Nouns Exercise

Nouns Exercise

Free Prefixes and Suffixes Worksheets from The Teacher's Guide

Free Prefixes and Suffixes Worksheets from The Teacher's Guide

NON-FINITES EXERCISE

Rewrite the following sentences by changing the participle into a finite verb

1. Having learnt his lesson, he went out  to play cricket.

2. Walking along the street one day, I saw a dead cobra.

3. Leaving the forest we advanced into the open plain.

4. Driven out of his country, he sought asylum in a foreign land.

5. It being a very hot day, I remained in my tent.

6. A gipsy, wandering across the meadows, found the child.

7. I once saw a man walking on a rope.

8. Not knowing my way, I asked a policeman.

9. Hearing the noise, I woke up.

10. Being paralytic, he could not walk.

Answers

1. After he learnt his lesson, he went out to play cricket.

2. While I was walking along the street one day, I saw a dead cobra.

3. We left the forest and advanced into the open plain.

4. As he was driven out of his country, he sought asylum in a foreign land.

5. As it was a very hot day, I remained in my tent.

6. A gipsy found the child while he was wandering across the meadows.

7. I once saw a man who was walking on a rope.

8. As I did not know my way, I asked a policeman.

9. When I heard the noise, I woke up.

10. As he was paralytic, he could not walk.

VOLUME OF HEXAGONAL PRISM

DIFFERENTIATION OF EXPONENTIAL FUNCTIONS

 

DERIVATIVE OF THE EXPONENTIAL FUNCTION

The derivative of e^x is quite remarkable. The expression for the derivative is the same as the expression that we started with; that is, e^x!

$What does this mean?$ It means the slope is the same as the function value (the y-value) for all points on the graph.

Example: Let's take the example when x = 2. At this point, the y-value is e² ≈ 7.39.
Since the derivative of e^x is e^x, then the slope of the tangent line at x = 2 is also e² ≈ 7.39.
We can see that it is true on the graph:

Let's now see if it is true at some other values of x.

We can see that at x = 4, the y-value is 54.6 and the slope of the tangent (in red) is also 54.6.
At x = 5, the y-value is 148.4, as is the value of the derivative and the slope of the tangent (in green).

DIFFERENTIATION OF EXPONENTIAL FUNCTIONS

The derivative of f(x) = b x is given by f '(x) = b x ln b Note: if f(x) = e x , then f '(x) = e x Example 1: Find the derivative of f(x) = 2 x Solution to Example 1: ·         Apply the formula above to obtain f '(x) = 2 x ln 2 Example 2: Find the derivative of f(x) = 3 x + 3x 2 Solution to Example 2: ·         Let g(x) = 3 x and h(x) = 3x 2, function f is the sum of functions g and h: f(x) = g(x) + h(x). Use the sum rule, f '(x) = g '(x) + h '(x), to find the derivative of function f f '(x) = 3 x ln 3 + 6x Example 3: Find the derivative of f(x) = e x / ( 1 + x ) Solution to Example 3: ·         Let g(x) = e x and h(x) = 1 + x, function f is the quotient of functions g and h: f(x) = g(x) / h(x). Hence we use the quotient rule, f '(x) = [ h(x) g '(x) - g(x) h '(x) ] / h(x) 2, to find the derivative of function f. g '(x) = e x h '(x) = 1 f '(x) = [ h(x) g '(x) - g(x) h '(x) ] / h(x) 2 = [ (1 + x)(e x) - (e x)(1) ] / (1 + x) 2 Multiply factors in the numerator and simplify  f '(x) = x e x / (1 + x) 2 Example 4: Find the derivative of f(x) = e 2x + 1 Solution to Example 4: ·         Let u = 2x + 1 and y = e u, Use the chain rule to find the derivative of function f as follows. f '(x) = (dy / du) (du / dx) ·         dy / du = e u and du / dx = 2 f '(x) = (e u)(2) = 2 e u ·         Substitute u = 2x + 1 in f '(x) above f '(x) = 2 e 2x + 1 Exercises Find the derivative of each function. 1 - f(x) = e x 2 x 2 - g(x) = 3 x - 3x 3 3 - h(x) = e x / (2x - 3) 4 - j(x) = e (x2 + 2) solutions to the above exercises 1 - f '(x) = e x 2 x ( ln 2 + 1) 2 - g '(x) = 3 x ln 3 - 9x 2 3 - h '(x) = e x(2x -5) / (2x - 3) 2 4 - j '(x) = 2x e (x2 + 2)

   

Solve the following problem

Differentiate y=e^(ax+b) where a and b are constants

Let u = ax + b and y = e ^u

 Use the chain rule to find the derivative of function as follows 

 dy/dx = (dy / du) (du / dx) 

dy / du = e ^u and du / dx = a  ( Since the derivative of the constant b is 0)

Hence dy/dx = (e ^u)(a) = a e ^u

Substitute u = ax + b in dy/dx above 

dy/dx = a e ^ax + b

VOLUME OF A TRIANGULAR PRISM

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How Do You Find the Volume of a Triangular Prism?

