Sec 2 Mathematics Quadratic Expressions & Equations topical questions

Expand and simplify each product.

1. (a)(x + 1)(x + 4)[2]
2. (b)(x − 2)(x + 6)[2]

Expand each expression, using the identities where they fit.

1. (a)(x + 3)²[1]
2. (b)(x − 5)²[1]
3. (c)(x + 7)(x − 7)[1]
4. (d)Which of (a) to (c) is a difference of two squares once expanded?[1]

Factorise each expression.

1. (a)5x² − 10x[1]
2. (b)x² + 9x + 18[1]
3. (c)x² − 25[1]

Expand each expression.

1. (a)(x + 2)(x + 9)[2]
2. (b)(x − 4)²[2]

Factorise each expression completely.

1. (a)x² − 81[1]
2. (b)6x² − 15x[1]

Factorise each four-term expression by grouping.

1. (a)ax + ay + bx + by[2]
2. (b)mx + my + 3x + 3y[2]

Factorise each quadratic.

1. (a)x² − 3x − 10[2]
2. (b)x² + 2x − 24[2]

The equation x² + 8x + 15 = 0 is to be solved by factorisation.

1. (a)State the solutions of (x − 4)(x + 9) = 0.[1]
2. (b)Factorise and solve x² + 8x + 15 = 0.[2]
3. (c)Verify one of your solutions by substitution.[1]

Two short equations.

1. (a)Solve x² − 5x = 0.[2]
2. (b)Solve x² = 121.[1]
3. (c)Explain why part (a) has the solution x = 0 as well as x = 5.[1]

The equation x² + 3x − 28 = 0 is to be solved by factorisation.

1. (a)Find the factor pair that works.[1]
2. (b)Solve the equation.[2]

A rectangular notice board in an HDB corridor has length (x + 3) m and width x m, and its area is 10 m².

1. (a)Show that x satisfies x² + 3x − 10 = 0.[2]
2. (b)Solve the equation.[1]
3. (c)State the dimensions of the board.[1]

Two whole numbers are consecutive, and their product is 56.

1. (a)Write an equation for the product of the numbers n and n + 1.[2]
2. (b)Solve the equation.[2]
3. (c)State the two whole numbers.[1]

A rectangle has length (x + 5) cm and width (x − 1) cm, and its area is 16 cm².

1. (a)Show that x satisfies x² + 4x − 21 = 0.[2]
2. (b)Solve the equation.[2]
3. (c)Explain why one root must be rejected, and state the rectangle’s dimensions.[1]

The graph of y = x² − 4x − 5 is drawn on a grid.

1. (a)Factorise x² − 4x − 5.[1]
2. (b)State the x-intercepts of the graph.[1]
3. (c)State the y-intercept of the graph.[1]
4. (d)Find the coordinates of the turning point, using the symmetry of the roots.[2]

The function y = x² − 6x + 8 is drawn as a parabola.

1. (a)Factorise x² − 6x + 8.[1]
2. (b)State the x-intercepts of the graph.[1]
3. (c)State the y-intercept.[1]
4. (d)Find the coordinates of the turning point.[1]
5. (e)Write the equation of the line of symmetry.[1]