hosted by miss leman (acknowledgements to wanganui high school)

Hostedby

Miss Leman(Acknowledgements to Wanganui High School)

100100 100100

200 200

400400 400

300

400400

Algebra Probability Number Triangles

300 300 300300

200

400

200

100

500 500 500 500

100

Graphs Measurement

200

300

400

100100

500

200

300

400400

100

500

50 50 505050 5050 5050

150 150 150150 150 150

250250 250 250 250 250

350 350 350350 350 350

Row 1, Col 1

Simplify

4p + 2q – p + 4q

ANSWER: 3p + 6q

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

1,3

Write 35 out of 40 as a percentage

ANSWER: 35/40 x 100 = 87.5%

1,4

Find cos30 = _____

ANSWER: Cos 30 = 0.866 (3dp)

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)

1,6

What is the perimeter of this shape?

ANSWER = 12 + 5 + 7 + 5 +5 = 34 cm

5

12 cm

7

2,1

Expand and simplify

3w(w + 5)

ANSWER: 3w +152

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

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 %

2,4

Find x

sin x = 0.6

ANSWER:

X = sin^-1 0.6

X = 36.87

2,5

Plot the graph y= 2x +1

ANSWER:

−6 −4 −2 2 4 6 8 10

2

4

6

x

y

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

3,1

Solve

ANSWER :

253 )2( yx

1064 yx

3,2

ANSWER: a) 10/32 b) 5/12 c) 30/32

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

3,4

ANSWER: Use Pythagoras.

cmAC

AC

AC

43.9

)85(

85

22

222

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

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

4,1

ANSWER: x/4 = 3 – 7

x= -4/4

x= -1

2

374

x

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

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

4,4

ANSWER: Using Trig – Sine rule

cmKM

KM

KM

05.7

36sin1212

36sin

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=

4,6

What is the circumference of this circle?

ANSWER:

Remember you can also use

2.4 cm

cmrnceCircumfere 07.154.222

dnceCircumfere

5,1

Factorise

ANSWER : 3x(2x-3y)

xyx 96 2

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

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

5,4

ANSWER

1.4517

12cos

17

12cos

1

BAC

BAC

BAC

5,5

ANSWER:

Draw the line y = 3

−6 −4 −2 2 4 6

−4

−3

−2

−1

1

2

3

4

x

y

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

6,1

Calculate m if t = 3 and r = 7

ANSWER : m = 1/2

4

)( 2 rtm

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.

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

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

ANSWER a) 60 m shown by y intercept

b) 7 hours

c) Every hour it fills 20m (shown by the gradient)

6,6

Calculate the Volume of this shape

ANSWER: 3 x 5 x 4 = 60 cm

Please remember your correct units!

3

6,1

Simplify

ANSWER : 5x

2

5

3

15

x

x

3

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

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

4,4

Calculate the height of this triangle

ANSWER:

10m

24

mx

x

x

23.2

24tan55

24tan

4,5

Plot y = - 3x - 2

ANSWER:

−6 −4 −2 2 4 6

−4

−3

−2

−1

1

2

3

4

x

y

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

6,1

ANSWER: (2x -6) = 8 x 4

2x = 32 +6

2x = 38

x = 38 / 2

x = 19

Calculate x

84

)62(

x

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

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

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

4,5

ANSWERS: a) (0,8) b) -1 c) y= -x + 8

a) (0,1) b) 3 c) y= 3x + 1

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

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

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

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

4,4

4,5

Write the rule connecting the plumber cost,C to the hours worked, h.

ANSWER: C = 35H + 40

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