Find the volume of the triangular prism below

SUMMARY

1. B stands for the area of the base
2. Since our bases are triangles, we can use (1/2)bh for B
3. We can call the height of the triangle h₁ and the height of the prism h₂ to avoid confusion
4. Volume is measured in units cubed, so we have 50 cm³

 

NOTES

1. 
    
   1. The volume of a prism is V=Bh
   2. B is the area of the base of the prism
   3. h is the height of the prism
   4. The base of our prism is a triangle, so we can use (1/2)bh, the area of a triangle, for B
   5. We can call the height of the triangle h₁ and the height of the prism h₂ to avoid confusion
2. 
    
   1. V is the volume, which is what we are trying to find
   2. b is the base of the triangle, which is 5 cm
   3. h₁ is the height of the triangle, which is 2 cm
   4. h₂ is the height of the prism, which is 10 cm
3. 
    
   1. We can plug 5 in for 'b', 2 in for 'h₁', and 10 in for 'h₂' in our equation
4. 
    
   1. We need to use the order of operations to simplify the right hand side
   2. First multiply 5•2 in the innermost parentheses
   3. Then multiply (1/2)•10 within the next set of parentheses
   4. This is the same as 10/2, or 5
   5. Then multiply 5•10 to get 50 cm³

VOLUME OF A RECTANGULAR PRISM

Volume of a rectangular prism or box examples: Let's do some example problems together in which we use the area times length formula for finding volume.

MATHS IS BETTER IN COLOUR

Maths is better in colour. Level Up your skills with this channel. -->https://t.co/B5AD6XVjcO #maths #tutor pic.twitter.com/QaIBog1w4z

— Maths From Scratch (@MathsfrmScratch) February 16, 2016

INTRANSITIVE VERBS AS TRANSITIVE VERBS

INTRANSITIVE VERBS AS TRANSITIVE VERBS

When an intransitive verb is used in a causative sense, it becomes transitive.

Study the examples given below.

The horse walks. (Intransitive)

The man walks the horse. (Transitive – here the man causes the horse to walk.)

Birds fly. (Intransitive)

The boys fly their kites. (Transitive)

The spellings of certain common verbs indicate whether they are transitive or intransitive.

Many trees fell in the storm. (Intransitive)

Woodcutters felled the trees. (Transitive)

Lie still. (Intransitive)

Lay the basket on the table. (Transitive)

Rise early with the lark. (Intransitive)

Raise your hands. (= Cause your hands to rise.)

Sit here.

Set the lamp on the table.

Some intransitive verbs become transitive when a preposition is added to them.

His friends laughed at him. (Laugh is an intransitive verb and does not take any object. Laugh at is a transitive verb and takes the object ‘him’.)

He soon ran through his fortune. (The verb run is intransitive whereas run through is transitive. To run through one’s fortune is to use it rapidly.)

Please look into the matter carefully.

I wish for nothing.

Sometimes the preposition is prefixed to the verb.

He overcame his enemy. (Come is an intransitive verb, but overcome is transitive.)

He bravely withstood the attack. (Stand is an intransitive verb, but withstand is transitive.)

PAST CONTINUOUS TENSE WORKSHEET

PAST CONTINUOUS TENSE WORKSHEET

MAKE SENTENCES IN THE PAST CONTINUOUS TENSE USING THE VERB GIVEN IN THE BRACKETS.

We make past continuous tense forms by putting was or werebefore the -ing form of the verb. Was is used with singular subjects.Were is used with plural subjects.

1. The boy ————————— (sleep).

2. I ———————– (read) when the lights went out.

3. She ———————– (wash) the clothes.

4. I ————————- (cook) dinner when the visitors arrived.

5. Julia ————————- (do) her homework at 8 pm.

6. James ————————– (repair) the car.

7. Janet ————————- (rehearse) for the play.

8. Sophia ————————– (wait) for the bus.

9. The birds ————————– (chirp).

10. The boys ———————— (learn) their lesson.

11. She ———————— (get) dressed.

12. He ————————– (search) for his purse.

13. The cat ————————- (chase) the mouse.

14. It ————————- (rain).

15. The wind —————————– (blow) fiercely.

16. The dogs —————————– (bark).

Answers

1. The boy was sleeping.

2. I was reading when the lights went out.

3. She was washing the clothes.

4. I was cooking dinner when the visitors arrived.

5. Julia was doing her homework at 8 pm.

6. James was repairing the car.

7. Janet was rehearsing for the play.

8. Sophia was waiting for the bus.

9. The birds were chirping.

10. The boys were learning their lesson.

11. She was getting dressed.

12. He was searching for his purse.

13. The cat was chasing the mouse.

14. It was raining.

15. The wind was blowing fiercely.

16. The dogs were barking.