5th Math: Operations & Algebraic Thinking practice questions and exam guide

On a coordinate plane, the point (3, 5) means:

1. 8 units right
2. 5 units right, 3 units up
3. 3 units up, 5 units right
4. 3 units right, 5 units up

Answer: D — 3 units right, 5 units up

D) Correct — Move right by the first number, then up by the second. A) Adds the numbers into one move. B) Swaps the coordinates; the first number is the move right and the second is the move up. C) Uses the 3 for up and the 5 for right, which swaps the directions.

Which expression represents 'three times the sum of 5 and 2'?

1. 3 × 5 + 2
2. 3 × (5 + 2)
3. 3 + 5 × 2
4. 3 + 5 + 2

Answer: B — 3 × (5 + 2)

B) Correct — "The sum of 5 and 2" is one group, (5 + 2), and "three times" multiplies the whole group. A) Triples only the 5. C) Adds 3 instead of tripling, and doubles the 5. D) Adds 3 instead of tripling.

Which way does the y-axis run?

1. Diagonal
2. Horizontal (side to side)
3. Vertical (up and down)
4. Along the top edge of the grid

Answer: C — Vertical (up and down)

C) Correct — The y-axis runs up and down. A) Neither axis is slanted; they cross at a right angle. B) That is the x-axis. D) The y-axis runs up the left side, through the origin.

A rectangle is 9 m long and 4 m wide. Which expression gives its perimeter?

1. 9 × 4
2. 9 + 4
3. 2 × 9 × 4
4. 2 × 9 + 2 × 4

Answer: D — 2 × 9 + 2 × 4

D) Correct — A rectangle has two lengths and two widths. A) Is the area, not the perimeter. B) Is only half the perimeter. C) Doubles the area.

Which expression means "the sum of 14 and 6, divided by 2"?

1. 14 ÷ 2 + 6
2. 14 + 6 ÷ 2
3. (14 + 6) ÷ 2
4. 2 ÷ (14 + 6)

Answer: C — (14 + 6) ÷ 2

C) Correct — Add first (the parentheses), then divide the sum by 2. A) Divides only the 14. B) Divides only the 6. D) Divides in the wrong order.

Which symbol makes this true? (2 + 3) × 4 ___ 2 + (3 × 4)

1. =
2. <
3. >
4. Cannot tell

Answer: C — >

C) Correct — (2 + 3) × 4 = 20 and 2 + (3 × 4) = 14, and 20 > 14. A) Same numbers, but the parentheses change the order and the value. B) Reverses the comparison. D) Both sides can be evaluated: 20 and 14.

Where is the origin?

1. (0, 0)
2. (1, 1)
3. (0, 1)
4. The middle of the grid

Answer: A — (0, 0)

A) Correct — The origin is where the two axes cross. B) Is 1 unit right and 1 unit up from the origin. C) Is 1 unit up the y-axis. D) On a first-quadrant grid the origin is at the bottom-left corner.

Evaluate: (2 + 4)³ ÷ 8

1. 10
2. 6
3. 27
4. 216

Answer: C — 27

C) Correct — 2 + 4 = 6; 6³ = 216; 216 ÷ 8 = 27. A) Ignores the grouping symbols; what is inside parentheses or brackets comes first. B) Stops partway: 6 is only the result of step 1 (2 + 4 = 6). D) Stops partway: 216 is only the result of step 2 (6³ = 216).

Which point is farther to the right: (5, 3) or (3, 5)?

1. (3, 5)
2. They are equally far right
3. You cannot tell without a graph
4. (5, 3)

Answer: D — (5, 3)

D) Correct — Distance to the right is the x-coordinate, and 5 is more than 3. A) Is higher up, but only 3 units to the right. B) Their x-coordinates are different: 5 and 3. C) The x-coordinate tells you directly.

Which point is 5 units from the y-axis and 3 units from the x-axis?

1. (3, 5)
2. (5, 3)
3. (5, 5)
4. (3, 3)

Answer: B — (5, 3)

B) Correct — 5 units from the y-axis means x = 5; 3 units from the x-axis means y = 3. A) Mixes up the two axes: x is the distance from the y-axis. C) Is 5 units from both axes. D) Is 3 units from both axes.

Which expression means "5 less than the quotient of 36 and 3"?

1. 5 − 36 ÷ 3
2. (36 − 5) ÷ 3
3. 36 − 5 ÷ 3
4. 36 ÷ 3 − 5

Answer: D — 36 ÷ 3 − 5

D) Correct — Find the quotient 36 ÷ 3 first, then take 5 away from it. A) Reverses the order; "5 less than" means subtract the 5. B) Subtracts before dividing. C) Divides only the 5.

Which expression means "the product of 4 and the sum of 6 and 3"?

1. 4 × (6 + 3)
2. 4 × 6 + 3
3. 4 + 6 + 3
4. 4 + 6 × 3

Answer: A — 4 × (6 + 3)

A) Correct — The sum is one group, and 4 multiplies the whole group. B) Multiplies only the 6. C) Adds 4 instead of multiplying. D) Adds the 4 and multiplies the wrong numbers.

Evaluate: 3 + 4 × 2.

11. (Multiply first: 4 × 2 = 8; then 3 + 8 = 11.)

Two patterns: A = 0, 3, 6, 9... B = 0, 6, 12, 18... What's the relationship?

B is always 2× A.

What does the y-coordinate tell you?

How far to move vertically (up or down).

What is the order of operations? (PEMDAS)

Parentheses → Exponents → Multiplication & Division (left to right) → Addition & Subtraction (left to right).

If you're plotting weight gained per week, what should be on the y-axis?

Weight (the dependent variable).

Evaluate: 4 × (5 + 3) ÷ 2.

16. (5+3=8; 4×8=32; 32÷2=16.)