Selective Mock Test 1 — Mathematical Reasoning (Year 6)
A free NSW Selective High School placement test practice paper for Year 6 in the format of the real test: 35 questions in 40 minutes, covering Section A — Number, algebra and patterns; Section B — Measurement and geometry; Section C — Statistics, probability and problem solving. No calculator. Choose the best answer. Answer every question — there is no penalty for a wrong answer. Attempt it online — every question is marked instantly and the correct answers are shown at the end.
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Q1. A bike costs $120. Its price is increased by 20%. Later, the new price is decreased by 25%. What is the final price?
Q2. Anna, Ben and Cal share $540 in the ratio 2 : 3 : 4. How much more does Cal receive than Anna?
Q3. A bag holds red and blue marbles in the ratio 3 : 5. After 12 more red marbles are put in, there are equal numbers of red and blue marbles. How many marbles were in the bag at the start?
Q4. Three identical machines make 60 toys in 4 hours. Working at the same rate, how many toys would 5 of these machines make in 6 hours?
Q5. What is the value of 48 ÷ (2 + 6) × 3 − 22 ?
Q6. Two lights flash together at exactly 9:00 am. One flashes every 12 seconds and the other every 18 seconds. How many more times will they flash together up to and including 9:03 am?
Q7. What is the smallest whole number n so that 180 × n is a perfect square?
Q8. In the five-digit number 52▢8▢, each box stands for a digit. The number is divisible by both 4 and 9. What is the largest possible value of the number?
Q9. The pattern 7, 11, 15, 19, … continues by adding 4 each time. Which of these numbers is in the pattern?
Q10. Mia thinks of a number. She multiplies it by 3, subtracts 7, then halves the answer. Her final answer is 19. What number did Mia start with?
Q11. At 5 am the temperature was −8 °C. It rose by 3 °C every hour until 1 pm, then fell by 2 °C every hour until 7 pm. What was the temperature at 7 pm?
Q12. The mean of five numbers is 18. One number is removed and the mean of the remaining four numbers is 16. Which number was removed?
Q13. Sam spent 1/3 of his money on a book. He then spent 3/4 of the money he had left on lunch. He had $12 remaining. How much money did Sam have at the start?
Q14. In the diagram, the two horizontal lines are parallel. What is the size of angle x?
Q15. Triangle ABC has AB = AC and angle BAC = 40°. The side BC is extended to D. What is the size of angle y (angle ACD)?
Q16. Each interior angle of a regular polygon is 156°. How many sides does the polygon have?
Q17. A 14 cm by 8 cm rectangle has a 4 cm by 3 cm rectangle cut out of the middle of its top side, as shown. What is the perimeter of the shape that is left?
Q18. A square of side 10 cm has a right-angled triangle cut off each corner, as shown by the dashed lines. Each triangle has two 3 cm sides. What is the area of the shaded shape?
Q19. A 6 cm × 4 cm × 3 cm block is painted on all six faces. It is then cut into 1 cm cubes. How many of the small cubes have paint on exactly two faces?
Q20. A closed box shaped like a rectangular prism has a volume of 120 cm³. Its length is 6 cm and its width is 5 cm. What is the total surface area of the box?
Q21. A plane leaves Sydney at 22:40 on Monday (Sydney time). The flight takes 13 hours 50 minutes. London time is 10 hours behind Sydney time. What is the time in London when the plane lands?
Q22. Leah reaches the Park St bus stop at 8:26 am and catches the next bus to the Library. How many minutes after reaching Park St does she arrive at the Library?
Q23. A cyclist rides 24 km at 12 km/h and then another 36 km at 36 km/h. What is her average speed for the whole 60 km?
Q24. The map shows Tom's walk from Home to School, going past the Bridge. The lengths on the map are shown. Tom walks at 4.5 km/h. How long does his walk take?
Q25. Triangle PQR is reflected in the x-axis. The image is then moved 4 units to the left and 1 unit up. What are the coordinates of the final position of P?
Q26. The graph shows how many smoothies a café sold from Monday to Friday. The café wants to sell a mean (average) of 32 smoothies per day over the six days from Monday to Saturday. How many must it sell on Saturday?
Q27. Five whole numbers have a median of 5 and a mean of 6. The number 4 appears more often than any other number in the list. What is the largest possible value of the biggest number?
Q28. A bag contains 4 red, 5 blue and 3 green counters. How many green counters must be added so that the probability of picking a green counter is 1/2?
Q29. Two ordinary six-sided dice are rolled and the numbers are added. What is the probability that the total is 8?
Q30. Using the digits 1, 2, 3, 4 and 5, with no digit used more than once, how many different even three-digit numbers can be made?
Q31. Six teams are in a competition. Each team plays every other team twice, once at home and once away. How many games are played altogether?
Q32. I am a two-digit number. My digits add up to 11. If my digits are swapped, the new number is 27 more than me. What number am I?
Q33. Phone plan A costs $20 a month plus 10 cents per minute of calls. Plan B costs $35 a month plus 4 cents per minute. For how many minutes of calls in a month do the two plans cost exactly the same?
Q34. The pie chart shows how the students at a school travel to school. 30 students ride a bike. How many students walk?
Q35. In a class of 30 students, 18 play soccer, 14 play tennis and 5 play neither sport. How many students play both soccer and tennis?
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