GRADE DName: ______________________________________ Date:______________

Stage 6 – Revision Topics 1 – 3

Use your exercise books, topic booklets and any revision guides to help you answer the questions below.

This revision work should last no more than------ minutes. Use the remaining time to do the revision question at the back of your booklets. (Hints have been provided)

Topic 1: Probability and Scatter Graphs.

1. Types of Correlation

This diagram has a This diagram has a This diagram has

__________________ __________________ __________________

__________________ ___________________ __________________

2. All probability adds up to ___________

3. A student is investigating the relationship between a person’s age and their reaction time. The table shows her results.

a) On the grid below complete the scatter diagram. The first four points have been plotted. [2]

b) Describe the correlation shown by the graph. [1]

c) Draw a line of best fit and use it to estimate the reaction time of a person aged 40.(You will need to draw a straight line on your graph then use this line by drawing two more lines to answer the questions – basically no lines = no marks)

[2]

Age (Years)

35 18 30 22 58 45 47 62 42 54

Reaction Time

(Seconds)

0.38 0.36 0.42 0.45 0.56 0.43 0.52 0.55 0.52 0.48

4. CHOCTIME put a scratchcard in each tube of chocolates. Some scratchcards win a prize.

a) The probability of not winning a prize is 0.88. What is the probability of winning a prize?

[1]

b) The tops of the tubes come in three colours, yellow, red and green. The probability that a particular top is yellow is 0.3. The probability that it is red is equal to the probability that it is green.

What is the probability that a particular top is green?

[2]

5 a) The price of a mathematics textbook is £13.40.

A school bought 36 of these books. Calculate the total cost of the books. 

(a) £

 b) When Brian, Mike and John wrote a textbook, they agreed to share any money they made in the ratio 15 : 8 : 7.

   (i) In the first year they made £3600 from the sale of the book.

How much was John's share?(work out the total number of parts – then the value of 1 part – then work out how much each man gets – John is 7 parts)

 

 (b) (i) £

 

(ii) In the second year, Mike's share was £1600. How much was Brian's share?(Mike = 8 parts = 1600. Work out the value of 1 part from this – then work out how much Brian will get (15 parts))

(b) (i) £

6. Volume of a cuboid = __________ x ____________ x _____________

7. This is a full sized net of a cuboid. (will need a ruler to measure)

The net is folded to make the cuboid.

a) Which other points meet with E? [1]

b) Calculate the volume of the cuboid.Write down any measurements that you make. [3]

Name: ______________________________________ Date:______________

Stage 6 – Revision Topics 4 – 6

1. Complete the table below for y = 2x – 7 A y value = (2 times an x value) – 7

X 0 1 2 3 4y -7

Draw the graph of y = 2x – 7 on the grid below (be careful with the scales)

On the same axes plot the graph of y = 2x –2 A y value = (2 times an x value) – 2

X 0 1 2 3 4y -2

What do you notice about these graphs?

2.

a) On the grid above plot the special line x = 2

b) On the grid above plot the special line y = -3

c) On the grid above plot the line x + y = 4 (an x number + a y number always makes 4)

Use the table below to help you X 0 1 2 3 4y -2

3. Area of a Rectangle = ___________ x _________________

length

width

Area = ______ x _______

= _____ x _____

= _____

or = ______ x _______

= _____ x _____

= _____

4. Area of a Triangle = _______ x _______ 2

base

height

5. Area of a Parallelogram = ____________ x _________________

6. What is the connection between the height and the base?

height

base

Area of a Trapezium

The formula to calculate the area of a trapezium = (a + b) x height2

The height of a trapezium is always between the parallel sides and at right angles to them

YOU DO NOT NEED TO REMEMBER THIS FORMULA – IT IS ALWAYS GIVEN TO YOU!!!!

6. ABCD is a rectangle measuring 4cm by 7cm

Work out the area of the grey triangle.

.

