MECHANICS A2 Tracking Test 4

Time 1 hour

50 marks total

7 QUESTIONS

NAME …………………

EXPECTED GRADE BEFORE ………………

PREDICTED GRADE AFTER ………………

1. 

Given that the binomial expansion of (1 + kx)–4, < 1, is

1 – 6x + Ax2 + …

(a) find the value of the constant k,

(2)

(b) find the value of the constant A, giving your answer in its simplest form.

(3)

2.

The curve C has the equation ye–2x = 2x + y2.

(a) Find in terms of x and y.

(5)

The point P on C has coordinates (0, 1).

(b) Find the equation of the normal to C at P, giving your answer in the form ax + by + c = 0, where a, b and c are integers.

(4)

3.

f(x) = = + + .

(a) Find the values of the constants A, B and C.

(4)

(b) (i) Hence find .

(3)

(ii) Find in the form ln k, where k is a constant.

(3)

4.

Figure 2

Figure 2 shows a sketch of the curve with equation y =, 0 £ x £ 3.

The finite region R, shown shaded in Figure 2, is bounded by the curve, the x-axis, and the yaxis.

(a) Use the substitution x = 1 + 2 sin q to show that

= ,

where k is a constant to be determined. (5)

(b) Hence find, by integration, the exact area of R.

(3)

5.

Find .

(5)

6.

Figure 1

The uniform lamina OABCD, shown in Figure 1, is formed by removing the triangle OAD from the square ABCD with centre O. The square has sides of length 2a.

(a) Show that the centre of mass of OABCD is a from O.

(4)

7.

A particle P moves on the positive x-axis. The velocity of P at time t seconds is

(2t2 – 9t + 4)ms–1. When t = 0, P is 15 m from the origin O.

Find

(a) the values of t when P is instantaneously at rest,

(3)

(b) the total distance travelled by P in the interval 0 £ t £ 5. (5)

c) the acceleration of P in terms of t (1)

NOW CHECK FOR EXPENSIVE ERRORS

Total: 50 marks

MECHANICS A2 Tracking Test 4 – MARK SCHEME

1.

(a) / Either or / see notes / M1
leading to / / A1
[2]
(b) / / Either or or / M1
Either or / M1
/ or 22.5 / A1
[3]

2.

(a) / A1 correct RHS / M1 A1
/ B1
/ M1
/ A1 (5)
(b) / At P, / M1
Using / M1
/ M1
or any integer multiple / A1 (4)
(9 marks)

3.

(a) /
/ M1
A method for evaluating one constant / M1
, any one correct constant / A1
,
, all three constants correct / A1 (4)
(b) (i) /
A1 two ln terms correct / M1 A1ft
All three ln terms correct and “+C” ; ft constants / A1ft (3)
(ii) /
/ M1
/ M1
/ A1 (3)
(10 marks)

4.

5.

(a) / , 1st Application: , 2nd Application:
/ , / M1
/ A1 oe
/ Either
or for / M1
/ / M1
Correct answer, with/without / A1
(5)

6.

7.

a)

b)

c)