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Transcript of Hosted by Miss Leman (Acknowledgements to Wanganui High School)
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Hostedby
Miss Leman(Acknowledgements to Wanganui High School)
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Algebra Probability Number Triangles
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Graphs Measurement
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Row 1, Col 1
Simplify
4p + 2q – p + 4q
ANSWER: 3p + 6q
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1,2
In a bag, there are 90 blue counters and25 red counters. What is the probability
I pick at random a red counter?
ANSWER : P(Red counter) = 25/115 = 5/23
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1,3
Write 35 out of 40 as a percentage
ANSWER: 35/40 x 100 = 87.5%
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1,4
Find cos30 = _____
ANSWER: Cos 30 = 0.866 (3dp)
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1,5
The general formula for a Straight line is y = mx +c
What does the m stand for and what does the c stand for?
ANSWER: m = gradient (rise over run or change in y over change in x) and c = the y intercept (where the line cuts the y axis)
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1,6
What is the perimeter of this shape?
ANSWER = 12 + 5 + 7 + 5 +5 = 34 cm
5
12 cm
7
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2,1
Expand and simplify
3w(w + 5)
ANSWER: 3w +152
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2,2
What is the probability on a random daythere will be a)17 cars in the carparkb)Less that 16 cars in the carpark
ANSWER : a) 5/34 b) (13 + 16) / 34 = 29/34
No. of cars in carpark (x)
Frequency Relative Frequency
15 13
16 16
17 5
18 2
TOTAL 34
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2,3
Complete this table
ANSWER: 0.2, 1/5, 20% - 0.5, ½, 50% -
0.625, 5/8, 62.5 – 0.125, 1/8, 12.5%
0.2
50%
5/8
12.5 %
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2,4
Find x
sin x = 0.6
ANSWER:
X = sin^-1 0.6
X = 36.87
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2,5
Plot the graph y= 2x +1
ANSWER:
−6 −4 −2 2 4 6 8 10
2
4
6
x
y
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2,6
Convert
a)120 cm to metersb) 1.2 L into millilitersc)8500 g into kilograms
ANSWER : a) 1.2 m
b) 1200 mL
c) 8.5 kg
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3,1
Solve
ANSWER :
253 )2( yx
1064 yx
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3,2
ANSWER: a) 10/32 b) 5/12 c) 30/32
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3,3
a)Find 30 % of $15b) Find 2/3 of 66 kg
ANSWER: a) 30/100 x 15 = $4.50
b) 2/3 x 66 = 44 kg
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3,4
ANSWER: Use Pythagoras.
cmAC
AC
AC
43.9
)85(
85
22
222
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3,5
ANSWER: A parabola that has been shifted up 1 unit.
Draw the graph and state the transformation it has gone through.
12 xy
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3,6
What is the area of this shape?
ANSWER: ½ base x height = ½ x 6 x 8 = 24 m
Please remember your units!!!
6 m
8 m
2
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4,1
ANSWER: x/4 = 3 – 7
x= -4/4
x= -1
2
374
x
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4,2
Draw a probability tree that shows all outcomes for tossing 2 coins.
What is the probability of getting Heads on both coins?
ANSWER :
H
H
HT
T
HH
HT
TH
TT
T
P(H,H) = 1/4
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4,3
a) Write the number 756000 in standard formb) Write 0.000405 in standard form
ANSWER: a) 7.56 x 10^5
b) 4.05 x 10^-4
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4,4
ANSWER: Using Trig – Sine rule
cmKM
KM
KM
05.7
36sin1212
36sin
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4,5
ANSWER: S = 3T
Triangles (T) No. of sides (s)
1 3
2 6
3 9
4 12
Write the rule for this pattern
S=
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4,6
What is the circumference of this circle?
ANSWER:
Remember you can also use
2.4 cm
cmrnceCircumfere 07.154.222
dnceCircumfere
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5,1
Factorise
ANSWER : 3x(2x-3y)
xyx 96 2
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5,2
If we rolled a dice 300 times –How many times would you
expect an even number to show?
ANSWER: P(even number) = ½
Therefore expected number = ½ x 300 = 150 times
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5,3
Five friends including the Newton twins went for a meal at Pizza Hut. The meal cost $46 and John wanted to pay for himself and his brother.
Divide the $46 cost of the meal in the ratio 2:3 to work out the twins share.
ANSWER : 2 + 3 = 5 parts. $46 / 5 = $9.20 per part.
2 x 9.20 = $18.40 3 x 9.20 = 27.60
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5,4
ANSWER
1.4517
12cos
17
12cos
1
BAC
BAC
BAC
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5,5
ANSWER:
Draw the line y = 3
−6 −4 −2 2 4 6
−4
−3
−2
−1
1
2
3
4
x
y
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5,6
What are the limits of accuracy fora)X = 12.4 cm?
b)Y = 2 L?
