### 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 x^{2} – 9x – 22 ≥ 0

ANS
Marks shown at end question i.e. [2]

i) x ≥ 11 or x ≤ –2 [4]

###### 2. Complete the square
Menu

i) Express 5x^{2} + 30x + 36 in the form

5(x + a)^{2} + b

ii) Hence write down the equation of the line of symmetry of the curve 5x^{2} + 30x + 36

ANS
Marks shown at end question i.e. [2]

i) 5 (x + 3)^{2} – 9 [4]

ii) x = – 3 [1]

###### 3. Graph transformations
Menu

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 = x^{3} to y = (- x)^{3}

ANS
Marks shown at end question i.e. [2]

i)

[1]

ii) [2]

iii) Reflect the curve in the y-axis (or x-axis) [2]

###### 4. Solve Quadratic equation
Menu

Solve the equation

ANS
Marks shown at end question i.e. [2]

i) y = 27/125 or y = –8 [5]

###### 5. Surds
Menu

i) Express in the form

ii) Simplify

iii) Simplify

ANS
Marks shown at end question i.e. [2]

i) 10 + 2√7 [3]

ii) 12 y^{5/4} [2]

iii) 72 [2]

###### 6. Differentiation
Menu

i) Expand y = ( 4x + 3 )^{2}( 2x – 4 )

ii) Find

iii) Find

iv) Find for y =

ANS
Marks shown at end question i.e. [2]

i) 32x^{3} – 16x^{2} – 78x – 36 [3]

ii) 96x^{2} – 32x – 78 [2]

iii) 192x – 32 [2]

iv) 1/5 x^{–4/5} [2]

###### 7. Roots, discriminant
Menu

i) State the number of real roots of the equation

5x^{2} + 30x –3 = 0

ii) Calculate the discriminant of
4x^{2} – 4x + 7

iii) Sketch the curve 4x^{2} – 4x + 7

Label the points where it crosses the axes and the
minimum point

iv) State the number of real roots of the equation
4x^{2} – 4x + 7

ANS
Marks shown at end question i.e. [2]

i) 2 roots [1]

ii) discriminant is 0 [1]

iii) 4x^{2} – 4x + 7 = (x – 2)^{2} + 3

[2]

iv) No real roots - does not cross x axis [1]

###### 8. Simultaneous equation
Menu

a) Describe the curve (x – 5 )^{2} + y^{2} = 36

b) Find the co-ordinates of the points of intersection of the curve and line given below.

x^{2} + y^{2} = 4

y – 2x – 1 = 0

Leave your answer in surd form.

ANS
Marks shown at end question i.e. [2]

i) A circle with centre ( 5 , 0) and radius = 6 [2]

ii) [5]

###### 9.Co-ordinate geometry
Menu

i) What is the gradient of a line *l*_{1} which has the equation
5x –2y + 3 = 0

ii) Find the equation of a line *l*_{2} which passes through the point (2, 3) which is perpendicular to the line *l*_{1}.

Give your answer in the form ax + by + c = 0

Line* l*_{1} crosses the x-axis at A and line *l*_{2} 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
Marks shown at end question i.e. [2]

i) 5/2 [1]

ii) 2x + 5y – 19 = 0 [4]

iii) (– 3/10, 19/10) [3]

iv) √370/5 [3]

###### 10. Stationary points
Menu

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/