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Questions and Answers
Sandy's watch reads 1850. What is the time one quarter of an hour later, in 12-hour format?
Sandy's watch reads 1850. What is the time one quarter of an hour later, in 12-hour format?
6:45 pm
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?
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?
Nicola multiplies the smallest four-digit whole number by the largest two-digit whole number. What is the answer?
Nicola multiplies the smallest four-digit whole number by the largest two-digit whole number. What is the answer?
99 990
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?
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?
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'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?
'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?
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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?
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?
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Rectangles P and Q both have the same area. What is the length of rectangle Q?
Rectangles P and Q both have the same area. What is the length of rectangle Q?
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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?
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?
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Always represents the same number. represents a different number. If 9 × = 108 and = 36 what is ?
Always represents the same number. represents a different number. If 9 × = 108 and = 36 what is ?
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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?
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?
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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?
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?
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The graph shows the average monthly rainfall in Cairns for one year. Here are three statements about the graph:
1 June had more than twice as much rainfall as August.
2 December had 9 cm more rainfall than November.
3 The rainfall in February, March and April combined was more than 1 metre.
Which of these statements are correct?
The graph shows the average monthly rainfall in Cairns for one year. Here are three statements about the graph: 1 June had more than twice as much rainfall as August. 2 December had 9 cm more rainfall than November. 3 The rainfall in February, March and April combined was more than 1 metre. Which of these statements are correct?
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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?
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?
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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?
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?
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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?
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?
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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?
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?
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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?
1 Carlo ate less than half of the chocolate bar
2 Andy ate more than one quarter of the chocolate bar
3 Andy and Bella ate less than three quarters of the chocolate bar altogether
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? 1 Carlo ate less than half of the chocolate bar 2 Andy ate more than one quarter of the chocolate bar 3 Andy and Bella ate less than three quarters of the chocolate bar altogether
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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◆?
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◆?
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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 3/4
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 3/4
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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?
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?
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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?
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?
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Here is a graph showing the outdoor temperature during a period of 9 hours. Which of these statements are true?
1 The temperature was 10°C at four different times.
2 The temperature change between 1 hour and 3 hours was greater than the temperature change between 4 hours and 6 hours.
3 The lowest temperature was 5°C.
Here is a graph showing the outdoor temperature during a period of 9 hours. Which of these statements are true? 1 The temperature was 10°C at four different times. 2 The temperature change between 1 hour and 3 hours was greater than the temperature change between 4 hours and 6 hours. 3 The lowest temperature was 5°C.
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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?
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?
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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?
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?
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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?
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?
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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?
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?
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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?
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?
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Here is a shape made of black and white parts. What is the total area that is black?
Here is a shape made of black and white parts. What is the total area that is black?
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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?
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?
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The equilateral triangle above is rotated anti-clockwise into the position shown below. Through what angle is it rotated anti-clockwise?
The equilateral triangle above is rotated anti-clockwise into the position shown below. Through what angle is it rotated anti-clockwise?
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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?
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?
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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?
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?
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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?
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?
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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?
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?
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How many whole numbers between 1 and 100 are multiples of 3, but are not multiples of 8?
How many whole numbers between 1 and 100 are multiples of 3, but are not multiples of 8?
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Study Notes
Selective High School Placement Test - Practice Test 1
- Test duration: 40 minutes
- Number of questions: 35
- Answer format: Multiple choice (A to E)
- Answer sheet: Separate answer sheet required; fill in student details
- Instructions: Do not open question paper until instructed; answer all questions; no extra time for transferring answers; no extra paper allowed; calculators and dictionaries are not permitted.
- Question type examples: Time calculation, problem solving using visual aids, calculations involving fractions, finding the smallest and largest numbers, calculating weight, identifying symmetry in numbers, calculating perimeter, determining time differences.
Question 1
- Question: Sandy's watch reads 1850. What is the time one quarter of an hour later, in 12-hour format?
- Answer Choices: 6:35 am, 7:05 am, 6:35 pm, 6:45 pm, 7:05 pm
- Correct Answer: 6:45 pm
Question 2
- Question: 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?
- Visual Aid: A diagram shows sections of a wall. Purple sections are illustrated.
- Answer Choices: 1, 2, 3, 4, 5
- Correct Answer: 3
Question 3
- Question: Nicola multiplies the smallest four-digit whole number by the largest two-digit whole number. What is the answer?
- Answer Choices: 99 000, 99 990, 990 000, 999 900, 999 999
- Correct Answer: 990 000
Question 4
- Question: 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?
- Visual Aid: A scale with a measurement of 330 g.
- Answer Choices: 100 g, 130 g, 200 g, 230 g, 430 g
- Correct Answer: 320 g
Question 5
- Question:'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?
- Visual Aid: A list of calculator numbers.
- Answer Choices: 52, 83, 88, 96, 99
- Correct Answer: 96
Question 6
- Question: 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?
- Answer Choices: 31, 36, 38, 39, 43
- Correct Answer: 31
Question 7
- Question: Rectangles P and Q both have the same area. Rectangle P has dimensions 10 cm by 6 cm. Rectangle Q has dimensions of 4 cm by an unknown length. What is the length of rectangle Q?
- Visual Aid: Diagrams of rectangle P and Q, with given measurements.
- Answer Choices: 8, 12, 15, 32, 60
- Correct Answer: 15 cm
Question 8
- Question: 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?
- Answer Choices: 240 mL, 260 mL, 740 mL, 760 mL, 990 mL
- Correct Answer: 740 mL
Question 9
- Question: 9 × □ = 108 and 9 ÷ □ = 36. What is □?
- Answer Choices: 3, 12, 24, 28, 48
- Correct Answer: 12
Question 10
- Question: 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?
- Visual Aid: Partially completed pattern.
- Answer Choices: 2, 3, 6, 8, 9
- Correct Answer: 3
... (and so on for the rest of the questions)
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Description
Prepare for the Selective High School Placement Test with this practice test consisting of 35 multiple-choice questions. The quiz covers various topics such as time calculations, problem solving, and basic math operations, all designed to help you hone your skills before the actual test. Aim to manage your time and accuracy as you solve each question within the 40-minute time limit.
