S4 Mathematics - Term 1

Topic 2: Equations and Inequalities

Lesson 8: Equations Review and Assessment

Duration: 40 minutes

Our Journey So Far

• Lessons 1-2: Building formulas from words
• Lessons 3-4: Changing the subject
• Lessons 5-7: Solving equations and word problems

Today: Review and assess your skills!

Skills Checklist

Can you...?

• Translate words to algebra
• Use inverse operations
• Solve linear equations
• Check solutions
• Interpret answers in context

Station 1: Subject Change

Make the indicated variable the subject:

1. y = 3x + 7 (make x)
2. A = pi r squared (make r)
3. v = u + at (make a)

Station 1: Answers

1. y = 3x + 7
   x = (y - 7)/3

2. A = pi r squared
   r = sqrt(A/pi)

3. v = u + at
   a = (v - u)/t

Station 2: Solve Equations

1. 4x - 5 = 15
2. 3(x + 2) = 21
3. 5x + 3 = 2x + 15

Station 2: Answers

1. 4x - 5 = 15
   4x = 20, x = 5

2. 3(x + 2) = 21
   3x + 6 = 21, 3x = 15, x = 5

3. 5x + 3 = 2x + 15
   3x = 12, x = 4

Station 3: Word Problems

1. "Twice a number plus 7 equals 23. Find the number."

2. "The sum of two consecutive even numbers is 54."

Station 3: Answers

1. 2n + 7 = 23
   2n = 16
   n = 8

2. n + (n + 2) = 54
   2n + 2 = 54
   n = 26
   Numbers: 26 and 28

Station 4: Geometry

1. "In a triangle, one angle is twice another, and the third is 60 degrees. Find all angles."

2. "Supplementary angles differ by 30 degrees."

Station 4: Answers

1. x + 2x + 60 = 180
   3x = 120
   x = 40
   Angles: 40 degrees, 80 degrees, 60 degrees

2. x + (x + 30) = 180
   2x = 150
   Angles: 75 degrees and 105 degrees

Assessment Time

Work individually on the assessment.

Time: 15 minutes

Show all your working!

Part A: Subject Change (4 marks)

1. P = 2l + 2w (make l) [1]
2. F = ma (make a) [1]
3. s = ut + (1/2)at squared (make u) [2]

Part B: Solve Equations (4 marks)

1. 3x + 8 = 20 [1]
2. 2(x - 4) = 10 [1]
3. 4x + 5 = x + 17 [2]

Part C: Word Problems (6 marks)

1. "Three times a number decreased by 5 equals 22." [2]

2. "A rectangle's length is 4 cm more than its width. Perimeter is 32 cm." [2]

3. "The sum of three consecutive odd numbers is 57." [2]

Part D: Geometry (4 marks)

1. "Two complementary angles: one is 10 degrees more than twice the other." [2]

2. "Triangle angles in ratio 2:3:5. Find the largest." [2]

Answers: Part A

1. P = 2l + 2w
   l = (P - 2w)/2

2. F = ma
   a = F/m

3. s = ut + (1/2)at squared
   u = (s - (1/2)at squared)/t

Answers: Part B

1. 3x + 8 = 20
   x = 4

2. 2(x - 4) = 10
   2x - 8 = 10, x = 9

3. 4x + 5 = x + 17
   3x = 12, x = 4

Answers: Part C

1. 3n - 5 = 22; n = 9

2. Width = w, Length = w + 4
   2(w + 4) + 2w = 32
   4w + 8 = 32, w = 6
   Width: 6 cm, Length: 10 cm

3. n + (n+2) + (n+4) = 57
   3n + 6 = 57, n = 17
   Numbers: 17, 19, 21

Answers: Part D

1. x + (2x + 10) = 90
   3x = 80, x = 26 and 2/3
   Angles: 26 and 2/3 degrees and 63 and 1/3 degrees

2. 2k + 3k + 5k = 180
   10k = 180, k = 18
   Largest angle: 5 times 18 = 90 degrees

Self-Assessment

Rate yourself 1-5:

1 = I need a lot more practice
3 = I understand but make some errors
5 = I'm confident with equations

Which area needs more work?

Next Lesson

Lesson 9: Introduction to Inequalities

We'll use the same solving techniques, but with a new twist:

• ">" (greater than)
• "<" (less than)
• Representing solutions on number lines

Homework

Review your assessment:

• Identify what went wrong
• Write the correct solution
• Create a similar problem and solve it

Credits

Created: December 2025
Based on: NCDC Lower Secondary Mathematics Syllabus (2019)

Source: National Curriculum Development Centre (NCDC), Uganda