110-minute revision sequence

Double revision lesson

A two-period lesson for diagnosing skills, rebuilding methods, and finishing with focused mixed practice. Students can work directly from this page.

2 x 55 minutes Lesson 1: diagnose and rebuild Lesson 2: apply and consolidate Open student task pack

Student task pack

What each student needs

Use a notebook or loose-leaf paper for working. Each answer should include the rule used, the key algebra line, and a clearly labelled final answer.

Readiness check Skill stations Timed mixed practice Exit ticket

Teacher flow

Lesson 1: diagnose and rebuild

Start broad, then let students target the topic areas that need the most immediate repair.

0-8 min

Readiness check

State the domain of $f (x) = \sqrt{x + 3}$ .
Solve $x^{2} - 5 x + 6 = 0$ .
Find the period of $y = 3 \sin (2 x)$ .
Find $\Pr (A \cap B)$ when $\Pr (A) = 0.6$ and $\Pr (B | A) = 0.25$ .
Find the midpoint of $A (- 4, 7)$ and $B (2, - 1)$ .
State whether $h (x) = - 2 \sqrt{x - 1} + 5$ has a maximum or minimum value, and give that value.

8-18 min

Traffic-light marking

Green: correct method and correct answer.
Amber: correct idea but incomplete notation or arithmetic error.
Red: unsure how to start.
Choose two red or amber topics for the station block.

18-38 min

Skill stations

Choose two stations based on your traffic-light result. Complete all questions in the chosen stations before moving to extension.

Functions For

f (x) = \sqrt{10 - 2 x}

, state the domain and range, then write full function notation.

Trig Solve

2 \cos (x) + 1 = 0

for

0 \leq x \leq 2 π

, then state the reference angle.

Quadratics A quadratic has turning point

(- 1, 6)

and passes through

(1, - 2)

. Find its rule.

Transformations Describe the transformations from

y = \sqrt{x}

y = 3 \sqrt{x + 4} - 2

Probability A two-stage event has

\Pr (A) = 0.45

\Pr (B | A) = 0.8

. Find

\Pr (A \cap B)

Coordinate geometry For

P (- 3, 4)

and

Q (5, 0)

, find distance, midpoint, gradient, and the line equation.

38-50 min

Error hunt

For each case, complete three jobs: identify the error, explain why it is wrong, then write a corrected solution.

Case 1: Inverse functions

Student working

For $g : [1, \infty) \to R$ , $g (x) = {(x - 1)}^{2} + 4$ :

$g^{- 1} (x) = 1 \pm \sqrt{x - 4}$ , domain $[1, \infty)$ , range $[4, \infty)$ .

Circle the part of the inverse rule that does not match the restricted domain.
Correct the inverse rule.
State the correct domain and range of $g^{- 1}$ .

Reveal correction

Because the original domain is $x \geq 1$ , the inverse uses the positive branch only. The correct inverse is $g^{- 1} (x) = 1 + \sqrt{x - 4}$ , with domain $[4, \infty)$ and range $[1, \infty)$ .

Case 2: Trigonometric period

Student working

For $y = 2 \cos (3 x) - 1$ :

Period $= 2 π \times 3 = 6 π$ .

Write the correct period formula for sine and cosine.
Explain why multiplying by $3$ gives the wrong direction of change.
State the correct period.

Reveal correction

For $y = a \cos (n x) + k$ , period is $\frac{2 π}{| n |}$ . Here $n = 3$ , so the period is $\frac{2 π}{3}$ .

Case 3: Square-root domain and range

Student working

For $h (x) = \sqrt{5 - 2 x} + 1$ :

Domain $= [5, \infty)$ and range $= (- \infty, 1]$ .

Set up the inequality under the square root.
Solve it carefully, including the sign change when dividing by a negative.
Correct the range after considering the smallest square-root value.

Reveal correction

Require $5 - 2 x \geq 0$ , so $x \leq \frac{5}{2}$ . Domain: $(- \infty, \frac{5}{2}]$ . Since the square-root part is at least $0$ , the range is $[1, \infty)$ .

Case 4: Conditional probability

Student working

Given $\Pr (A) = 0.4$ and $\Pr (B | A) = 0.3$ :

$\Pr (A \cap B) = 0.4 + 0.3 = 0.7$ .

Write the conditional probability multiplication rule.
Decide whether the calculation should use addition or multiplication.
Correct the intersection probability.

Reveal correction

Use $\Pr (A \cap B) = \Pr (A) \times \Pr (B | A)$ . Therefore $\Pr (A \cap B) = 0.4 \times 0.3 = 0.12$ .

50-55 min

Reset checkpoint

Write one sentence: "The topic I need to stabilise before mixed practice is..." Then write the first action that would improve it.

Second period

Lesson 2: apply and consolidate

Move from targeted repair into timed, mixed, clearly communicated mathematical work.

0-5 min

Re-entry warm-up

Choose the matching quick question from your checkpoint topic.

Functions: state the domain of $\sqrt{x - 6}$ .
Trig: find the period of $y = \tan (4 x)$ .
Quadratics: calculate the discriminant of $2 x^{2} - 3 x + 5$ .

5-25 min

Timed mixed practice

For $p (x) = \sqrt{2 x + 8} - 3$ , state the maximal domain and range.
Solve $x^{2} - 7 x + 10 = 0$ .
For $x^{2} + k x + 9 = 0$ , find the values of $k$ that give one repeated real solution.
Sketch $y = - 2 \sin (x) + 1$ for $0 \leq x \leq 2 π$ .
A repeated independent trial has success probability $0.2$ and is performed three times. Find the probability of at least one success.
Find the equation of the line through $(- 2, 8)$ and $(4, 2)$ .
Find the inverse of $q : [0, \infty) \to R$ , $q (x) = x^{2} + 5$ .
Create a two-piece function with one linear rule and one quadratic rule over adjacent non-overlapping domains.

25-38 min

Pair explanation

Choose one response from timed practice.
Explain the first line, the key method step, and the final answer.
Partner checks notation, domain restrictions, and graph labels.

38-48 min

Independent correction

Use the topic cards, drills, and worked solutions to improve one incomplete response. The corrected version should show the method, not just the answer.

48-55 min

Exit ticket

Solve $2 \sin (x) = 1$ for $0 \leq x \leq 2 π$ .
State the domain and range of $r (x) = - \sqrt{x + 2} + 4$ .
Write the first revision task you will complete at home and the evidence you will use to know it is done well.

Student links

Resources for the lesson

Topic checklist Revision drills Worked solutions Printable worksheet Homework set