# Jupeb 2021 Mathematics Answers for 2021 Examinations

[9:23 am, 20/09/2021] DR: 1. D   2. C
3. A
4. C
5. D
[9:39 am, 20/09/2021] DR: JUPEB

[9:46 am, 20/09/2021] DR: JUPEB
[9:50 am, 20/09/2021] DR: Jupeb

[9:57 am, 20/09/2021] DR: JUPEB MATHS

(7a)
(i) Hypothesis is an assumption that is made on the basis of some evidence. This is the initial point of any investigation that translates the research questions into a prediction. It includes components like variables, population and the relation between the variables. A research hypothesis is a hypothesis that is used to test the relationship between two or more variables.

(ii) The null hypothesis often denoted H0 is a default hypothesis that a quantity to be measured is zero or null. A null hypothesis is a type of conjecture used in statistics that proposes that there is no difference between certain characteristics of a population or data-generating process.

(iii) An alternative hypothesis is one in which a difference or an effect bet…
[10:11 am, 20/09/2021] DR: Jupeb obj
[10:11 am, 20/09/2021] DR: Obj solutions
1D 2C 3A 4C 5D 6B 7B 8B 9B 10B 11C 12B 13B 14B 15D 16. 3t/2 17C 18A 19A 20C

36C 37B 38C 39

47B 48C 49D 50A

Solving the rest
[10:28 am, 20/09/2021] DR: 3a. ∫ e^(3x) + 3 dx
—————–
(e^(3x) + 9x + 2)

from denominator :

d(e^(3x) + 9x + 2)/dx = 3e^(3x) + 9 = 3(e^(3x) + 3)

Following Integral property :

∫ f'(x)/f(x) dx = Ln|f(x)| + C

Hence : ∫ e^(3x) + 3 dx
—————–
(e^(3x) + 9x + 2) =

Ln|e^(3x) + 9x + 2| + C

b. ∫ 8x dx
———
(3 + 2x)⁴

set (3 + 2x) = u

x = (u – 3)/2

du/dx = 2 : dx = du/2 , by transformation

∫ 4(u – 3)du/2u⁴

2∫(u – 3)du/u⁴ = 2∫(1/u³ – 3/u⁴)du = – 1/2u² + 1/u³ + C

Recall u = 3 + 2x

Integral = – 1/2(3 + 2x)² + 1/(3 + 2x)³ + C