IGCSE Mathematics Worksheet - Differentiation (Calculus) -1

Answer the following

1.
      

     

      Find the maximum value of A.

 2.

  (c) State whether the turning point is a maximum or a minimum.
3.


4.


Find the coordinates of the point of y=f(x) where the gradient is 8
5.

Downloaded from https://qusaistuition.blogspot.com

Leave your comment

0 comments

IGCSE Mathematics Worksheet - Vectors-2

Answer the following

1. 

OPQ is a triangle. T is the point on PQ for which PT : TQ = 2 : 1.
= a and = b.

(a) Write down, in terms of a and b, an expression for .

(b) Express in terms of a and b.  Give your answer in its simplest form.

2. 

ABCD is a parallelogram. AB is parallel to DC. AD is parallel to BC. = p        = q

Express, in terms of p and q

(i)

(ii)

3.

= 2b = 2a = 6a

M is the midpoint of PQ and N is the midpoint of OR.

(a) Find the vector in terms of a and b.

X is the midpoint of MN and Y is the midpoint of QR.

(b) Prove that XY is parallel to OR.

4. (a)Express in terms of a and/orb

(i)   

(ii) 

 X is the midpoint of BC.

(b) Express in terms of a and/or b

Downloaded from https://qusaistuition.blogspot.com

1 comment

1 comments

IGCSE CIE Mathematics Revision Sheet - 1

                                                                                    Marks: 48

Answer the following

1.
 
(a) (i) Draw the reflection of triangle T in the line x = 0. [2]
(ii) Draw the rotation of triangle T about (–2, –1) through 90° clockwise. [2]

(b) Describe fully the single transformation that maps triangle T onto triangle U. [2]

2.  

        [3]
         b)
                                        [3]

3. 

(a) Solve the equation f(x) = g(1)      [2]

(b) Find f -1(x).        [2]

(c) Find gf(x) in its simplest form.     [3]

(d) Solve the equation h-1(x) = 0.5    [1]

  [1]

4.



AB is parallel to DC.
AB = 55 m, BD = 70 m, angle ABD = 40° and angle BCD = 32°.
(a) Calculate AD                  [4]

(b) Calculate BC.                  [4]

(c) Calculate the area of ABCD.      [3]

5. (i) Show that the volume of a metal sphere of radius 15 cm is 14 140 cm3, correct to 4 s.f                                                                             [2]
   

(ii)Calculate the volume of water needed to fill the tank     [3]

(iii) The sphere is removed from the tank. Calculate the depth, d, of water in the tank.    [2]



6. [6]
(b) Determine whether each of the turning points is a maximum or a minimum.
Give reasons for your answers.     [3]

Downloaded from https://qusaistuition.blogspot.com

Leave your comment

0 comments

GCSE Mathematics Worksheet - Compound Measures-1-Notes

Distance-time graphs

• In a distance-time graph, the gradient of the line is equal to the speed of the object. The greater the gradient (and the steeper the line) the faster the object is moving.
• If an object is accelerating or decelerating, its speed can be calculated at any particular time by:    
• drawing a tangent to the curve at that time
• measuring the gradient of the tangent

Velocity-time graphs

• The gradient of the line is equal to the acceleration of the object.
• The displacement of an object can be calculated from the area under a velocity-time graph.         

       
Acceleration

• Acceleration is the rate of change of velocity. It is the amount that velocity changes per unit time.
• The change in velocity can be calculated using the equation:

• change in velocity = final velocity - initial velocity

     

• The average acceleration of an object can be calculated using the equation:

        
     This is when:

• acceleration (α) is measured in metres per second squared (m/s²)

• change in velocity (∆v) is measured in metres per second (m/s)

• time taken (t) is measured in seconds (s)

• If an object is slowing down, it is decelerating (and its acceleration has a negative value).

Velocity, acceleration and distance

• This equation applies to objects in uniform acceleration:

      (final velocity)2 - (initial velocity) 2  = 2 × acceleration × distance

       

• This is when:

• final velocity (v) is measured in metres per second (m/s)

• initial velocity (u) is measured in metres per second (m/s)

• acceleration (a) is measured in metres per second squared (m/s2)

• displacement (s) is measured in metres (m)          

Downloaded from https://qusaistuition.blogspot.com

Leave your comment

0 comments

IGCSE Mathematics Worksheet - Ratio & Proportion-2

Answer the following

1. Melissa is 13 years old. Becky is 12 years old. Daniel is 10 years old. Melissa, Becky and Daniel share £28 in the ratio of their ages. Becky gives a third of her share to her mother. How much should Becky now have?

2. Ann and Bob shared £240 in the ratio 3 : 5 Ann gave a half of her share to Colin. Bob gave a tenth of his share to Colin. What fraction of the £240 did Colin receive?

3. Peter won £75 as a prize. He gave 4/5 of the prize money as a present to Roger and Bethan. Roger and Bethan shared the present in the ratio 2:3 Work out how much they each got.

4. A shop sells CDs and DVDs. In one week the number of CDs sold and the number of DVDs sold were in the ratio 3:5 The total number of CDs and DVDs sold in the week was 728 Work out the number of CDs sold.

5. Rosa prepares the ingredients for pizzas. She uses cheese,topping and dough in the ratio 2 : 3 : 5 Rose uses 70 grams of dough. Work out the number of grams of cheese and the number of grams of topping Rosa uses.

6. Last year Kerry’s take home pay was £15 000 She spent 40% of her take home pay on rent. She used the rest of her take home pay for living expenses, clothes and entertainment in the ratio 3 : 1 : 2 How much did Kerry spend on entertainment last year?

7. Fred has a recipe for 30 biscuits. Here is a list of ingredients for 30 biscuits.

Self-raising flour : 230 g

Butter : 150 g

Caster sugar : 100 g

Eggs : 2

Fred wants to make 45 biscuits.

(a) Complete his new list of ingredients for 45 biscuits

Gill has only 1 kilogram of self-raising flour. She has plenty of the other ingredients.

(b) Work out the maximum number of biscuits that Gill could bake.

8. 4 men can build a shed in 20 hours. Calculate how long the same shed would take to build:
(a) if there was 1 man
(b) if there were 5 men.

9. The yield of wheat from 8 hectares of land is 360 quintals. Find the number of hectares of land required for a yield of 540 quintals?

10. 3 gallons of paint cover 900 square feet. How many gallons will cover 300 square feet?

Downloaded from https://qusaistuition.blogspot.com

Leave your comment

0 comments

IGCSE Mathematics Worksheet - Data Handling & Statistics-2

Answer the following

1. The stem and leaf diagram shows a sample of 50 scores in a boy’s golf tournament.

    
a) Write down the median golf score.

b) Calculate the interquartile range & semi-interquartile range for these scores

    2. The histogram shows information about the time, t minutes, spent in a shop by each of 80 people.

      Complete the frequency table
   

    3. The time taken for each of 120 students to complete a cooking challenge is shown in the table.
   

(i) Write down the modal time interval.

(ii) Calculate an estimate of the mean time.

(iii)Complete the cumulative frequency table.



(iv)On the grid, draw a cumulative frequency diagram to show this information.


(v) Find the median time. ......................................... min
(vi) Find the interquartile range. ......................................... min
(vii) Find the number of students who took more than 37 minutes to complete the cooking challenge
Downloaded from https://qusaistuition.blogspot.com

Leave your comment

0 comments