Download Module 5 Homework 1: Non-Calculator

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Module 5 Foundation Homework
Module 5 Homework 9: Non-Calculator
1) This is trapezium ABCD.
State whether the following statements are true or false
A
a) Length AD = Length BC (1)
b) The shape has two lines of symmetry (1)
c) Angle DAB = Angle CBA
(1)
d) This is an ‘isosceles’ trapezium (1)
e) The diagonals are perpendicular to each other (1)
B
D
C
2) This is a list of values
17
9
13
21
5
25
a) Write down a square number from the list (1)
b) Write down the smallest prime number in the list (1)
When the values are written in size order from smallest to largest they form a sequence
c) Write down the next value in the sequence (1)
d) Write down the rules for the sequence (1)
e) Show that the rule for the nth term can be written as 4n + 1 (2)
3) Here are some rectangles made from cm2;
a) Write down the names of 2 rectangles
which would form a square (1)
b) Work out the area of rectangle E (1)
c) Work out the perimeter of rectangle A (2)
d) Write down the dimensions of a
rectangle which would have the same area
as rectangle B, but a different perimeter (2)
B
C
A
D
E
4 a) Draw a coordinate grid with the y axis from 0 to 10 and the x axis from 0 to 10 (2)
b) Plot the points A(5,4) and B(7, 0) on the grid (2)
c) Write down the coordinates of the midpoint of AB (1)
d) Draw a circle with centre, A where AB is the radius of the circle. (1)
5 a) Write
18 as
81
a fraction in its simplest form (1)
b) Show which fraction is smaller; 2 or 3 (2)
5
c) Simplify
45x
9
7
(1)
d) Solve x  4 (1)
9
e) Given that 4  0.571428... write down 4 of 10 (to 1 decimal place)
7
7
(2)
6) A shop hires out bicycles. The cost of hiring a bicycle is calculated using the formula;
C = d + 10 × n (where C is the total cost, d is the deposit and n is the number of days.)
a) Work out the total cost, C when d = £20 and n = 3 (2)
b) Billy pays a total cost of £100. Work out for how many days he hired a bicycle (3)
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Module 5 Foundation Homework
7) This is an extract from a bus timetable.
a) How long does the 0534 bus from
Middleton Thorpe Lane take to travel
to Leeds Vicar Lane? (2)
b) What time does the 0512 bus from
Belle Isle Road Grey Goose arrive in
Roundhay Park?
(1)
c) The cost of traveling on any bus is
calculated at 20 pence per minute.
Work out the cost of traveling from
Middleton Arms to Hunslet Centre on
the Number 12 bus. (3)
This solid is made from centimetre cubes.
a) Work out the volume of the solid (1)
b) There are 3 cubes in the solid with 5 faces showing. Work out how
many cubes in the solid have just 2 faces showing. (1)
c) Draw the side elevation of the solid (1)
d) Draw the front elevation of the solid (1)
e) Draw the plan view of the solid (1)
8)
9 a) Copy and complete the following conversions;
i) 1 foot is approximately ……. centimetres (1)
ii) 8 kilometres is approximately …….. miles (1)
iii) 1 kilogram is approximately ………. pounds (1)
b) A scientist estimates that a snail travels at an average of 15 mm per second.
i) How many millimetres can a snail travel in 1 minute? (2)
ii) How long will it take a snail to travel 6 cm? (2)
10 a) Solve the equation 6x – 4 = 44 (2)
b) Write down an integer which satisfies the inequality 6a < 48 (1)
c) Write down an inequality to represent the following diagram;
6
11)
y-axis (x=0)
-2
4
C
2
x-axis (y=0)
-8
-6
-4
-2
2
-2
B
-4
4
6
A
8
-1
0
1
(2)
2
a) Copy the diagram and reflect triangle A in
the x axis (2)
b) Describe the single transformation that maps
triangle A onto triangle B (2)
c) Write down the vector which describes the
transl;ation of triangle A onto triangle C (1)
-6
12) Calculate the size of an interior angle in a regular octagon (3)
13)
A cylinder has a cross sectional area of 80 cm2. The volume of the
cylinder is 480 cm3. Work out the height of the cylinder. (2)
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Module 5 Foundation Homework
This is an extract from a train timetable
2)
This 3D shape is made up of cubic centimeters.
a) Write down the volume of the shape (2)
b) Write down the mathematical name of the shape (1)
c) Draw the plan view (2)
3) Here is a list of numbers;
2 5 7 9 13 17
a) Write down the number which is not prime (1)
b) Write down the value which is equal to 49 (1)
The numbers in this list are part of a sequence; 1 2 4
c) Write down the term-to-term rule (1)
d) Write down the next two terms in the sequence (2)
4)
8
…
…
Line segments AB and DC are parallel. Point O is joined to each vertex as shown
a) Write down the name of quadrilateral ABCD (1)
A
b) Write down the sum of angles w,x,y and z (1)
D
w z
B c) Angle x is between 90 and 180 degrees. Write down
the name for an angle between 90 and 180 degrees (1)
x y
d) x + w = 245o. w = 75o. Work out the size of x (1)
e) Line segments DO and OC are of equal length.
