Year11 MATH 3-2-1 Algebra and Functions warm-up workbook

Unit 1

1. Algebra and Functions

Focus: Quadratics, polynomials, and function notation.

1. Factorise $x^2 – 7x + 10$.
2. Solve for $x$: $2x^2 + 5x – 3 = 0$.
3. If $f(x) = 3x^2 – 2x$, find $f(-2)$.
4. Determine the domain and range of $f(x) = \sqrt{x – 4}$.
5. Complete the square for $x^2 + 6x + 1$.
6. Simplify $\frac{x^2 – 9}{x + 3}$.
7. Find the coordinates of the turning point for $y = (x – 2)^2 + 5$.
8. Solve the simultaneous equations: $y = 2x + 1$ and $y = x^2 – 2$.
9. Describe the transformation of $y = x^2$ to $y = -(x + 3)^2$.
10. State the remainder when $P(x) = x^3 – 2x^2 + 4$ is divided by $(x – 1)$.

Answers:

1. $(x – 5)(x – 2)$ | 2. $x = 0.5, x = -3$ | 3. 16 | 4. Domain: $$[4, \infty)$, Range: $[0, \infty)$ | 5. $(x + 3)^2 – 8$ | 6. $x – 3$ | 7. $(2, 5)$ | 8. $(3, 7)$ and $(-1, -1)$ | 9. Reflected over x-axis, translated 3 units left | 10. $P(1) = 3$.