A2 Maths with Mechanics Test π (pi) Version O

1) Evaluate 0π4sin2x dx, giving an exact answer.

2) Solve the equation cos2x=3 sinx+2 ()

3) Sketch y=1-2ex Show clearly any asymptotes, vertical and horizontal, and any crossings with the coordinate axes.

4) Eliminate t from this pair of equations: x=tant, y=1cost

5) A particle P of mass 0.5 kg is moving under the action of a single force F Newtons. At time t seconds, F = (1.5t 2 – 3)i + 2tj.

When t = 2, the velocity of P is

(a) Find the acceleration of P at time t seconds.

(b) Find the velocity of P when t = 3

6) Using integration by parts, find the exact integral: 23x3ex2dx

A2 Maths with Mechanics Test π (pi) Version P

1) Evaluate 0π42sin2x dx, giving an exact answer.

2) Solve the equation 2cos2x=6 sinx+4 ()

3) Sketch y=1+2ex Show clearly any asymptotes, vertical and horizontal, and any crossings with the coordinate axes.

4) Eliminate t from this pair of equations: x=cott, y=1sint

5) A particle P of mass 2 kg is moving under the action of a single force F Newtons. At time t seconds, F = (1.5t 2 – 3)i + 2tj.

When t = 2, the velocity of P is

(a) Find the acceleration of P at time t seconds.

(b) Find the velocity of P when t = 3

6) Using integration by parts, find the exact integral: 12x3ex2dx

A2 Maths with Mechanics Test π (pi) Version Q

1) Evaluate 0π43sin2x dx, giving an exact answer.

2) Solve the equation 12cos2x=32 sinx+1 ()

3) Sketch y=2+2ex Show clearly any asymptotes, vertical and horizontal, and any crossings with the coordinate axes.

4) Eliminate t from this pair of equations: x=1cosec t, y=1sect

5) A particle P of mass 0.25 kg is moving under the action of a single force F Newtons. At time t seconds, F = (1.5t 2 – 3)i + 2tj. When t = 2, the velocity of P is

(a) Find the acceleration of P at time t seconds.

(b) Find the velocity of P when t = 3

6) Using integration by parts, find the exact integral: 02x3ex2dx

A2 Maths with Mechanics Test π (pi) Version R

1) Evaluate 0π4a sin2x dx, giving an exact answer.

2) Solve the equation a2 cos2x=3a2 sinx+a ()

3) Sketch y=2-2ex Show clearly any asymptotes, vertical and horizontal, and any crossings with the coordinate axes.

4) Eliminate t from this pair of equations: x=cos t tant, y=1cosect

5) A particle P of mass 0.1 kg is moving under the action of a single force F Newtons. At time t seconds, F = (1.5t 2 – 3)i + 2tj.

When t = 2, the velocity of P is

(a) Find the acceleration of P at time t seconds.

(b) Find the velocity of P when t = 3

6) Using integration by parts, find the exact integral: 1ax3ex2dx

Answers Version O

1)  π8-14

2) 210°, 270°, 330°

3)

4) y2=x2+1

5) a) a=(3t2-6)i + 4tj

b)

6) 4e9-32e4

Answers version P

1) π4-12

2) 210°, 270°, 330°

3)

4) y2=x2+1

5) a) a=(0.75t2-1.5)i + tj

b) v =-114i+152j

6) 3e42

Answers version Q

1) 3π8-34

2) 210°, 270°, 330°

3)

4) x2+ y2=1

5a) a=(6t2-12)i + 8tj

b) 22i + 25j

6) 12+32e4

Answers Version R

1) aπ8-a4

2) 210°, 270°, 330°

3)

4) y=x

5) a) a=(15t2-30)i + 20tj

b) v = i + 55 j

6) 12ea2(a2-1)