Revise with this OCR core 2 maths online test(1) with answers. (detail at end)

72 marks, A=80%, B=70% etc

The 30th term of an arithmetic progression is 77 and the 40th term is 107.

i) Find the first term and the common difference.

ii) Show that the sum of the first 26 terms is 715.

ANS

Triangle XYZ has XY = 20cm, YZ = 5 cm and angle Y = 60. Calculate

i) the length of third side ZX,

ii) the area of the triangle,

iii) the size of angle X.

ANS

i) Find the first three terms of the expansion, in ascending powers of x, of (1 – 3x)^{10}

ii) Hence find the coefficient of x^{2} in the expansion of

(1 + x)(1 – 3x)^{10}

ANS

In the figure, OAB represents a sector of a circle with centre O.

The angle AOB is 1.5 radians. The points C and D lie on OA and OB respectively.

It is given that OA = OB = 30 cm and OC = OD = 20 cm. The shaded region is bounded by the arcs AB and CD and by the lines CA and DB.

i) Find the perimeter of the shaded region.

ii) Find the area of the shaded region.

ANS

The first term of a geometric progression is 6 and the second term is 5.1.

i) Find the sum to infinity.

ii) The sum of the first n terms is > 30.

Show that 0.85^{n} < 0.25, and use logarithms to calculate the smallest possible value of n.

ANS

Express the following in terms of log_{10}*u* and log_{10}v

i)

ii)

iii) Given that

.

Find the value of *v* correct to 3 decimal places.

ANS

ƒ(x) is a polynomial given by x^{3} + px^{2} – 5x + 6 = 0. One of its factor is (x – 3)

i) Find the value of p and factorise ƒ(x) completely.

ii) Find .

iii) Sketch the polynomial.

Show that the area of the region between ƒ(x) and the x-axis over the interval (–2, 3) is given by the sum of the areas of the regions between the interval (–2, 1) and (1, 3)

ANS

i) Sketch on one graph, with values of x from –180 ° to 180° the graphs of

and y = 2 cos x,

ii) The equation has two roots α and β in the interval –180 ° ≤ x ≤ 180°

Mark α and β on the sketch and express β in terms α.

iii) Show that the equation can be written as

and hence find the value of β – α.

Detailed answer paper at core-2-ocr-ans-paper-1 dot pdf

NB this is not a link, type the address in after the .co.uk/

NB this is not a link, type the address in after the .co.uk/

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