### Diagnostic Elementary School Math Quiz (Gr. 6-7)

This is a diagnostic elementary school math quiz based on the Ontario curriculum for grades 6 to 7. It is meant to provide your 4P Academy tutor with information they can use to optimize your learning experience, focusing on developing your weaker skills while leveraging your strengths to help you advance in your studies and gain confidence!

All questions are unique and written by representatives of 4P Academy, as with all other quizzes and solutions we provide. Solutions to our quiz questions can be shared upon request.

1. If a rubics cube has 9 squares on one side, how many squares does it have on all sides combined?
34
36
54
56

2. How old is the boy if he was born 96360 hours ago?
10
12
9
11

3. By how much is 1 and 1/2 greater than 3/4?
4/3
3/4
1/2
5/4

4. If 4 batteries cost $3.75 at your convenience store, how much does a single battery cost (what is the cost per battery) if you buy it in a pack of eight at a store where batteries are two times cheaper than in the convenience store?
$0.47 per battery
$0.46 per battery
$0.45 per battery
$0.48 per battery

5. If you want to measure the perimeter of your house and your math notebook, which units of measurement would you use for them, in order?
kilometers, centimeters
meters, meters
centimeters, meters
meters, centimeters

6. How many grams are in one serving of ice cream if 1.5 kg will be shared between six people?
0.25 grams
1500 grams
250 grams
300 grams

7. What are the two missing numbers in this pattern? 3, 9, 15, _ , 27, 33, _, 45.
20, 39
21, 39
19, 38
21, 40

8. If a square and an equilateral triangle with all sides 4 centimeters in length are put side-by-side to make one shape that looks like a house, what is the perimeter and area of the new shape?
24 centimeters
28 centimeters
16 centimeters
20 centimeters

9. If a pencil is pointing North and is turned clockwise to point the opposite way (South) and then turned counter-clockwise until is points to the left of the original direction it pointed to (West), how many degrees was the pencil moved in total and by how many degrees did it move from its original place?
450 degrees in total, 90 degrees from original direction
270 degrees in total, 90 degrees from original direction
90 degrees in total, 45 degrees from original direction
270 degrees in total, 180 degrees from original direction

10. Determine the value of the variable n in the equation 2 x n + 3 = 11
-3
2
6
4

11. A regular backpack weighs 5 kilograms, a big backpack weighs 9 kilograms, and a small backpack weighs 3 kilograms. Estimate their average (mean) weight.
6.2 kilograms
5.7 kilograms
5.4 kilograms
5.6 kilograms

12. If a Ferris wheel takes 5 minutes to go around, taking you from the ground, up and back down, how many seconds did you spend on the Ferris wheel if you took the ride 3 times?
150 seconds
300 seconds
900 seconds
700 seconds

13. If you throw a regular six-sided dice on the table, what is the probability you get 2 and if you throw it again after, what is the probability that it shows you 2 again?
1/6, 1
2/6, 1/6
2, 1/6
1/6, 1/6

14. Estimate how many evergreen trees you need to plant in order to make a circular forest 2 kilometers in radius if each evergreen tree has a radius of 2 meters.
2 000 030
900 000
1 000 030
1 000 400

15. What are the square roots of 16, 49, and 81?
4, 7, 8
4, 7, 9
5, 7, 9
4, 8, 9

16. You have a piano, a couch, a table, an armchair, and a bookshelf around you in a room. You go to the centre of the room and spin with your eyes closed. Predict how many times you will open your eyes and see the piano after 25 spins.
3
10
5
25

17. You go to a store to buy balloons. 25 pink balloons cost $12.95, and 10 red balloons cost $5.78. Which is the better deal and what is the 13% tax on the better deal?
Pink balloons, $1.68 tax
Red balloons, $0.75 tax
Pink balloons, $1.32 tax
Red balloons, $0.82 tax

18. At your supermarket, pears are on sale for $11.50 for one kilogram. How much would it cost to purchase 150 g of pears?
$2.73
$2.83
$1.63
$1.73

19. A pool has a base shape of a trapezoid. This pool is 175 centimeters deep, has a base 400 cm long at the front, 500 cm long at the back, and 300 cm wide (the walls connecting the front and back walls are 300cm long). Find the capacity (volume) of the pool and convert it to meters cubed. Tip: Drawing the base could help to find which formulas and equations you need.
21.41 meters cubed
20.67 meters cubed
20.73 meters cubed
19.41 meters cubed

20. What is the perimeter and area of a hexagon if one of its sides is 3.5 centimeters?
17.5, 30.34 cm^2
17.5, 31.83 cm^2
21, 31.83 cm^2
21, 30.34 cm^2

21. A block of clay with a base of 10cm by 5cm is placed on the centre of a table. It is shifted to the right by 2cm, stretched out sideways to increase its base length by 4 cm, moved clockwise 45 degrees about its centre, and is flipped along a horizontal line that divides the clay in half. Using math language, describe what was done with the block of clay.
Translations: right, transformation, clockwise, reflection
Changes: translation, dilatation, rotation, reflection
Transformations: translation, dilatations, rotation, reflection
Movements: motion, stretch, rotation, flip

22. Represent 8, 11, 14, 17, ... as a pattern rule and determine the algebraic expression for it.
Start at 8 and add 4 each time, tn = 8 + 3n
Add 3 each time, tn = 3(n-1)
Start at 8 and add 3 each time, tn = 8 + 3(n-1)
Start at 8 and add 4 each time, tn = 8 + 4(n-1)

23. Solve 9 + x = 17 and 19 – x = -7 for x. (Find the value of x.)
17, 9
8, 26
8, 17
26, -26

24. Find the median, mode and mean of this set of data: {1, 3, 6, 1, 9, 2, 1, 7, 6}
3, 1, 4
4, 1, 3
1, 3, 4
3, 4, 1

25. The probability that a fish from Lake Dalrymple is a cod is 39%. Predict how many cod will be caught by a fisher in the middle of the lake, if they catch 300 fish.
119
120
115
117

26. Represent 120% as a fraction and as a decimal.
5/4, 1.25
5/6, 0.8
6/5, 1.2
5/4, 1.2

27. The ratio of sand to limestone in glass is 5 to 3. How many bags of limestone are needed if 15 bags of sand are put into the mixture to make glass?
9
10
7
12

28. You buy a pack of water with 20 cylindrical bottles for $9.70. If each bottle is 20 centimeters in height and 3 centimeters in radius, how much did you pay for each liter of water?
$3.24 per liter
$3.12 per liter
$2.36 per liter
$2.57 per liter

29. A right-angled triangle has a hypotenuse length of 5cm and one side length of 3cm. What is the length of the missing side?
5
4
3
2

30. Find the value of d given 4a + 3b = -7c – d/2 where a = 1.5, b = 3, and c = 1/7
16
32
-32
-16

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