Elective Maths 25

Elective Maths 25

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Question 1 of 20

1. Question
If $\int_{-2}^{3}{(ct-1)dt=0}$ find the value of c.
- -2
- – 2/5
- 2/5
- 2
Correct

Incorrect
Question 2 of 20

2. Question
Evaluate $\int_{-1}^{1}{(x^3-x)dx}$
- -1
- -1/2
- 0
- ½
Correct

Incorrect
Question 3 of 20

3. Question
Evaluate $\int_{1}^{2}{(4x^3-6x^2+1)dx}$ .
- 2
- 3
- 4
- 5
Correct

Incorrect
Question 4 of 20

4. Question
Evaluate $\int_{0}^{3}{(x+1)(2x+1)dx}$
- 24
- 25
- 21
- 18
Correct

Incorrect
Question 5 of 20

5. Question
Evaluate $\int_{1}^{3}{(3x^2+2x-5)dx}$
- 34
- 25
- 24
- 18
Correct

Incorrect
Question 6 of 20

6. Question
The gradient of a curve is given by 2x-5. If the curve passes through the point P(1,2), find its equation.
- $y=x^2 -5x$
- $y=x^2 -5x-6$
- $y=x^2 -5x+2$
- $y=x^2 -5x+6$
Correct

Incorrect
Question 7 of 20

7. Question
The velocity of a particle in ms^-1 after time t seconds, is v=3t² +2t. Find the distance, s, travelled after 3 seconds given that s = 0 when t = 0.
- 36 m
- 33 m
- 27 m
- 18 m
Correct

Incorrect
Question 8 of 20

8. Question
A particle starts from rest and moves in a straight line in a such a way that its velocity, v ms^-1 at time t seconds is given by . Calculate the distance travelled in the first 4 seconds
- 12 m
- 16 m
- 64 m
- 96 m
Correct

Incorrect
Question 9 of 20

9. Question
The gradient of a curve is given by $\frac{dy}{dx}=2x+5$ . If (-1,2) lies on the curve. Find its equation.
- $x^2 + 5x +6$
- $\frac{1}{2}x^2 + 5x +6$
- $x^2 + 5x -6$
- $x^2 - 5x +6$
Correct

Incorrect
Question 10 of 20

10. Question
A particle starting from rest has an acceleration (8 – 2t)ms^-2 at time t. When will the particle come to rest again?
- 2 seconds
- 4 seconds
- 6 seconds
- 8 seconds
Correct

Incorrect
Question 11 of 20

11. Question
A curve passes through the point (2,7) and the gradient function is 6x² -8x+1. Find the equation of the curve.
- $y =x^3 -4x^2 +x+5$
- $y=2x^3 +x^2 +x-5$
- $y=2x^3 -4x^2 +x-5$
- $y=2x^3 - 4x^2 +x+5$
Correct

Incorrect
Question 12 of 20

12. Question
The gradient of a curve at any point (x, y) is 2x . If the curve passes through the point (4,9), find its equation.
- $y=x^2$
- $y =x^2 -7$
- $y=x^2 -65$
- $y =x^2 +7$
Correct

Incorrect
Question 13 of 20

13. Question
The gradient of a curve is given by $\frac{dy}{dx}=\ 2x\ +\ 3$ . If (1,2) lies on the curve, find the equation of the curve.
- $y=2x^2 +3x+1$
- $y=x^2 +3x-9$
- $y =x^2 +3x+1$
- $y =x^2 +3x-2$
Correct

Incorrect
Question 14 of 20

14. Question
Calculate, correct to two decimal places, the area enclosed by the line 3x-5y + 4=0 and the axes.
- 0.50
- 0.51
- 0.53
- 0.54
Correct

Incorrect
Question 15 of 20

15. Question
The gradient function of a curve is given by f'(x)=3x² -8x +5. If 2 is the root of the equation of the curve, find the equation of the curve. A. 6x-8
- 6x-8
- $3x^3-8x^2+5x$
- $x^3-4x^2+5x+2$
- $x^3-4x^2+5x-2$
Correct

Incorrect
Question 16 of 20

16. Question
The speed, v ms ^-1 of a body moving in a straight line is given by v=24t – 3t² time t seconds. Find the distance at the end of 3 seconds.
- 6m
- 42 m
- 81 m
- 135 m
Correct

Incorrect
Question 17 of 20

17. Question
The gradient function of a curve is given by f'(x)=3×2 -2x -1. If the curve passes through the point (1,1), find its equation.
- $f(x)=x^3-5x^2+2x+2$
- $f(x)=x^3-x^2-x+2$
- $f(x)=x^3-x^2-x+4$
- $f(x)=x^3-x^2-x+2$
Correct

Incorrect
Question 18 of 20

18. Question
A particle is projected from a point, O with a speed of 5 ms^-1. It moves in a straight line with an acceleration of (6- 2t) ms^-2, t seconds after leaving O. Calculate the speed after 2 seconds
- $2 ms^{-1}$
- $7 ms^{-1}$
- $13 ms^{-1}$
- $14 ms^{-1}$
Correct

Incorrect
Question 19 of 20

19. Question
A particle is projected from a point, O with a speed of 5 ms^-1. It moves in a straight line with an acceleration of (6- 2t) ms^-2, t seconds after leaving O. Calculate the maximum speed of the particle.
- $27 ms^{-1}$
- $14 ms^{-1}$
- [latex]10 ms^{-1}[/latex]
- $9 ms^{-1}$
Correct

Incorrect
Question 20 of 20

20. Question
The gradient of a curve is 4x. If the point (2,0) lies on the curve, find its equation.
- $y= x^2 +8$
- $y= x^2 -8$
- $y= 2x^2 +8$
- $y= 2x^2 -8$
Correct

Incorrect

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