Jane painted some hexagons in the four figures pictured below.
All hexagons are the same size.
Which of these figures has the largest area that is painted green.
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Aussie Maths & Science Teachers: Save your time with SmarterEd
Jane painted some hexagons in the four figures pictured below.
All hexagons are the same size.
Which of these figures has the largest area that is painted green.
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`text{Largest area painted = figure with the most hexagons painted green.}`
`text{Check each option:}`
`text{1st Figure – 11 hexagons}`
`text{2nd Figure – 9 hexagons}`
`text{3rd Figure – 13 hexagons}`
`text{4th Figure – 9 hexagons}`
`therefore \ text{3rd Figure has the largest area painted green.}`
In a bakery Michelle bought one slice of cake, one donut and a croissant.
She gave the cashier $10.00.
How much change should Michelle receive?
$5.10 | $5.60 | $5.80 | $6.00 |
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`$6.00`
`text{Total cost}` | `= 1.35 + 1.20 + 1.45 ` |
`= $4.00` |
`text{Change}` | `= 10 – 4` |
`= $6.00` |
Alexander went shopping and bought the following items.
He gave the cashier $50.
How much change should Alexander receive?
$17.00 | $18.20 | $31.80 | $33.00 |
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`$17.00`
`text{Total cost}` | `= 9.50 + 12.10 + 11.40 ` |
`= $33.00` |
`text{Change}` | `= 50 – 33.00 ` |
`= $17.00` |
Timothy started with 53 millilitres of oil in a beaker.
He saw that there was some unused oil in a test tube and returned it to the beaker.
How much of the chemical solution was poured int0 the test tube?
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13 millilitres |
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23 millilitres |
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27 millilitres |
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37 millilitres |
`27 \ text{millilitres}`
`text{Oil in the test tube }` | `= text{New volume} – text{Original volume}` |
`= 80 – 53` | |
`= 27 \ text{millilitres}` |
A chemist started with 685 millilitres of a solution.
He then poured some of the solution into a test tube.
How much of the chemical solution was poured into the test tube?
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90 millilitres |
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135 millilitres |
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145 millilitres |
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185 millilitres |
`185 \ text{millilitres}`
`text{Solution in test tube }` | `= text{New volume} – text{Original volume}` |
`= 685 – 500` | |
`= 185 \ text{millilitres}` |
In a neighborhood 10 villagers were asked if how many pets they own.
The results were: 3, 2, 1, 1, 1, 4, 2, 4, 5, 2
Select the dot plot that displays the data recorded
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`text{A dot represents the number of persons that owns N pets}`
`text{From the data above:}`
`text{Owns one pet = 3}`
`text{Owns two pets = 3}`
`text{Owns three pets = 1}`
`text{Owns four pets = 2}`
`text{Owns five pets = 1}`
`therefore \ text{the correct dot plot is:}`
10 people were asked how often they went to the doctor in the last 12 months.
Their responses were: 2, 3, 3, 4, 1, 2, 5, 1, 1, 2
Choose the dot plot which correctly displays the data.
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`text{From the data above:}`
`text{1 visit = 3 people}`
`text{2 visits = 3 people}`
`text{3 visits = 2 people}`
`text{4 visits = 1 person}`
`text{5 visits = 1 person}`
A bridge is drawn below.
The angle `y°` is marked from the foot of the bridge to the diagonal support.
The value of angle `y°` is
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Less than 90° |
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More than 180° |
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Equal to 90° |
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More than 90° but less than 180° |
`text{Less than} \ 90^@`
`text{The angle from the foot to the diagonal support is less than} \ 90^@`
A charity event was held for three weeks. On the first week $5000 was raised, on the second week $3500 was raised and on the last week $2000 was raised.
In the tables below, O = $500
Which table correctly shows the amount of donations raised in the 3 weeks?
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`text{O represents $500 in donations.}`
`text{1st week:} \ 5000 \div 500 = 10`
`therefore \ text{Ten O symbols needed.}`
`text{2nd week:} \ 3500 \div 500 = 7`
`therefore \ text{Seven O symbols needed.}`
`text{3rd week:} \ 2000 \div 500 = 4`
`therefore \ text{Four O symbols needed.}`
In a certain school, the number of Year 7 students is 120, Year 8 students is 80, and Year 9 students is 100.
In the tables below, V = 20 students
Which table correctly shows the number of students per year level?
