu

 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 minimum point

iv) State the number of real roots of the equation 4x2 – 4x + 7


8. Simultaneous equation  Menu

  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.

9.Co-ordinate geometry  Menu

 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  Menu

 i) Given that find

ii) What are the co-ordinates of the stationary points of the curve stationary points
Leave your answer as a fraction

iii) Determine whether each stationary point is a maximum or minimum

iv) Given that 12x + 2y – 5 = 0 is the equation of the tangent to the curve at the point (a , b ).
Find a and b


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/