9q1 Homework 17
Due Wednesday 17/2 /11
1. Check previous homework & complete corrections
2. Revise topics covered this term – see table and example questions on the next page.
Shape & Space:
• Use units of measurement to calculate, estimate, measure and solve problems in a
variety of contexts; convert between area measures (mm 2 to cm2, cm2 to m2,
•
•
etc).
Know and use the formulae for the circumference and area of a circle.
Calculate the surface area and volume of right prisms.
Number:
• multiply and divide by any integer power of 10 (100, 1000, etc)
• Use rounding to make estimates; round numbers to the nearest whole number or
to one or two decimal places.
• Know that a recurring decimal is a fraction.
• Use standard methods to add and subtract integers and decimals of any size,
including a mixture of large and small numbers with differing numbers of decimal
places.
• multiply and divide by decimals, dividing by transforming to division by an integer
(eg divide by 3 instead of 0.003, then move the decimal in the answer)
• Check answers using appropriate methods
• Use a calculator efficiently and appropriately to perform complex calculations with
numbers of any size, knowing not to round during intermediate steps of a
calculation; use the constant, p and sign change keys, function keys for powers,
roots and fractions, brackets and the memory.
• Enter numbers into a calculator and interpret the display in context (negative
numbers, fractions, decimals, percentages, money, metric measures, time).
• Solve substantial problems by breaking them into simpler tasks, using a range of
efficient techniques, methods and resources, including ICT;
• use trial and improvement where a more efficient method is not obvious.
The next page has a question or 2 from each topic – Answers are at the end of the
document.
Shape & Space:
• Use units of measurement to calculate, estimate, measure and solve problems in a
variety of contexts; convert between area measures (mm 2 to cm2, cm2 to m2, etc).
Q – Show that 4 hours 15 minutes is the same as 255 minutes
Q – A bathroom tile measures 10 cm by 10 cm. How many do you need for a shower
cubicle with wall area of 3 m2?
Q – 2m 11mm 24cm 0.8mm 80cm
Which of these distances would be about right for:
a) length of a maths exercise book
b) thickness of a pencil
c) height of a door
d) Thickness of a bank / credit card
e) Width of a door
•
Know and use the formulae for the circumference and area of a circle.
Q – Find the area and circumference of a circle with diameter 40 cm
Q – What is the radius of a circle whose circumference is 3m?
Q – Find the shaded area on
the circle pictured.
•
Calculate the surface area and volume of right prisms.
Q – What is the surface area and volume of a cereal box measuring 6 cm deep by 20 cm
wide by 45 cm tall?
Q – Find the surface area and volume of the triangular prim below
Q – Find the volume of the cylinder to the right.
Number
• multiply and divide by any integer power of 10 (100, 1000, etc)
Q–
0.03 x 10,000 =
80 ÷ 1000 =
•
•
Use rounding to make estimates; round numbers to the nearest whole number or to
one or two decimal places.
multiply and divide by decimals, dividing by transforming to division by an integer
(eg divide by 3 instead of 0.003, then move the decimal in the answer)
Q - £460 ÷ 9
0.003 x 0.4
2500 x 30
0.006 x 20
50kg ÷ 12 (give answer to nearest 10 grams)
• Know that a recurring decimal is a fraction.
Q – What is 1/3 as a decimal?
What is 3/11 as a decimal?
•
Use standard methods to add and subtract integers and decimals of any size,
including a mixture of large and small numbers with differing numbers of decimal
places.
Q – I have £1,236.35 in my bank. I earn £210 in wages, spend £450 on rent for the month
and £6.78 on food for dinner. How much have I got left?
•
•
Check answers using appropriate methods
Use a calculator efficiently and appropriately to perform complex calculations with
numbers of any size, knowing not to round during intermediate steps of a
calculation; find powers, roots and fractions,
Q – use a calculator to find √20
- write down the full calculator display.
•
Enter numbers into a calculator and interpret the display in context (negative
numbers, fractions, decimals, percentages, money, metric measures, time).
•
Solve substantial problems by breaking them into simpler tasks, using a range of
efficient techniques, methods and resources, including ICT;
•
use trial and improvement where a more efficient method is not obvious.
Q - What number cubed gives the answer 343000?
Q – Which chamber of the revolver has a bullet in it?
Shape & Space:
• Use units of measurement to calculate, estimate, measure and solve problems in a
variety of contexts; convert between area measures (mm 2 to cm2, cm2 to m2, etc).
Q – Show that 4 hours 15 minutes is the same as 255 minutes
4 x 60 = 240 240 + 15 = 255.
