9th grade Math practice sheet
Alabama Course of Study · from Gradelings · Name: ______________________
Question 1
What does it mean to say the rational numbers are dense?
- There is a largest rational number
- Every rational number is a whole number
- Between any two rational numbers there is always another one
- Rational numbers cannot be written as fractions
Between any two rational numbers there is always another one
Hint: Dense means there are no gaps: the average of two rational numbers is another rational number between them.
Question 2
To solve 6x + 14 = 50, Jay first subtracts 14 from both sides. What equation comes next?
- 6x = 64
- 6x = 50
- 6x = 36
- x + 14 = 50
6x = 36
Hint: Whatever you do to one side, do to the other. Subtracting keeps the equation balanced.
Question 3
Which point is in the region y > x + 3?
- (−1, 2)
- (1, 5)
- (4, 4)
- (−3, −2)
(1, 5)
Hint: Put each point into the inequality. A point on the line is not included because the sign is strict, and the other side of the line is the wrong region.
Question 4
What is the slope of the line through (-4, -1) and (-3, 1)?
answer box
2
Hint: slope = rise ÷ run = (1 − (−1)) ÷ (-3 − (−4)) = 2 ÷ 1 = 2.
Question 5
Triangle ABC has vertices A(1, −2), B(0, 2) and C(8, 4). Is the angle at B a right angle?
- No
- Yes
Yes
Hint: Find the slopes of BA and BC. The angle is a right angle only if the slopes multiply to −1.
Question 6
Triangle B is an enlargement of triangle A. A side of 2 cm on triangle A matches a side of 8 cm on triangle B. What is the scale factor?
answer box
4
Hint: Scale factor = new length ÷ original length = 8 ÷ 2 = 4.
Question 7
Every edge of a cube is multiplied by 2. By what factor does the volume change?
answer boxtimes
8 times
Hint: Volume depends on length × width × height, so the factor is cubed.
Question 8
In a right triangle, the side opposite angle A is 12, the side next to angle A is 9 and the hypotenuse is 15. What is cos A?
- 3/4
- 4/3
- 4/5
- 3/5
3/5
Hint: SOH CAH TOA: sin = opposite ÷ hypotenuse, cos = adjacent ÷ hypotenuse, tan = opposite ÷ adjacent.
Question 9
A circle has radius 10 cm. A chord is 16 cm long. How far is the chord from the center, in cm?
answer boxcm
6 cm
Hint: The perpendicular from the center meets the chord at its midpoint, 8 cm from each end. Use a right triangle with hypotenuse 10 and one leg 8: 10² − 8² = 36, and √36 = 6.
Question 10
What is the order of rotation symmetry of a regular hexagon?
- 12
- 3
- 6
6
Hint: A regular polygon's order equals its number of sides.
Answer key
- 1. Between any two rational numbers there is always another one (Number Sets)
- 2. 6x = 36 (Rearranging Formulas)
- 3. (1, 5) (Lines & Intersections)
- 4. 2 (Linear Relations)
- 5. Yes (Coordinate Geometry)
- 6. 4 (Similarity & Scale)
- 7. 8 times (Right Triangles & Scaling)
- 8. 3/5 (Right-Triangle Trig)
- 9. 6 cm (Circle Properties)
- 10. 6 (Line & Rotation Symmetry)
Want more than 10 questions?
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