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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
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