Module 4 - Part 5

Cumulative test, lessons 15 to 18

Lesson 15     Algebraic functions
Lesson 16     Exponential equations
Lesson 17     Logarithmic equations
Lesson 18     Trigonometry

This summative assessment will allow you to measure your comprehension of the notions presented in Lessons 15, 16, 17, and 18.

Before proceeding to the questions, ensure that you have a pencil, some paper, and a calculator handy.

You may now begin the first question, or review the lessons if you wish.

For each question, click on the box corresponding to your answer, and then click on the 'Submit Answer' button.

1- Calculate the images of 3, -10 and x+h , assuming f(x) = x + 1

f(3)=4
f(-10)=-3
f(x+h)= x+1 + h
f(3)= 2
f(-10)
f(x+h)= x+h+1
f(3)= 2
f(-10)
f(x+h)= x+1 + h

2- If s(t) = v₀t + where a and v₀ are constants, calculate s(4)

s(4) = 4v₀ + 8a
s(4) = v₀ X 4 + X 16 Neither of these answers is correct.

3- If f(x) = x³ and g(x) = 2x - 1, find

5/11 1 I need help.

4- Solve the following equation: 8^2x-1 = 1/4

5/6 1/6 I need help.

5- Solve the following equation: ()^1-x =

x = -1 x = 1 I need help.

6- Solve: 3^x+1 X 27^x X 9 = 81

x = 1/4 x = -7/4 I need help.

7- Solve: 45 X 4^x = 360

x = 2/3 x = 3/2 I need help.

8- Express the following in the form of a single logarithm: log 8 - 2 X log 2 + log 3

log 6 log 7 I need help.

9- Solve: x X log 4 = 2 X log 4 - 2 X log2

x = 0 x = 1 Neither of these answers is correct.

10- With the aid of your calculator, evaluate the following expression:

-5.5775 -7.2315 Neither of these answers is correct.

11- With the aid of a calculator, and using the properties of logarithms, solve: 5^4x = 7 X 4^x

0.3852 8.7201 I need help.

12- Using triangle ABC, find the value of the following trigonometric relations:
sin A, cos A, tan A

sin A = 0.6
cos A = 0.8
tan A = 0.75
sin A = 3/5
cos A = 4/5
tan A = 3/4
Neither of these answers is correct.

13- Given triangle ABC in the diagram, find the length of the side b.

b = -7.23 b = 6.55 b = 4.59

14- Solve the equation 2x X sin 35° - cos 45° = x X cos 76°

x = 0.7811 x = -0.3126 Neither of these answers is correct.

15- A tree casts a shadow on the ground measuring 53 meters in length when the sun is at a 30° incline from the earth. What is the height of the tree?

26.5 meters tall. 45.9 meters tall. 30.6 meters tall.

1- Calculate the images of 3, -10 and x+h , assuming f(x) = x + 1
f(3)=4 f(-10)=-3 f(x+h)= x+1 + h	f(3)= 2 f(-10) f(x+h)= x+h+1	f(3)= 2 f(-10) f(x+h)= x+1 + h

2- If s(t) = v₀t + where a and v₀ are constants, calculate s(4)
s(4) = 4v₀ + 8a	s(4) = v₀ X 4 + X 16	Neither of these answers is correct.

3- If f(x) = x³ and g(x) = 2x - 1, find
5/11	1	I need help.

5- Solve the following equation: ()^1-x =
x = -1	x = 1	I need help.

6- Solve: 3^x+1 X 27^x X 9 = 81
x = 1/4	x = -7/4	I need help.

8- Express the following in the form of a single logarithm: log 8 - 2 X log 2 + log 3
log 6	log 7	I need help.

9- Solve: x X log 4 = 2 X log 4 - 2 X log2
x = 0	x = 1	Neither of these answers is correct.

10- With the aid of your calculator, evaluate the following expression:
-5.5775	-7.2315	Neither of these answers is correct.

11- With the aid of a calculator, and using the properties of logarithms, solve: 5^4x = 7 X 4^x
0.3852	8.7201	I need help.

12- Using triangle ABC, find the value of the following trigonometric relations: sin A, cos A, tan A
sin A = 0.6 cos A = 0.8 tan A = 0.75	sin A = 3/5 cos A = 4/5 tan A = 3/4	Neither of these answers is correct.

13- Given triangle ABC in the diagram, find the length of the side b.
b = -7.23	b = 6.55	b = 4.59

14- Solve the equation 2x X sin 35° - cos 45° = x X cos 76°
x = 0.7811	x = -0.3126	Neither of these answers is correct.

15- A tree casts a shadow on the ground measuring 53 meters in length when the sun is at a 30° incline from the earth. What is the height of the tree?
26.5 meters tall.	45.9 meters tall.	30.6 meters tall.