Selective High School Placement Test
Mathematical Reasoning Online Quiz
Please read this page carefully.
There are 35 questions in this quiz. For each question there are five possible answers. Choose the one correct answer.
You will not lose marks for incorrect answers, so you should attempt all 35 questions.
You must complete the quiz within 40 minutes and you can retake the quiz twice.
0 of 35 questions completed
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading…
You must sign in or sign up to start the quiz.
You must first complete the following:
0 of 35 questions answered correctly
Time has elapsed
You have reached 0 of 0 point(s), (0)
Earned Point(s): 0 of 0, (0)
0 Essay(s) Pending (Possible Point(s): 0)
|Table is loading|
|No data available|
Sandy’s watch reads 1850.
What is the time one quarter of an hour later, in 12-hour format?CorrectIncorrect
Jack divides a white wall into equal sections.
He paints some sections purple, as shown.
Jack then paints 2⁄5 of the whole wall yellow.
Finally, he paints the rest of the wall green.
How many sections does he paint green?CorrectIncorrect
Nicola multiplies the smallest four-digit whole number by the largest two-digit whole number.
What is the answer?CorrectIncorrect
Rana needs 650 grams of cooking sauce.
She places a glass jar of cooking sauce on a scale.
The glass jar weighs 330 g when empty.
How much more cooking sauce does Rana need?CorrectIncorrect
‘Calculator numbers’ are written in the style of digits on a calculator, as shown.
The calculator number eleven is the smallest two-digit number with two lines of symmetry.
Which of the numbers below is the largest two-digit calculator number that has just one line of symmetry?CorrectIncorrect
Kim and Jamie each think of a different whole number that is greater than zero and less than 50.
Kim’s number is a multiple of 5.
Jamie’s number is an even number which is a multiple of 7.
What is the difference between the largest possible value of Kim’s number and the smallest
possible value of Jamie’s number?CorrectIncorrect
Rectangles P and Q both have the same area.
[diagram not to scale]
What is the length of rectangle Q?CorrectIncorrect
Sooyoung has a glass containing 250 millilitres of cordial, and a bottle containing 1 litre of water.
Sooyoung drinks 10 mL of the cordial.
She finds the drink too strong, so she pours water from the bottle into the glass until the water reaches the 500 mL mark.
How much water is left in the bottle?CorrectIncorrect
□ always represents the same number.
▲ represents a different number.
If 9 × □ = 108
and ▲ + □ = 36
what is ▲ ?CorrectIncorrect
Tahnee is making a pattern out of white and black tiles.
She hasn’t finished yet. She wants the finished pattern to have one vertical line of symmetry.
What is the smallest number of tiles she needs to add onto the right of the pattern?CorrectIncorrect
Jessica has blue, green, red and yellow buttons in a bag.
There are twice as many red buttons as blue buttons.
If she takes one button out of the bag without looking:
- the probability that it is blue is 0.2
- the probability that it is green is 0.3
What is the probability that Jessica takes out a yellow button?CorrectIncorrect
The graph shows the average monthly rainfall in Cairns for one year.
Here are three statements about the graph.
- June had more than twice as much rainfall as August.
- December had 9 cm more rainfall than November.
- The rainfall in February, March and April combined was more than 1 metre.
Which of these statements are correct?CorrectIncorrect
Alan had $10. He gave some of this money to Kiana.
Alan then gave half of what he had left to Jason.
Jason gave half of what he was given to Lenny.
Lenny received $1.60.
How much did Alan give to Kiana?CorrectIncorrect
Noah is drawing an accurate copy of this shape:
The shape has one line of symmetry.
He starts drawing the shape as follows:
What is the size of angle S?CorrectIncorrect
When 117 chocolates are shared between 14 people, each person gets 8 chocolates and there
are 5 chocolates left over.
Which number sentence shows this information?CorrectIncorrect
A large rectangle has sides 8 cm and 10 cm.
Two small rectangles are removed from this large rectangle.
This leaves the shaded shape.
What is the perimeter of the shaded shape?CorrectIncorrect
Andy, Bella and Carlo shared a chocolate bar.
Andy ate 1⁄5 of the bar, Bella ate 2⁄5 of the bar and Carlo ate the rest.
Which of the following statements are correct?
- Carlo ate less than half of the chocolate bar.
- Andy ate more than one quarter of the chocolate bar.
- Andy and Bella ate less than three quarters of the chocolate bar altogether.
In a ‘magic square’, each row, each column and each diagonal add up to the same total.
