Number
Patterns & Algebra
Probability & Statistics
Measurement
Financial Maths
100
Which digit is incorrect in this subtraction?
a. 4
b. 8
c. 0
d. 2
ANSWER: 8
Explanation
Working through this subtraction, we start with
7 - 5 in the ones (units) column, which leaves 2.
Moving to the tens column, we have:
0 - 6, which we cannot do.
So, we re-group the 9 in the hundreds column, making it 8 hundreds and 10 tens.
These 10 tens are moved to the tens column so we now have:
10 - 6, leaving 4 in the tens column.
In the hundreds column, having regrouped, we now have:
8 - 1, which leaves 7 in the hundreds.
Hence, the 8 shown in the answer in the hundreds column is incorrect.
100
. Express the following in index form:
a) m • m • m • m • m
b) a • a • a • a • a • a • a
a) m5
b) a7
100
There are 2 egg sandwiches, 3 chicken sandwiches, 4 cheese sandwiches and 1 salad sandwich on a plate.
Keith takes a sandwich at random.
Which filling is he most likely to have taken?
Cheese
At 4 out of 10, cheese is the most frequently occurring filling, so this has the highest probability of being chosen at random.
100
Find the perimeter of a square paddock of side 35 m.
Solution:
So, the perimeter is 140 m.
100
Define cost price and selling price.
Cost price: The price at which an item is purchased.
Selling price: The price at which an item is sold.
200
What is the sum of 1/3 and 3/4?
ANSWER: 1 1/12
Explanation
We can only add fractions that have the same sized "pieces"; ie the same denominator. To change the fractions to equivalent fractions with the same denominator, find the lowest common multiple of the two denominators: 3 and 4. This is 12.
Now, change both fractions into 12ths:
1/3 = 4/12
3/4 = 9/12
We can now add the fractions:
4 + 9
= 13
13/12
= 1 1/12
200
Jeff correctly solved an equation.
He wrote:
3k + 9 = 4
3k = -5
What was his next step?
Answer: k = -5 ÷ 3
3k = -5
To get the k by itself, he needs to "un-do" the multiply by 3. The opposite of multiplying by 3 is dividing by 3.
To keep the equation balanced, he needs to do the same operation to both sides.
Dividing by 3 on both sides, his next line would read:
k = -5 ÷ 3
(We would normally write that as:
k = - 5/3)
200
Two bushwalkers set out, without a map, from Woollawa Hut.
At the cross roads they choose their next track at random.
What is the probability that their chosen path goes to Boola Lake?
ANSWER 2/3
Explanation
Three tracks leave the intersection (not counting the one they came from).
Two of those tracks lead to Boola Lake.
Probability is given by the formula
P = number of desired events / number of possible events.
Thus the probability is 2/3.
200
The table shows the Bell Times for morning school lessons.
George was 1 hour and 15 minutes late for school.
Which lesson was in progress when George arrived?
ANSWER: Maths
George needed to be at assembly at 8.55 am. We add 1 hr 15 min to this time. We could either add on 1 hr (to 9.55 am) and and then another 15 minutes, bringing the time to 10.10am, or we could do an addition like this:
Hours:
8 + 1 = 9
Minutes:
55 + 15 = 70
70 min = 1 hr 10 min
Adding these back together we get:
9 + 1 hr 10 min = 10:10 am
We then check on the timetable to see what subject is scheduled at that time, and we find that Maths started at 9.50am and would continue until 10.20am.
200
Calculate each of these percentages
1) 10% of $360.50
2) 32% of $729
3) 190% of 850
ANSWERS
1) $36.05
2) $233.28
3) $1615
300
Ellie worked out the temperature of the day by counting 31 cricket chirps in 15 seconds.
Ellie used a formula for the Temperature:
What was the temperature?
Explanation
Substitute the number of cricket chirps into the equation:
(5 x 31 + 25)/9
Using the BOMDAS order of operations, we must do the multiplication first.
(155 + 25)/9
Because everything is divided by 9, we must simplify the numerator before dividing:
180/9
Temperature = 20°C
300
The graph is based on the hire charge $C for a Taxi, which is $3.20 Flag Fall and $1.93 per kilometre.
Which of these coordinates could represent point A
a. (32.15, 15)
b. (15, 32.15)
c. (15, 28.95)
d. (28.95, 15)
The coordinates are (x,y) = (d,C) = (15, 32.15).
300
A 20c coin and a 10c coin are tossed at the same time.
What is the probability of getting two tails?
ANSWER: 0.25
A tree diagram can be used to show all the possible outcomes of tossing the two coins.
Starting with the 20c coin, consider the possible outcomes: head or tail.
Now consider the 10c coin. Once again, there are two possible outcomes (head or tail).
