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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

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