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`text{V represents 20 students.}`
`text{Year 7 students:} \ 120 \div 20 = 6`
`therefore \ text{Six V symbols needed}`
`text{Year 8 students:} \ 80 \div 20 = 4`
`therefore \ text{Four V symbols needed}`
`text{Year 9 students:} \ 100 \div 20 = 5`
`therefore \ text{Five V symbols needed}`
Ana recycles 3 kilograms of plastic bottles in her first week of recycling.
She then recycles twice as much as she recycled the previous week for the next 5 weeks.
The total weight, in kilograms, of the plastic bottles she recycles in any given week will be
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always even |
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always odd |
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sometimes even or sometimes odd |
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none of the above |
`text{Always odd}`
`text{1st week: 3 kg (odd)}`
`text{2nd week: 3 + 6 = 9 kg (odd)}`
`text{3rd week: 9 + 18 = 27 kg (odd)}`
`vdots`
`text{Any week: odd + even = odd}`
Leo puts $15 into his piggy bank to start saving money.
He then puts the same amount into the piggy bank at the end of each month.
The total amount of money in his piggy bank will be which of the following:
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Always an even number |
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Always an odd number |
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Sometimes odd sometimes even |
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None of the above |
`text{Sometimes odd sometimes even}`
`text{Starting amount = $15 (odd)}`
`text{End of 1st month = 15 + 15 = $30 (even)}`
`text{End of 2nd month = 30 + 15 = $45 (odd)}`
`:.\ text{Total amount will be either an odd or even number.}`
Michael’s company is shown in the map.
Michael rides home 5 kilometres west, walks 3 kilometres south and walks another 1 kilometre west.
In which cell on the map is Michael’s home?
D1 | E2 | C1 | D2 |
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`text{D1}`
Phil’s home is shown in the map below.
Everyday he drives 3 kilometres east and 2 kilometres south from home to work
In which cell on the map is Phil’s office?
A5 | B5 | E5 | D5 |
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`text{E5}`
Louise donated money to two charities
She donated $125 to the first charity and donated $45 to the second charity.
Which number sentence could be used to find total amount of money Louise donated?
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120 + 40 = 160 |
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130 + 50 = 180 |
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120 + 40 + 5 = 165 |
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130 + 50 – 10 = 170 |
`130 + 50 – 10 = 170`
`text(Total amount donated to charity)`
`= 125 + 45`
`= 130 – 5 + 50 – 5`
`= 130 + 50 – 10`
`= 170`
Shane played two basketball games.
She scored 35 points in the first game.
In the second game she scored 25 points.
Which number sentence could be used to find the total number of points Shane scored in the first two games?
30 + 20 + 5 = 55 | 40 + 30 = 70 | 30 + 20 + 10 = 60 | 30 + 20 = 50 |
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`30 + 20 + 10 = 60`
`text(Total points in first 2 games)`
`= 35 + 25`
`= 30 + 5 + 20 + 5`
`= 30 + 20 + 10`
`= 60`
Sarah drew a straight line on a shape.
The line divided the shape into two rectangles.
Which of these could have been Sarah’s shape?
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`text{Drawing any horizontal straight line on this shape divides it}`
`text{into two rectangles.}`
Troy drew a straight line through a shape.
The line divided the shape into two equal triangles.
Which of these could not have been Troy’s shape?
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`text{Drawing a diagonal line will produce two quadrilaterals.}`
Rudy uses the number sentence 24 – 6 = 18
Which of the following problems can he solve with this number sentence?
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Rudy shared 24 slices of cake equally between 6 of his friends. How many slices does each of his friends get? |
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Rudy has 24 slices of cake and gave 6 slices to his friends. How many slices does Rudy have left? |
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Rudy took 6 slices of cake and shared them between 24 of his friends. How many slices does each friend receive? |
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Rudy has 24 slices of cake and gave 18 of them to his friends. How many slices does Rudy have left? |
`text{Rudy has 24 slices of cake and gave 6 slices to his friends.}`
`text{How many slices does Rudy have left?}`
`text{Rudy has 24 slices of cake and gave 6 slices to his friends.}`
`text(Expressing this as an equation:)`
`text(Slices Rudy has left)` | `=24 -6` | |
`18` | `=20 – 6` |
Shawn uses the number sentence 20 × 6 = 120
Which of the following problems can he solve with this number sentence?