In the magic square below, some of the numbers are missing.
What is the missing number at ♦ ?CorrectIncorrect
Chen has a spinner that is split into four equal sections.
He spins the spinner and it lands on 4.
Now Emily is going to spin the spinner once. Which of these statements are correct?
X. The probability of Emily getting a 4 is 1⁄4
Y. The probability that Emily’s number is less than Chen’s is 1⁄2
Z. The probability that Emily and Chen’s scores add up to make more than 5 is 3⁄4CorrectIncorrect
There is something wrong with these scales. As shown, the pointer does not start at 0 kilograms when there is nothing on the scales:
Apart from this, the scales work normally: the pointer goes up by 1 kg for every kilogram added to the scales.
Two identical blocks are placed on the scales. The pointer makes less than a full turn.
What is the mass, in kg, of one of the blocks?CorrectIncorrect
Alinta and Tau both round the number 4 850 000.
Alinta rounds the number to the nearest million.
Tau rounds the number to the nearest hundred thousand.
What is the difference between their answers?CorrectIncorrect
Here is a graph showing the outdoor temperature during a period of 9 hours.
Which of these statements are true?
- The temperature was 10°C at four different times.
- The temperature change between 1 hour and 3 hours was greater than the temperature change between 4 hours and 6 hours.
- The lowest temperature was 5°C
Quoc bought 4 pizzas to share with Amina, Fred and Sally.
Amina ate 4⁄5 of a pizza.
Fred ate 1 1⁄5 pizzas.
Sally ate 3⁄5 of a pizza.
Quoc ate all of the pizza that was left.
How much more pizza did Quoc eat than Amina?CorrectIncorrect
Three different boxes are weighed in pairs. Different pairs of boxes have combined weights of 28 kg, 32 kg and 38 kg as shown.
When the three boxes are weighed together, what is their combined weight?CorrectIncorrect
What is the sum of the number of faces, the number of edges and the number of vertices of a pyramid with a hexagonal base?CorrectIncorrect
In our number system, the value represented by a digit depends on its position. For example, in the number 273, the digit 7 represents 70.
In the number 30 060, how many times larger is the value represented by the digit 3 than the value represented by the digit 6?CorrectIncorrect
Kylie lives in Las Vegas and she visits her cousin Mike, who lives in Sydney.
Kylie leaves Las Vegas on Friday at 1300 local time on a 6-hour flight to New York.
She spends 24 hours in New York.
She then catches a 20-hour flight to Sydney.
The time in Las Vegas is 17 hours behind the time in Sydney.
What time is it in Sydney when Kylie arrives?CorrectIncorrect
Here is a shape made of black and white parts:
What is the total area that is black?CorrectIncorrect
Jan is making a mixed fruit drink for a party.
She puts some orange juice into the jug, as shown.
She then adds 6 times as much apple juice.
How many millilitres of fruit drink does Jan make?CorrectIncorrect
The equilateral triangle above is rotated anti-clockwise into the position shown below.
Through what angle is it rotated anti-clockwise?CorrectIncorrect
Vinayak’s little brother tried to draw three different nets of a cube, but he got it wrong. He only drew five squares for each net, but a complete cube net has six squares.
Here are his three drawings:
Vinayak wants to help, by adding one more square to each net to make a correct cube net. However, he is not sure if this is possible for all of the drawings.
Which of the three drawings can be made into complete cube nets by adding one square?CorrectIncorrect
Harry is making shapes out of identical rectangular cards with the letter H on.
He makes shape X, then adds another card to make shape Y, as shown.
The perimeter of shape X is 64 cm and the perimeter of shape Y is 82 cm.
What is the width of each of Harry’s rectangles?CorrectIncorrect
Claudia makes a number pattern using these rules:
- Choose the first three numbers.
- After this, each number is the sum of the three numbers before it.
Here is Claudia’s pattern with three missing numbers labelled X, Y and Z.
2, X, 0, Y, 6, Z
All the numbers are whole numbers.
What number does Z represent?CorrectIncorrect
In a game, I collect stars and hearts.
I get points when I collect a star. The number of points for a star is always the same.
I get a different number of points when I collect a heart. The number of points for a heart is always the same.
If I collect 3 stars and 5 hearts, I get 27 points.
If I collect 5 stars and 7 hearts, I get 41 points.
How many points do I get if I collect 1 star and 1 heart?CorrectIncorrect
How many whole numbers between 1 and 100 are multiples of 3, but are not multiples of 8?
You should include 3 itself.CorrectIncorrect