Date:

Grade 10 Mathematics Initial Assessment

Directions: This assessment will evaluate your understanding of key mathematical concepts. Show all your work and calculations in the spaces provided. You may use a calculator for the designated sections only.

Section I: Algebraic Expressions and Equations

1. Solve for x: 2x + 5 = 3x - 7

2. Simplify the expression: 3(2x - 4) - 5(x + 2)

3. Factor completely: x² - 9x + 18

Section II: Linear Functions

4. Find the slope and y-intercept of the line: 3x - 2y = 6

5. Write the equation of a line that passes through the points (2, 5) and (4, 9) in slope-intercept form (y = mx + b).

Grade 10 Mathematics Initial Assessment (continued)

Section III: Quadratic Functions

6. Solve the quadratic equation by factoring: x² - 7x + 12 = 0

7. Find the vertex of the quadratic function: f(x) = 2x² - 8x + 7

Section IV: Systems of Equations

8. Solve the system of equations using substitution or elimination:

2x + y = 7

x - y = 1

Section V: Word Problems

9. A rectangular garden has a perimeter of 36 meters. If the length is 4 meters more than the width, find the dimensions of the garden.

10. A ball is thrown upward from a height of 6 feet with an initial velocity of 40 feet per second. The height h (in feet) of the ball after t seconds is given by h = -16t² + 40t + 6. How long will it take for the ball to hit the ground?