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Shawn buys 20 toys and gave 6 of them to his nephew. How many toys does Shaun's nephew have now? |
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Shawn buys 20 toys and received another 6 toys from friends. How many toys does Shaun have now? |
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Shawn buys 20 toys and divides them up between his 6 nephews. How many toys does each nephew get? |
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Shawn has 20 nephews and gives 6 toys to each one. Altogether, how many toys does Shaun give to his nephews? |
`text{Shawn has 20 nephews and gives 6 toys to each one.}`
`text{Shawn has 20 nephews and gives 6 toys to each one.}`
`text(Expressing this as an equation:)`
`text(Total toys to nephews)` | `=20 xx 6` | |
`120` | `=20 xx 6` |
Gary folded this piece of paper along the dashed lines to make a solid figure.
Which of these models did Gary make?
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`text{By folding the paper along the dashed lines we could obtain a figure of:}`
Justin owns a collection of action figures which is more than 674 action figures and less than 764.
Which of these numbers could represent the number of action figures that Justin owns?
792 | 724 | 648 | 772 |
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`724`
`text{The number of action figures must be between 674 and 764 action figures}`
`text{Check each option:}`
`text{792 is more than 764 ⇒ incorrect}`
`text{724 is more than 674 and less than 764 ⇒ correct}`
`text{648 is less than 674 ⇒ incorrect}`
`text{772 is more than 764 ⇒ incorrect}`
Eric owns a book which has more than 258 pages but less than 285 pages
Which of these could represent the number of pages in Eric’s book?
287 | 294 | 249 | 262 |
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`262`
`text{Check each option:}`
`text{287 is more than 285 ⇒ incorrect}`
`text{294 is more than 285 ⇒ incorrect}`
`text{249 is less than 258 ⇒ incorrect}`
`text{262 is more than 258 and less than 285 ⇒ correct}`
A circle is divided into 8 equal parts, as shown in the image below.
What percentage of the circle’s area has been labelled with letters?
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30% |
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37.5% |
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42.5% |
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45% |
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47.5% |
`text(37.5%)`
`text(S)text(ince all areas are equal:)`
`text(Percentage)` | `= text(Number of letters)/text(Total number of sections) xx 100` |
`= 3/8 xx 100` | |
`= 37.5text(%)` |
Yohan was driving from the hospital to his house.
What directions best describe Yohan’s travel from the hospital to his house?
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East, north-east, north |
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West, north-west, north |
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East, north-east, south |
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West, north-west, south |
`text(East, north-east, north)`
`text(The directions travelled by Yohan:)`
`text(The direction was East, North-East, and North)`
A man drives from his house to his office.
What directions best describe his way to the office?
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North, north-west, west, south-west |
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North, north-east, east, south-east |
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North, north-east, east, south |
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North, north-west, east, south-east |
`text(North, north-east, east, south-east)`
Four triangular shaped playgrounds are shown below.
Which of these play grounds has the least surface area?
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`text(Check each option:)`
`text(Option 1 -)\ \ 1/2 xx 34 xx 15 = 255\ text(m)^2`
`text(Option 2 -)\ \ 1/2 xx 20 xx 26 = 260\ text(m)^2`
`text(Option 3 -)\ \ 1/2 xx40 xx 18 = 360\ text(m)^2`
`text(Option 4 -)\ \ 1/2 xx28 xx 25 = 350\ text(m)^2`
`:.\ text(The backyard with the least area is:`
In a suburb, four families measured the dimensions of their rectangular backyards.
Which backyard has the largest area?
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`text(Checking each option:)`
`text(Option 1:)\ 11 xx 18 = 198 text(m)^2`
`text(Option 2:)\ 16 xx 6 = 96 text(m)^2`
`text(Option 3:)\ 15 xx 10 = 150 text(m)^2`
`text(Option 4:)\ 14 xx 12 = 168 text(m)^2`
`:. text(The backyard with the largest area is the)\ 11\ text(m) xx 18\ text(m)`
`text(with a total area of 198 square metres.)`
A man spins a wheel with 5 different coloured sections and records which colour it lands on each time.
He repeats the process multiple times.
The table below shows the results.
Using the table, what is the probability that the next spin will be yellow?
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`6/31` |
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`16/84` |
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`1/7` |
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`2/5` |
`1/7`
`P(text(Yellow))` | `= text(Number of yellow)/text(Total number of throws)` |
`= 24/(42 + 24 + 38 + 27 + 37)` | |
`= 24/168` | |
`=1/7` |
Sam painted grids in the larger square areas pictured below.
