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


ANS

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  


ANS

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


ANS

4. Solve Quadratic equation  Menu

Solve the equation solve quadratic equation


ANS



5. Surds  Menu

i) Express in the form

ii) Simplify

iii) Simplify


ANS

6. Differentiation  Menu

 i) Expand y = ( 4x + 3 )2( 2x – 4 )

ii) Find

iii) Find

iv) Find for y =


ANS

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


ANS

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.


ANS
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

ANS
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


ANS


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/

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