Work out the size of angle OCD (2)
C
O
5) Write down the metric unit of measure which should be used
a) to measure the length of a football pitch (1)
b) to estimate the weight of a man (1)
c) to measure the capacity of a can of coke (1)
Copy and complete each of the conversions
d) 2 cm = … mm (1)
e) 2.5 km = … m (2)
f) 24 km = … miles (2)
4 cm
The diagram shows an irregular 5-sided shape
a) Write down the name for a 5-sided shape (1)
b) Work out the perimeter of the shape (2)
3 cm
5 cm
4
Module 5 Foundation Homework
6)
7) The diagram shows three points; A, B and C. The scale is 1 cm = 1 km
N
120o
N
40o
B
N
a) Write down the bearing of B from A (1)
b) Write down the bearing of B from C (2)
c) Write down the distance CA (2)
A
C
8) Solve each of the following equations;
a) 3x = 15 (1)
b) 3b – 2 = 10 (2)
c) 3(y + 1) = 18 (2)
d) Chris thinks of a number, doubles it, then adds 3. The answer is 15.
What is the number he thinks of? (2)
9) Factorise fully;
a) 3x + 9 (1)
b) 2x2 – 4x (2)
c) List all of the factors of 16 (2)
10) Look at the following patterns;
a) Draw the next pattern in the sequence (1)
b) Write down the rule for the number of white
squares (1)
c) Write down the total number of squares in
the 5th pattern (1)
d) Write down the nth term for the total number of
squares (2)
11)
A
a) Copy the diagram and reflect shape A in
the mirror line. Label the image A` (2)
b) On the same diagram, translate shape A
4 spaces down and 1 space to the right.
Label the image A`` (2)
c) Write the order of rotational symmetry
of a rectangle (1)
12) Rearrange the following to make x the subject;
a) xz = y (1)
x y
 z (2)
b)
2
c) Find the value of a given that b = -2 and c = ½ in the formula; a = 2b + bc (2)
13 a) Draw the graph of y = x2 – 1 for values of x between -3 and 3 (3)
b) Draw the graph of y = 2x + 2 for value of x between -3 and 3 (2)
c) Hence find the values of x which satisfy the equation x2 – 1 = 2x + 2 (2)
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Module 5 Foundation Homework
Module 5 Homework 8: Calculator
1) Write down the value indicated by the arrow on each scale
a)
(1)
b)
(1) c)
(1)
2) Choose the most suitable estimate for the measurements for a) to c);
a) The length of an ant
1 mm
1cm
0.1 m (1)
b) The weight of a bowling ball
1 pound 15 pounds 7 stone (1)
c) The speed of a plane
500 kilometres/hr 1 metres/sec 1000 metres/hr (1)
d) Convert the following; 10 cm = … inches (2)
e) Convert the following; 3 kg = … pounds (2)
3) Line segments AB and CD are parallel.
B
D
F 35o
x
A
E
a) Write down the name of the
transversal in the diagram (1)
b) Write down the size of angle x and
explain how you worked out your
answer (2)
c) Work out the size of angle AFE (2)
C
4) Here is a list of values; 17 28 81 68 98
a) Calculate the product of the two odd numbers in the list (2)
b) Write down the square number from the list of values (1)
c) Write down the HCF of 28 and 68 (1)
d) Write down the LCM of 17 and 68 (2)
5) Copy and complete the table for properties of shapes;
Name
Order of symmetry
Lines of symmetry
Diagonals perpendicularly bisect?
Rectangle
2
2
yes
(4)
Parallelogram
Rhombus
2
0
7)
Distance (km)
6) A circle has a diameter of 20 centimeters
a) Work out the circumference of the circle (2)
b) Work out the area of the circle (2)
c) Work out the volume of a cylinder with a height of 10 cm
8cm2
2
and a cross sectional area of 8 cm (2)
10cm
d) The volume of a cylinder is 60 cm3. Work out the cross-sectional area if the height
of the cylinder is 12 cm.
(2)
30
The diagram shows a distance time
graphs for a journey. Work out the
average speed of the journey. (3)
25
20
15
10
5
0
0
20
40
60
80
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Module 5 Foundation Homework
Time
(mins)
8) The diagram shows a compound solid
a) Draw the plan view (1)
b) Draw the front elevation (1)
c) Draw the side elevation (1)
d) Write down the names of the two 3D
shapes joined to make the solid (2)
9 a) Draw the net of a cube with side length 2cm (2)
b) Draw a rectangle with an area of 12cm2 (2)
10 a) Plot the following points on a coordinate grid; A:(6,8) B:(2, 4) (1)
b) Write the coordinates of the midpoint, M, of line segment AB (2)
c) Match up each of the equations with the lines shown (3)
4 y
A
B
3
2
1
-6
-4
-2
x
2
-1
-2
D
4
6
1)
2)
3)
4)
y=x+1
y = ½x
y=x–2
y = -x + 1
-3
C
-4
11) Prove that all numbers in the sequence given by the nth term; 2n + 6 are even. (2)
12) Henry knows that the solution to x2 + 2x = 22 lies between 3 and 4. Use trial and
improvement to work out the solution to the nearest tenth. (3)
13) 2cm
x
a) Calculate x and write your full calculator display (3)
b) Work out the area of the triangle (2)
5cm
14) Make an accurate drawing of the triangle shown in Q13) and identify the locus of all
points that are 2 cm away from the perimeter of the triangle (2)
15) The number grid shows a shape involving 3 squares. The shape is called L1 because
the number 1 is written in the top left corner.
a) Work out the sum of the numbers in shape L1 (1)
1
2
3
4
5
6
7
8
b) Work out the sum of the numbers in shape L21 (1)
9 10 11 12 13 14 15 16 c) Write down an expression for the sum of the
17 18 19 20 21 22 23 24
numbers in shape Ln (2)
25 26 27 28 29 30 31 32 d) The sum of the numbers in a different shape
33 34 35 36 37 38 39 40
on the grid, Tn is given as 4n + 12. Work out
41 42 43 44 45 46 47 48
the sum of the numbers in T3. (2)
e) Draw shape T3 (1)