All of the grids are the same size.
Which of the following squares has the largest area painted?
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`text(The largest area painted is the figure with the most squares painted grey.)`
`text(Checking each option:)`
`text(Option 1 – 9 square grids painted)`
`text(Option 2 – 13 square grids painted)`
`text{Option 3 – 16 square grids painted (Correct)}`
`text(Option 4 – 14 square grids painted)`
Andrei has a stack of cards that contains only Aces, Kings, Queens, Jacks and Jokers.
He picks one card without looking, records the card and puts it back again with the others.
He repeated this process 62 times.
Using the table, what are the chances of Andrei randomly selecting the Joker in his next pick?
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`8/33` |
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`6/31` |
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`11/62` |
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`6/25` |
`6/31`
`P(text(Joker))` | `= text(Number of Jokers)/text(Total number of draws)` |
`= 12/62` | |
`= 6/31` |
Marie grabs a coloured ball from a bag and records the colour. She then puts the ball back to the bag and repeats this process 96 times.
The results are shown in the table below.
Using the table, what is the probability that the next ball picked up by Marie will be yellow?
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`5/48` |
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`6/25` |
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`5/43` |
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`7/36` |
`5/48`
`P(5)` | `= text(Number of yellow)/text(Total number)` |
`= 10/96` | |
`= 5/48` |
A biased die has 6 faces numbered from 1 to 6.
Raven throws the die 50 times and recorded the results in the table below.
Using the table, what is the probability that Raven will be throwing a 5 on her next throw?
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`6/44` |
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`2/17` |
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`11/25` |
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`3/25` |
`3/25`
`P(5)` | `= text(Number of 5’s)/text(Total number of throws)` |
`= 6/50` | |
`= 3/25` |
The image below is a plan of a commercial garden.
The total planted area is 48 square metres.
What is the total unplanted area?
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60 m² |
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64 m² |
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78 m² |
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81 m² |
`text(64 m)^2`
`text(6 planted areas = 48 m)^2`
`text(1 hexagon grid) = 48 ÷ 6 = 8\ text(m)^2`
`text(Number of unplanted areas: 8)`
`:.\ text(Total unplanted area)` | `=8 xx 8` | |
`=64\ text(m²)` |
The image below shows a layout of a village.
The total area of the occupied lots is 60 m².
What is the total area of the unoccupied lots in the village?
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36 m² |
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42 m² |
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50 m² |
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54 m² |
`50\ text(m)^2`
`text(12 occupied lots = 60 m)^2`
`text(1 lot = 60 ÷ 12 = 5 m)^2`
`text(Number of unoccupied lots = 10)`
`:.\ text(Area of unoccupied lots)` | `=10 xx 5` | |
`=50\ text(m²)` |
A bookmaker's bag is filled with different types of notes.
The bag contains 16 ten-dollar notes, 11 twenty-dollar notes, 8 fifty-dollar notes and 3 hundred-dollar notes.
The bookmaker reaches in to the bag and randomly selects one note.
What is the chance that a fifty-dollar note is selected?
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`4/19` |
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`8/29` |
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`6/17` |
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`4/17` |
`4/19`
`P(text($50 bill))` | `= text(Number of $50 bills)/text(Total number of bills)` |
`= 8/(16 + 11 + 8 + 3)` | |
`= 8/38` | |
`= 4/19` |
A bag contains different coloured balls.
It contains 4 red balls, 8 green balls, 3 pink balls, 6 grey balls and 11 yellow balls.
Nathalie picks a ball from the bag without looking.
What is the chance that she draws a grey ball?
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`1/5` |
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`3/16` |
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`6/31` |
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`4/13` |
`3/16`
`P(text(Grey ball))` | `= text(Number of grey balls)/text(Total number of balls)` |
`= 6/(4 + 8 + 3 + 6 + 11)` | |
`= 6/32` | |
`=3/16` |
Which dotted line is a line of symmetry?
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`text(Option 3: the left side is the mirror reflection of the right side.)`
Which dotted line is a line of symmetry?
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`text(Option 1: the top side is the mirror reflection of the bottom side.)`
A certain plane rises 2 metres for every 12 metres of its base length.
If it rises by 1.6 metres, what will be its base length?