Q – A bathroom tile measures 10 cm by 10 cm. How many do you need for a shower
cubicle with wall area of 3 m2?
Each 1 m2 can fit 10 tiles across and 10 tiles up =
100 tiles per square metre. There are 3 square
meters = 300 tiles (assuming no breakages, cutting
of tiles or corners in the shower)
Q – 2m 11mm 24cm 0.8mm 80cm
Which of these distances would be about right for:
a) length of a maths exercise book 24cm
b) thickness of a pencil 11mm
c) height of a door 2m
d) Thickness of a bank / credit card 0.8mm
e) Width of a door 80 cm
•
Know and use the formulae for the circumference and area of a circle.
Q – Find the area and circumference of a circle with diameter 40 cm
A = π x r2 = 3.14 x 202 = 3.14 x 400 = 1256.00 = 1256cm2
C = 2 x π x r = 2 x 3.14 x 20 = 125.6 cm
Q – What is the radius of a circle whose circumference is 3m?
3=2xπxr
1.5 = π x r
r = 1.5 ÷ π = 0.4777 m
Q – Find the shaded area on the circle
pictured.
Big Circle
A = π x r2 = 3.14 x 52 = 78.5 cm2
Small (inner) circle
A = π x r2 = 3.14 x 32 = 28.3 cm2
Shaded Area = 78.5 – 28.3 = 50.2 cm2
•
Calculate the surface area and volume of right prisms.
Q – What is the surface area and volume of a cereal box measuring 6 cm deep by 20 cm
wide by 45 cm tall?
V = (area at end) x length = 6 x 20 x 45 = 5400 cm 3
Surface area = Find area of each side & add all
together
SA = 120 + 120 + 900 + 900 + 270 + 270
= 2580cm2
Q – Find the surface area and volume of the triangular prism below?
V = (area at end) x length
V = (½ x 5 x 12) x 7 = 30 x 7 = 210 cm2
Surface Area
Add up the area of all 5 sides
(½ x 5 x 12) + (½ x 5 x 12) + (5 x 7) + (12 x 7) + (13 x 7)
30 + 30 + 35 + 84 + 91 = 270 cm2
SA = 270 cm2
Q – Find the volume of the cylinder to the right.
V = (area at end) x length
= π x r2 x length = 3.14 x 0.52 x 19
= 14.9 cm3
Number
• multiply and divide by any integer power of 10 (100, 1000, etc)
Q–
0.03 x 10,000 = 300
80 ÷ 1000 = 0.08
•
•
Q-
Use rounding to make estimates; round numbers to the nearest whole number or to
one or two decimal places.
multiply and divide by decimals, dividing by transforming to division by an integer
(eg divide by 3 instead of 0.003, then move the decimal in the answer)
£460 ÷ 9 = £51.11
2500 x 30 = 75,000
0.003 x 0.4 = 0.0012
0.006 x 20 = 0.12
.
50kg ÷ 12 (give answer to nearest 10 grams) 50 ÷ 12 = 4.16666
Answer – 4.16666.... kg rounds to 4.17 kg (or 4170g)
•
Know that a recurring decimal is a fraction.
.
Q–
What is 1/3 as a decimal?
0.33
..
Q–
•
What is 3/11 as a decimal? 0.272727272 = 0.27
Use standard methods to add and subtract integers and decimals of any size,
including a mixture of large and small numbers with differing numbers of decimal
places.
Q – I have £1,236.35 in my bank. I earn £210 in wages, spend £450 on rent for the month
and £6.78 on food for dinner. How much have I got left?
1 236.35 + 210 = 1 446.35
1446.35 – 450 = 996.35
996.35 – 6.78 = £989.57
• Check answers using appropriate methods
• Use a calculator efficiently and appropriately to perform complex calculations with
numbers of any size, knowing not to round during intermediate steps of a
calculation; find powers, roots and fractions,
Q – use a calculator to find √20 - write down the full calculator display.
Press the buttons √ 2 0 =
OR
2 0 √
Then write down full display ( 4.472135 – you might have a couple more or less digits on
your display)
•
•
•
Enter numbers into a calculator and interpret the display in context (negative
numbers, fractions, decimals, percentages, money, metric measures, time).
Solve substantial problems by breaking them into simpler tasks, using a range of
efficient techniques, methods and resources, including ICT;
use trial and improvement where a more efficient method is not obvious.
Q - What number cubed gives the answer 343 000?
Try10... 103 = 1 000... try 100...1003 = 1 000 000 … 503 = 125 000 … 803 = 512 000
703 = 343 000! cube root of 343 000 = 70.
Q – Which chamber of the revolver has a bullet in it? The last one.