ANSWER: Look for the smallest unit given. Then half it, then add and subtract that from the original amount.
a) 12.35 < x <12.45 cm
b) 1.5 L < y < 2.5 L
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6,1
Calculate m if t = 3 and r = 7
ANSWER : m = 1/2
4
)( 2 rtm
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6,2
ANSWER: a) Hit Hit 3/4 x 4/5 = 3/5
B) Hit Miss or Miss Hit. 3/4 x 1/5 + 1/4 x 4/5 = 7/20
H
M
M
M
H
H
1st shot2nd shot
3/4
1/4
4/5
1/5
4/5
1/5
a) What is the probability he hits both shots?
b) What is the probability that he misses exactly one shot on either his first or second try.
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6,3
If I paid $25 for a skirt that was onsale with 30% off, how much
was the skirt originally?
ANSWER:
Therefore $25 / 0.7 = $35.71
Sale Price Original Price
x 0.7
Divide by 0.7
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6,4
ANSWER: Using Pythagoras to make a right angle triangle. Therefore
Calculate the height of this triangle
10 cm
8 cm
cmheight
height
height
25.6
)58(
58
22
222
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ANSWER a) 60 m shown by y intercept
b) 7 hours
c) Every hour it fills 20m (shown by the gradient)
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6,6
Calculate the Volume of this shape
ANSWER: 3 x 5 x 4 = 60 cm
Please remember your correct units!
3
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6,1
Simplify
ANSWER : 5x
2
5
3
15
x
x
3
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6,2
If I paid $60 for a skirt – how muchGST did I pay? Then calculate
GST exclusive price.
ANSWER :GST is 12.5 %.
0.125 x 60 = $7.50 GSTTherefore GST exclusive is $60 - $7.50 = $52.50
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4,3
a)Increase $5000 by 20%b) Decrease $80000 by 12%
ANSWER: a) 20% of 5000 = $1000 therefore $5000 + $1000 = $6000
b) 12% of $80000 = $9600 therefore $80000 - $9600 = $70,400
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4,4
Calculate the height of this triangle
ANSWER:
10m
24
mx
x
x
23.2
24tan55
24tan
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4,5
Plot y = - 3x - 2
ANSWER:
−6 −4 −2 2 4 6
−4
−3
−2
−1
1
2
3
4
x
y
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4,6
ANSWER: Area of circle = 3.14 x 7 x 7 = 153. 94 cm
Volume Area x length = 153.94 x 21 = 3232.7 cm 3
2
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6,1
ANSWER: (2x -6) = 8 x 4
2x = 32 +6
2x = 38
x = 38 / 2
x = 19
Calculate x
84
)62(
x
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Round these numbersa)125589 to 2 s.fb)0.000443 to 1 s.fc)8.987 to 1 d.p 6,2
ANSWER : a) 130000
b) 0.0004
c) 9.0
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4,3
The Earth is approximately a sphere of radius 6400 km The surface area of a sphere is given
by the formula A = 4πr. Calculate the approximate surface area of the Earth. Give your answer
in standard form.
ANSWER: 5.147185404 x 10^8
2
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4,4
ANSWER: Find angle P then find H
2.1015
7.2tan
15
7.2tan
1
P
P
P
mH
H
H
8.10
2.10tan6060
2.10tan
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4,5
ANSWERS: a) (0,8) b) -1 c) y= -x + 8
a) (0,1) b) 3 c) y= 3x + 1
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4,6
2
3
ANSWER: Area of trapezium
(6.7 + 4.2)/2 x 3.6 = 50.652 cm
Length x Area of trapezium = 165 cm
Length = 165/ 50.652 = 3.26 cm
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6,1
Gabby is 5 years younger than Rebecca. Together their ages add to 27. Write an algebraic equation and solve to find out Gabby’s age.
ANSWER : Rebecca = x Gabby = x -5
x + x – 5 = 27
2x = 32
x = 16 years
Therefore Gabby is 11 years old
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I had 7 marbles in a bag. 3 are purple, 4 are green. I will take out 2 marbles without putting the first back into the bag before I take the 2nd. Draw a probability tree and calculatea) P(both purple)b) P(one of each colour)
ANSWER
1st marble2nd marble
P
P
PG
G
G3/7
2/6
4/7
3/6
3/6
4/6a) P(both purple = 3/7 x 2/6
= 1/7
b) P(one of each) = 3/7 x 4/6 + 4/7 x 3/6 = 4/7
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4,3
During 2005 the average wage earned by some factory workers in New Plymouth
rose from $950 to $1025. Calculate the percentage increase.
ANSWER: Amount change = 1025 – 950 = $75
Therefore Percentage Change = Change / Original x 100
75/ 950 x 100 = 7.89 % increase in pay
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4,4
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4,5
Write the rule connecting the plumber cost,C to the hours worked, h.
ANSWER: C = 35H + 40
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9,6
Calculate the capacity of this cuboid
Capacity is the amount of liquid that a container can contain. 1 ml is equivalent to 1 cm , 1 L is equivalent to 1000cm. Therefore the volume of this cuboid is 64cm
Therefore its capacity is 64 ml.
2 cm8 cm
4cm
3
3
3