[4]

a

height

12

3

Work out the area of the rectangleWork out the areas of triangles 1, 2, and 3 – then add them up.Subtract this from the area of the rectangle

7. A park is in the shape of a trapezium.

Calculate the area of the park.(use the trapezium formula – you don’t have to remember it)

[2]

Things you need to know about angles:

The angles on a straight line add up to180o

The angles inside a triangle add up to 180o

Angles inside a quadrilateral add up to 360o

x yx + y = 180o

a

b

c

a + b + c = 180o

a a

b Isosceles triangles have two equal sides and two equal angles

a + a + b = 180

d

e

f

g

d + e + f + g = 360o

8. In the diagram, ABC is an isosceles triangle.Angle A = 98o.

Work out angle x. Show your working out clearly.(Look for the isosceles triangle and angles on a straight line)

x =

Angles in parallel lines

x

xy

y

Corresponding Angles are equal.‘Same angle in same place’

‘F Angle’

Alternate Angles are equal.‘Same angle on the opposite side’

‘Z Angle’

ee

e

e

9. In the diagram, AE is parallel to BD.

Find the value of the marked angles, giving your reasons.

r = because

s = because

t = because

Interior angles

Exterior angles always add up to 360o

180o

180o

180o

180o

180o

180o

3 sides = 180o

‘1 triangle’ 4 sides = 360o

‘2 triangles’ 5 sides = 540o

‘3 triangles’ and so on….

Name: ______________________________________ Date:______________

Stage 6 – Revision Topics 7 – 9

1.

2.

A

B

O

C Line AB is called the _____________

Line OC is called the _____________

The curved distance around the outside of a circle is called the circumference.

Circumference = x ____________

C = x _______

The Area is the space inside the circle.

Area = x ____________

A = x _______

Area

3. A CD is packaged as shown on a square piece of cardboard.

Calculate the shaded area of cardboard. [Hint – work out the area of the square – then work out the area of the circle (using the radius!)- then subtract the two answers]

_______________cm2

4. A circular medal has a radius of 3.1cm.Calculate, giving your answers to a suitable degree of accuracy,

a. The circumference [Hint – what’s the diameter?]

Circumference = ______________cm

b. the area of the circle

Area = _______________cm2

5. A box of Daisy Jellies costs £1.22.Petra buys two boxes and pays with a £5 note.How much change should she get? (NO CALCULATOR)

[2]

6. Work out 0.8 x 0.2 (Hint what is 2 x 8, and remember that the answer will have the same number of figures after the point as all numbers in the question)

[1]

7. Work out (i) 0.7 x 0.4

[1](ii) 0.75 ÷ 2

Hint 2 0.75 remember you can add on zeros until you have no remainder

[2]

8. Calculate the total cost of 16 DVD’s at £14.32 each

Do 14.32 x 2 first, then 14.32 x 4, then 14.32 x 8 then 14.32 x 16

[3]

9. Expand x(x + 5)

Multiplied by x 5x

10. Expand 5(x + 2)

Multiplied by x 25

11. Multiply out 4(2x + 3)

Multiplied by 2x 34

12. Factorise 4a + 10 = 2 ( 2a + 5 )

The largest number that divides exactly into 4a and 10 goes outside the brackets.

You then divide 4a and 10 by that number – what is left goes inside the brackets

13. Factorise 5x + 10 = ___ ( + )

14. Factorise 6t + 9 = ___ ( + )

15. Factorise 6r2 + r = ___ ( + )

16. Solve

a. 2x = 7x = 7 ÷ 2x =

b. 3x - 5 = 133x = 13 + 53x = x =

c. 6x - 9 = x + 26letters = numbers

6x – x = 26 + 95x = 35x =

17. Solve

a. x/5 = 10

b. 3x + 2 = 22 – x

c. 2(x - 5) = 18

18. Solve these equations

a) 3x + 2 = 2x + 5

b) 2(x + 3) = 15

19. Solve

a. 2x - 5 = 21

b. 7x + 6 = 9 + x