When we consider tossing the two coins, we could get the following combined outcomes:
20c 10c Outcomes
H H
H T
T H
T T
We can see that TT would be expected to occur one in four times, giving a probability of 0.25.
Half (or 0.5) of the times the 20c coin is tossed we would expect a Tail, and when the 10c coin is tossed as well, half of these would be expected to be Tails. Of these, half the Tails occur with the 20c tails so the chance of getting TT is one half of one half: 0.5 × 0.5 which is 0.25.
300
A pixel is a very small square.
This computer graphic contains 500 pixels.
How many pixels high is the graphic?
Explanation
Identify the information you are given and what you need to find:
Area = 500 pixels
Length = 25 pixels
Height = ?
Find an equation that relates the above variables:
The equation for the area of a rectangle is Area = length x height
Substitute in the known values and solve:
500 = 25 x height
height = 500/25
height = 20.
The graphic is 20 pixels high.
300
Determine the best buy (HINT unitary method)
Option A
4kg for $2.50
or
Option B
3kg for $1.80
Option A
400
Complete the following sum:
How is the answer written in words?
Answer: One billion, one hundred and eleven million, one hundred and eleven thousand, one hundred and ten.
Explanation
Write the question, being careful to line up the place value columns correctly.
In words, this is:
One billion, one hundred and eleven million, one hundred and eleven thousand, one hundred and ten.
400
Which expression is equivalent to 6p + 24 + 3p - 9 ?
a. 3p + 5
b. 3(3p+5)
c. 3(2p-3)
d. 9(p+5)
Answer: 3(3p+5)
Explanation
6p + 24 + 3p - 9
Collecting like terms (the terms in p, and the constants), we have:
= 6p + 3p + 24 - 9
= 9p + 15
We can then factorise that expression by taking out the common factor of 3 from both terms:
= 3(3p + 5)
400
In a survey of 1000 voters,
33% say that they will vote for the Active Activist Party (AAP),
22% say they will vote for the Build Better Bridges Society (BBBS)
and 41% say that they will vote Campsites Clean-up Group (CCG).
The rest are undecided.
What is the probability that a voter chosen at random is undecided?
Answer: 0.04
Explanation
The three parties account for 33% + 22% + 41% = 96%
So, 4% were undecided. This is the same as 4/100 or 0.04.
The probability that a voter will be undecided is 0.04.
400
Phil is drawing a circle.
What is the diameter?
Answer: 6cm
Explanation
The distance from the centre of the circle to the edge is the radius. In this question, that is the 3cm from the point of the compass (which sits at the centre of the circle) and the pencil, as shown on the ruler.
The diameter of a circle is a straight line from any point on the edge, through the centre, to a point on the edge opposite. This distance is therefore twice the radius.
Hence, the diameter of Phil's circle is 2 × 3cm, which is 6 cm.
400
Answer the following:
1. Calculate 20% markup on $420
2. Calculate 20% discount on $420
1. $504
2. $336
500
An A0 sheet of paper is halved and halved again to make smaller standard sized sheets.
Approximately what percentage of the whole A0 sheet is the area of an A4 sheet?
a. 6.25%
b. 3.125%
c. 12.5%
d. 25%
Explanation
When we halve an A0 sheet, we get an A1 sheet. This is half the size of the A0 sheet. Fold it again, and we have an A2 sheet, which is half the size of the A1 sheet. Fold it twice more, and we get an A4 sheet. This takes a total of 4 folds.
So we need to find 50% of 50% of 50% of 50%. We can write this as a multiplication:
50% × 50% × 50% × 50%
Writing this in decimal form we get:
0.5 × 0.5 × 0.5 × 0.5 = 0.0625
To convert this back to a percentage, we multiply by 100%:
0.0625 × 100
= 6.25%.
Therefore, an A4 sheet is 6.25% of an A0 sheet.
500
Which of these points is halfway between the points (1, 4) and (5, 6)?
a. (3,5)
b. (1,2)
c. (5,3)
d. (2,1)
Answer: ( 3 , 5 )
Explanation
The mid-point is given by the average of the x values and the y values, so the formula is:
MP = ( (x1 + x2)/2 , (y1 + y2)/2)
= ( (1 + 5)/2 , (4 + 6)/2)
= ( 3 , 5 )
500
From the data in the adjacent stem-and-leaf plot, determine the median score.
Answer: 25.5
Explanation
The median is the middle number
Number of scores is 16
Middle scores are 8th and 9th (25 and 26)
Find the average of the two scores to obtain median
500
Find the total surface area of a box with dimensions 6 cm by 5 cm by 4 cm.
Solution:
500
For both of the following scenarios, state the value of the profit or loss. Then find the profit or loss as a percentage of the original price (to the nearest 1%).
a) cost price $48, selling price $34
b) cost price $112.50, selling price $240
a) $14 loss, 29%
b) $127.50 profit, 113%