Download Year 10 Sheet 13

Year 10 - Homework Sheet 13
Expand
4(x + 7)
EXPANDING AND FACTORISING
1.
2.
Why do we need to factorise?
Why do we need to expand?
4x + 28
Factorise
Complete this table of expressions in factorised and expanded form.
Factorised Form
3(x + 9)
Expanded Form
↔
↔
x(7 - y)
7 metres
x metres
Area = 49 m2
7 metres
10x + 15
↔
↔
Area = 7x m2
2ab - 16a
7(x + 7) =
ISBN: 9781877489150
3.
Expand the expressions below
3( x + 7)
=
4(x + 5)
=
x(2x + 7)
=
2x(3x + 9y) =
4( x - 2)
=
3(x - 8)
=
x(3x - 17)
=
3x(3x - y)
=
3(2x + 2)
=
2(5x + 6)
=
4(3x - 2)
=
7(4x - 3)
=
-4(1 + 2x)
=
-1 ( 3 - x)
=
2x(x + 4)
=
-x(1 + x)
=
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TRIANGULAR NUMBERS
The diagram below shows how a tower can be made out of snowballs.
1.
2.
Draw the next tower in the pattern (above), then complete the table below.
Tower Number (n)
1
Snowballs (s)
1
2
3
4
5
6
The number of balls needed to build each tower forms a sequence called
triangular numbers.
The formula for calculating the nth term of a triangular number is:
n2 + n
2
Use the formula to calculate how many snowballs would be needed for Tower 10.
3.
If you had 120 snow balls, what would be the Tower Number?
4.
Here are the first five terms of a number sequence: 5, 8, 11, 14, 17.
Circle the correct expression for the nth term of the sequence.
5n
5.
n2 + 4
n+4
3n + 2
Look at the three sequences of numbers below:
Sequence p:
4, 6, 8, 10, 12, . . .
Sequence q:
3, 8, 15, 24, 35, . . .
Sequence r:
5, 10, 17, 26, 37, . . .
Sequence r is obtained from p and q by the following formula: r = p2 + q2
Year 10, Worksheet 13, Page 2 - www.mathscentre.co.nz
ISBN: 9781877489150
Calculate the sixth term of each of the sequences p, q and r.
PERCENTAGES
1.
Elizabeth sees an advertisement for a new stereo. She
can purchase the stereo on “time payment” with a deposit
of 25% and then 18 monthly installments of $45.Complete
the calculations in the table below to calculate how much
extra Elizabeth will eventually pay by buying the stereo on
time payment.
25% Deposit
Total Cost of 18 monthly payments @ $45
Total cost Elizabeth will pay
Advertised Cost of the Stereo
Extra amount Elizabeth has to pay
2.
.
Elizabeth is looking to purchase a new shirt and jeans. She could either buy
them ready made or decide to save money and make them herself.
The cost of a new shirt and jeans is below. Find the total cost.
Shirt $59.95, Jeans $99.99, Total Cost
$
Elizabeth decides to save money by making the shirt herself. She calculates that
she will need two metres of material. This material usually costs $18.45 per
metre, however at sale price she can save 10%. Elizabeth also need to
purchase a shirt pattern ($15.95), 6 buttons (1.55 cents each) and a reel of
cotton ($3.30). How much does Elizabeth save by making her own shirt?
2 metres of material @ $18.45 =
10 % discount
=
Sale Price =
Shirt Pattern @ $15.95 =
ISBN: 9781877489150
6 buttons @ $1.55 =
Cotton @ $3.30
=
Total Cost
=
Saving
=
Comment on the savings.
Year 10, Homework Sheet 13, Page 3 - www.mathscentre.co.nz
CORN CALCULATIONS
1.
The equation y = 1000 - 50x gives the unharvested area (y) of the larger field (in
hectares) after x days. Write an equation giving the unharvested area y of the
smaller field (in hectares) after x days.
2.
Graph the two equations from 1. on the grid below.
3.
Identify the slope and y-intercept of each graph.
4.
What is the geometric relationship between the two line graphs?
How do you know?
5.
How long does it take for the farmers to harvest the corn in both fields?
Year 10, Homework Sheet 13, Page 4 - www.mathscentre.co.nz
ISBN: 9781877489150
Two farmers each harvest 50 hectares of corn per day from their fields. The area of one
farmer’s field is 1000 hectares, and the area of the other farmer’s field is 600 hectares.