Hosted by Miss Leman (Acknowledgements to Wanganui High School)

Algebra Probability NumberTriangles GraphsMeasurement

Row 1, Col 1 Simplify 4p + 2q – p + 4q ANSWER:3p + 6q

1,2 In a bag, there are 90 blue counters and 25 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 = (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 = = 34 cm 5 12 cm 7

2,1 Expand and simplify 3w(w + 5) ANSWER: 3w +15 2

2,2 What is the probability on a random day there will be a)17 cars in the carpark b)Less that 16 cars in the carpark ANSWER : a) 5/34b) ( ) / 34 = 29/34 No. of cars in carpark (x) FrequencyRelative Frequency TOTAL34

2,3 Complete this table ANSWER: 0.2, 1/5, 20% - 0.5, ½, 50% , 5/8, 62.5 – 0.125, 1/8, 12.5% % 5/ %

2,4 Find x sin x = 0.6 ANSWER: X = sin^ X = 36.87

2,5 Plot the graph y= 2x +1 ANSWER:

2,6 Convert a)120 cm to meters b) 1.2 L into milliliters c)8500 g into kilograms ANSWER : a) 1.2 m b) 1200 mL c) 8.5 kg

3,1 Solve ANSWER :

3,2 ANSWER: a) 10/32b) 5/12c) 30/32

3,3 a)Find 30 % of $15 b) 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.

3,5 ANSWER: A parabola that has been shifted up 1 unit. Draw the graph and state the transformation it has gone through.

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

4,1 ANSWER: x/4 = 3 – 7 x= -4/4 x= -1

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 H T T HH HT TH TT T P(H,H) = 1/4

4,3 a)Write the number in standard form b)Write in standard form ANSWER: a) 7.56 x 10^5 b) 4.05 x 10^-4

4,4 ANSWER: Using Trig – Sine rule

4,5 ANSWER: S = 3T Triangles (T)No. of sides (s) 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

5,1 Factorise ANSWER : 3x(2x-3y)

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 : = 5 parts. $46 / 5 = $9.20 per part. 2 x 9.20 = $ x 9.20 = 27.60

5,4 ANSWER

5,5 ANSWER: Draw the line y = 3

5,6 What are the limits of accuracy for a)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

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 1 st shot 2 nd 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 on sale with 30% off, how much was the skirt originally? ANSWER: Therefore $25 / 0.7 = $35.71 Sale PriceOriginal 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

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

6,2 If I paid $60 for a skirt – how much GST did I pay? Then calculate GST exclusive price. ANSWER : GST is 12.5 % x 60 = $7.50 GST Therefore 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 $ $1000 = $6000 b) 12% of $80000 = $9600 therefore $ $9600 = $70,400

4,4 Calculate the height of this triangle ANSWER: 10m 24

4,5 Plot y = - 3x - 2 ANSWER:

4,6 ANSWER: Area of circle = 3.14 x 7 x 7 = cm Volume Area x length = x 21 = cm

6,1 ANSWER: (2x -6) = 8 x 4 2x = x = 38 x = 38 / 2 x = 19 Calculate x

Round these numbers a) to 2 s.f b) to 1 s.f c)8.987 to 1 d.p 6,2 ANSWER : a) b) 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: x 10^8 2

4,4 ANSWER: Find angle P then find H

4,5 ANSWERS: a) (0,8) b) -1 c) y= -x + 8 a) (0,1) b) 3 c) y= 3x + 1

4,6 ANSWER: Area of trapezium ( )/2 x 3.6 = cm Length x Area of trapezium = 165 cm Length = 165/ = 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 = xGabby = 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 2 nd. Draw a probability tree and calculate a)P(both purple) b)P(one of each colour) ANSWER 1 st marble 2 nd marble P P P G G G 3/7 2/6 4/7 3/6 4/6 a)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 / 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 cm 8 cm 4cm 3 3 3