5th Math: Geometry practice questions and exam guide

Rule A starts at 0 and adds 5. Rule B starts at 0 and adds 10. How does each B term compare to the matching A term?

1. Each B term is 5 more than the A term
2. Each B term is half the A term
3. Each B term is 10 more than the A term
4. Each B term is twice the A term

Answer: D — Each B term is twice the A term

D) Correct — 0, 5, 10, 15 pairs with 0, 10, 20, 30, and each B is 2 × A. A) Works only for the second pair; the gap keeps growing. B) Reverses the relationship. C) Uses the step size of B, but the gap changes each step.

In an ordered pair (x, y), which value comes first?

1. y
2. x
3. The larger number
4. The smaller number

Answer: B — x

B) Correct — The x-coordinate (the move right) is always written first, then the y-coordinate (the move up). A) The y-coordinate is always written second. C) Order is set by direction, not size: (2, 9) and (9, 2) are different points. D) Order is set by direction, not size.

The tick marks on a y-axis are 0, 5, 10, 15, 20. A point is halfway between 10 and 15. What is its y-coordinate?

1. 12 1/2
2. 11
3. 15
4. 10 1/2

Answer: A — 12 1/2

A) Correct — Halfway between 10 and 15 is 2 1/2 more than 10. B) Treats each small space as 1 instead of reading the scale of 5. C) Rounds up to the next tick mark. D) Adds half a unit instead of half of the 5-unit space.

A graph of (days, pages left to read) shows (0, 30), (1, 25), (2, 20), (3, 15). What is happening?

1. 5 pages are added each day
2. 5 pages are read each day
3. 30 pages are read each day
4. The book gets longer each day

Answer: B — 5 pages are read each day

B) Correct — The pages left go down by 5 each day. A) Reverses the direction; the number of pages left is going down. C) Reads the starting total as the daily amount. D) The pages left shrink, so the reader is getting through the book.

What is the BEST reason that every square is a parallelogram?

1. A square has 4 equal sides
2. A square has 4 right angles
3. A square has 2 pairs of parallel sides
4. A square is a regular polygon

Answer: C — A square has 2 pairs of parallel sides

C) Correct — Having 2 pairs of parallel sides is the property that defines a parallelogram. A) True, but equal sides are what make it a rhombus, not a parallelogram. B) True, but right angles are what make it a rectangle. D) True, but being regular is not what makes a parallelogram.

Which property do rectangles have that some parallelograms do NOT have?

1. Opposite sides parallel
2. 4 sides
3. Opposite sides of equal length
4. 4 right angles

Answer: D — 4 right angles

D) Correct — Many parallelograms lean over and have no right angles. A) Every parallelogram has this. B) Every parallelogram has this. C) Every parallelogram has this.

Can an equilateral triangle be a right triangle?

1. No; each of its angles is 60°
2. Yes, always
3. Yes, if it is drawn large
4. No; equilateral triangles are obtuse

Answer: A — No; each of its angles is 60°

A) Correct — Equal sides force equal angles, and 180° ÷ 3 = 60°, so no angle is 90°. B) Its angles are all 60°, never 90°. C) Size does not change its angles. D) Right answer, wrong reason: its angles are all acute.

A rectangle has corners at (1, 1), (6, 1), (6, 4), and (1, 4). What is its area?

1. 16 square units
2. 15 square units
3. 24 square units
4. 8 square units

Answer: B — 15 square units

B) Correct — The sides are 5 and 3 units long, so 5 × 3 = 15. A) Is the perimeter number, not the area. C) Uses the coordinates 6 and 4 as side lengths (6 × 4). D) Adds the side lengths instead of multiplying.

Which point is closest to the y-axis?

1. (1, 8)
2. (4, 2)
3. (6, 1)
4. (3, 3)

Answer: A — (1, 8)

A) Correct — Distance from the y-axis is the move right, the x-coordinate, and 1 is the smallest. B) Is 4 units from the y-axis. C) Is close to the x-axis (y = 1) but 6 units from the y-axis. D) Is 3 units from the y-axis.

What kind of angle do the x-axis and the y-axis make where they cross?

1. A right angle
2. An acute angle
3. An obtuse angle
4. A straight angle

Answer: A — A right angle

A) Correct — One axis is horizontal and the other is vertical, so they meet at 90°. B) An acute angle is smaller than 90°. C) An obtuse angle is larger than 90°. D) A straight angle is 180°, a flat line.

A graph uses x = hours and y = plant height in cm. Which ordered pair shows "after 5 hours, the plant is 10 cm tall"?

1. (0, 10)
2. (10, 5)
3. (5, 15)
4. (5, 10)

Answer: D — (5, 10)

D) Correct — Hours go first (x) and height second (y). A) Leaves out the 5 hours. B) Swaps the coordinates. The first number is the move right; the second is the move up. C) Adds 5 + 10 for the height instead of using 10.

Which story matches the points (0, 2), (1, 4), (2, 6), (3, 8), with x = days and y = books in a stack?

1. The stack starts with 2 books and gains 2 each day
2. The stack starts empty and gains 2 each day
3. The stack starts with 2 books and doubles each day
4. The stack starts with 8 books and loses 2 each day

Answer: A — The stack starts with 2 books and gains 2 each day

A) Correct — At day 0 there are 2 books, and each day adds 2. B) Ignores the point (0, 2): there are 2 books at the start. C) 4 to 8 is a double, but 4 to 6 is not. D) Reverses the direction; the stack grows.

Draw a Venn diagram for parallelograms, rectangles, and squares — what's the relationship?

Squares ⊂ Rectangles ⊂ Parallelograms. Squares are rectangles, which are parallelograms.

What does the x-coordinate tell you?

How far to move horizontally (right or left).

Is a square a rectangle?

Yes. A square is a rectangle with all sides equal. (All squares are rectangles.)

Where does a trapezoid fit in the hierarchy?

A trapezoid is a quadrilateral with a pair of parallel sides. Most 5th-grade books say exactly 1 pair, which keeps it out of the parallelogram family. (Some books say "at least 1 pair," which would make every parallelogram a trapezoid too.)

What is the 'coordinate plane'?

Two number lines (x-axis horizontal, y-axis vertical) that intersect to form a grid for plotting points.