ALS International School

Academic Year 20 22 -2023

Fourth Quarter
Mathematics Exam
Grade 12
Question Marks
Question 1
Question 2
Question 3
Bonus

Total

1
 Fourth Quarter Exam Section 2022 / 2023
Grade 11 Math department

Question (1 )

1. Find the integral of x4 /5 dx

A x4+ C B x5+ C

C 1/5(x5) + C D x5

2. Find the integral of (3x2+2x)*(x3+x2)dx

A (x3+x2)2/2 + C B x(5x2+10x+6) + C

C 3x3+6x2+2x + C D x2(15x2+20x+6) + C

3. Find the integral of 2x*exdx

A ex(2x+2) + C B 2ex+ C

C (x-2)ex+ C D ln(2x) + C

4. A vehicle is moving at a velocity given by the equation v = 5(x3+4)/8, find the position at x
= 4 if when x = 2, p = 25/2

A 66 B 14

C 55 D 75

5. Find the equation for the velocity of an object whose acceleration is equal to 4x+14.

A 2x2+ 14x + C B 2x3/3+7x2+C

C 2x3/3+7x2 D 4+C

6. Find the area under a curve defined by the equation 5x4+3x+7 between the x values 0
and 4.

A 1200 B 1076

C 1/12 D 1134
 7. Find the integral of sinh x dx

A cosh x +C B C

C cos x + C

8. Find the integral of cosh x dx

A
sinh x + C C
B)

C sin x + C

9) What is the integral of sin u du answer choices

10. Find the integral of dx/x

A 1+C B dx + C

C -1/x2+ C D ln(x) + C
Question (2 )

1. Find the integral of -6sin(3x)dx

C 2cos(3x) + C D -2cos(3x)

2. Find the anti-derivative of sec2(4x)dx

A 8sec2(4x) + C B tan(4x)/4 + C

C -1/4tan(4x) + C D 8sec2(4x)tan(4x) + C

3.. ∫ (x−2 2 x )dx

A 2x − 2 B x2 −2x + C
1 3 2 1 3 2
C x −x +C D x −x
3 3
4. Find the integral of 4x3+7x6+5x4dx

A 12x2+ 42x5+ 20x3+ C B 4x3/3 + 7x6/6 + 5x4/4 + C

C x7 + x5 + x4 + C D 4x4/3 + 7x7/6 + 5x5/4 + C

5. Find the velocity of a vehicle whose acceleration is defined by the equation x2+4x+3, when
C=3 and x=6.

A 162 B 83

C 165 D 365

6.. ∫ 6x (x + 2) dx

A 2x3 +6x2 +C B x2 −2x + C

C 6x2 +12x + C D 3x2 +6x + C

7) ∫ 4 sin (−x) dx

A 4 cos (x) + C B −4 cos (−x) + C

C −4 sin (−x) + C D 4 cos (−x) + C

8)
What is the integral of cosu du?
A) -sinu B) sinu
C) -sinu + C D) sinu + C

9) u
What is the integral of e du?

A) eu C) eu +C
B) -eu D) -eu + C
1. What would you choose for your u here if you used integration by
parts?

A t B et

C 3t D don't use IBP, let u = 2t

E e2t

2.

3.

4.

5. What is the Integration by Parts Formula?

A B

C D
6. What would you choose for your u here if you used integration by parts?

A e-x B x4

C ex D x

7.

A B

C D

8. Solve via integration by parts

A 3(e2t) - (e2t)/4 + C B 3t(e2t)/2 - (e2t)/4 + C

C 3t(e2t)/2 - 3(e2t)/4 + C D 3t(e2t)⋅2 - 3(e2t)⋅4 + C

9. What method would you use here?

A u-substitution B normal integration

some method my teacher never taught