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12.4 m |
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10.8 m |
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9.6 m |
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8.4 m |
`text(9.6 m)`
`text(Every 2 metres of height → 12 metres of base)`
`text(Every 1 metre of height → 6 metres of base)`
`:.\ text(Base length)` | `= 1.6 xx 6` | |
`=9.6\ text(m)` |
A one-metre tall person casts a 4-metres shadow on level ground.
If a 1.8 metre tall person stands at the same position, how long will the shadow be?
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6.8 m |
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7.2 m |
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8.0 m |
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8.6 m |
`text(7.2 m)`
`text(1 metre height → 4 metre shadow)`
`:.\ text(1.8 m height shadow)` | `= 1.8 xx 4` | |
`=7.2/ text(m)` |
William has a St Bernard puppy that weighs 25 kilograms.
After another 8 months, the St Bernard weighs 12% more.
How much does the dog weigh now?
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28 kg |
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30 kg |
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32 kg |
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37 kg |
`text(28 kg)`
`text(Weight)` | `= 25 + (25 xx 12text(%))` |
`= 25 + 3` | |
`= 28\ text(kg)` |
`:.\ text(The weight of the St Bernard after 8 months is 28 kilograms.)`
Paul’s height is 146 centimetres when he was 15 years old.
On his 18th birthday he was 10% taller than when he was at 15 years old.
How tall was Paul when he was 18?
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160.6 cm |
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150.8 cm |
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168.2 cm |
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180.3 cm |
`text(160.6 cm)`
`text(Pauls new height)` | `= 146 + (146 xx 10text(%))` |
`= 146 + 14.6` | |
`= 160.6\ text(cm)` |
`:.\ text(Paul’s height on his 18th birthday is 160.6 centimetres.)`
A store sells second hand mobile phones.
The graph below shows the price of 2 similar second-hand phones.
Which of the following is true based on the graph shown?
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Phone A is older and less expensive than Phone B |
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Phone B is older and more expensive than phone A |
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Phone A is newer and more expensive than Phone B |
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Phone A is older and more expensive than Phone B |
`text(Phone A is newer and more expensive than Phone B)`
`text(Phone A is left of Phone B → it is newer.)`
`text(Phone A is higher than Phone B → it is more expensive.)`
`:.\ text(Phone A is newer and more expensive than Phone B.)`
A man bought a plot of land in the past and now he is selling it.
The graph marks the price of the land when the man bought it and the price of the land now.
Which of the following is true based on the graph shown?
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The land is less expensive now than when it was purchased. |
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The land is more expensive years ago than now. |
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The land is more expensive now than years ago. |
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The price of the land does not change with time. |
`text(The land is more expensive now than years ago.)`
`text(Z is further right on the x-axis → most recent price.)`
`text(Z is higher on the y-axis → more expensive.)`
`:.\ text(The land is more expensive now than years ago.)`
A circle is divided into 8 equal parts, as shown in the diagram below.
What percentage of the circle’s area has been labelled with even numbers?
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37.5% |
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50% |
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57.5% |
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62.5% |
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70% |
`text(62.5%)`
`text(S)text(ince all areas are equal:)`
`text(Percentage)` | `= text(Number of even numbers)/text(Total number of sections) xx 100` |
`= 5/8 xx 100` | |
`= 62.5text(%)` |
Julian was driving into town and hit a kangaroo `3/4` of a kilometre into his trip.
Which of these represent where Julian hit the kangaroo?
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`text(Each spacing is worth)\ 1/4\ text(km.)`
Axe went jogging and stopped after `2/6` of a kilometre to take a rest.
Which of these represents where Axe stopped jogging?
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`text(Each spacing is worth)\ 1/6\ text(km.)`
Aaron wants to find the missing number that will make this number sentence correct.
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`+ 12 = 106` |
Which of these could Aaron use to find the missing number?
`106 -: 12` | `106 xx 12` | `106-12` | `12+106` |
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`106-12`
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`+12= 106` |
`text(Subtract 12 from both sides:)`
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`= 106 – 12` |
Carryn wants to find the number that will make this number sentence correct.
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`xx 9 = 72` |
Which of these could Carryn use to find the missing number?
`72 -: 9` | `9 xx 72` | `72-9` | `9+72` |
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`72-:9`
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`xx 9 = 72` |
`text(Divide both sides by 9:)`
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`= 72 -: 9` |
Nathan places a notepad along a line of symmetry of a star shape.
How many points does the star have?
`6` | `8` | `9` | `10` | `12` |
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`10`
`text(Number of points = 10)`