### 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

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###### 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

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Sketch the curve of the following:

i)

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

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Solve the equation

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i) Express in the form

ii) Simplify

iii) Simplify

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i) Expand y = ( 4x + 3 )2( 2x – 4 )

ii) Find

iii) Find

iv) Find for y =

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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

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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

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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.

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i) Given that find

ii) What are the co-ordinates of the stationary points of the curve

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

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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/