Grade 10 Maths · Algebra

Set up an expression or equation

Turn a word problem or diagram into an equation by choosing a letter for the unknown (for example 'a number plus 5 is 12' gives x + 5 = 12).

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Translating Words To Algebraic Expressions Explained!The Organic Chemistry Tutor

Algebra Grade8: L9 Word Problems leading to EquationsOnline Maths by Miss Pythagoras

Algebraic Word ProblemsProfessor Dave Explains

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Question 10.1 · May/June 2024 · Paper 1 · National (DBE) · 4 marks

EHGF is a rectangle. HE is produced

x^{2}

cm to N and EH is produced

x^{2}

cm to P. NF produced intersects PG produced at M to form an isosceles triangle MNP with NM = MP. D lies on NP where MD

⊥

NP. NP = 4 cm and MD = 3 cm. Diagram for this question

10.1 Show that the area of

EFG H

is given by

A (x) = 6 x^{2} - 3 x^{4}

.(4)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: set up an expression or equation

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3. Question 3.2 · June 2025 · Paper 1 · Provincial · 4 marks
3.2 A father is twice as old as his son. Twelve years ago, the father was three times the son's age. How old is the son now?(4)
Show the memo (3 ticks)Memo
1. ✓
  Define variables for present ages and ages 12 years agoLet the son's current age be $x$ .
  The father's current age is $2 x$ .
  
  12 years ago:
  Son's age = $x - 12$
  Father's age = $2 x - 12$
  2 marks · Set up an expression or equation
2. ✓
  Set up the equation based on conditions 12 years ago $2 x - 12 = 3 (x - 12)$
  1 mark · Set up an expression or equation
3. ✓
  Solve for x $2 x - 12 = 3 x - 36$
  $36 - 12 = 3 x - 2 x$
  $24 = x$
  
  The son is currently $24$ years old.
  1 mark · Solve a linear equation
4. Question 2.3 · March 2023 · Provincial · 5 marks
2.3 George is 7 times as old as his son. In 25 years' time he will be twice as old as his son. Calculate his son's present age. HINT: variable x may be used to develop equations.(5)
Show the memo (5 ticks)Memo
1. ✓
  $x + 25$ Son's age now = $x$ , George = $7 x$ . In 25 years: Son = $x + 25$
  1 mark · Set up an expression or equation
2. ✓
  $7 x + 25$ In 25 years: George = $7 x + 25$
  1 mark · Set up an expression or equation
3. ✓
  $7 x + 25 = 2 x + 50$ $7 x + 25 = 2 (x + 25)$ , so $7 x + 25 = 2 x + 50$
  1 mark · Set up an expression or equation
4. ✓
  $5 x = 25$ $5 x = 25$
  1 mark · Solve a linear equation
5. ✓
  Answer $x = 5$ . His son is 5 years old.
  1 mark · Solve a linear equation
5. Question 2.4 · March 2023 · Provincial · 5 marks
2.4 The product of two numbers x and y is 60 and their sum is 15. Show that $\frac{1}{x} + \frac{1}{y} = \frac{1}{4}$ (5)
Show the memo (5 ticks)Memo
1. ✓
  Equation 1 (product) $x y = 60$
  1 mark · Set up an expression or equation
2. ✓
  Equation 2 (sum) $x + y = 15$
  1 mark · Set up an expression or equation
3. ✓
  Adding the reciprocals $\frac{1}{x} + \frac{1}{y}$
  1 mark · Add or subtract algebraic fractions
4. ✓
  Finding the LCD $= \frac{y + x}{x y}$
  1 mark · Add or subtract algebraic fractions
5. ✓
  Substitute and Simplify $\frac{15}{60} = \frac{1}{4}$
  1 mark · Substitute into a formula
6. Question 2.4 · March 2022 · Provincial · 3 marks
2.4 A picture is framed using four rectangular pieces of wood, as shown in the diagram. Find the area of the picture, in terms of x. Give your answer in simplified form.(3)
Show the memo (3 ticks)Memo
1. ✓
  Determine inner dimensionsLength $= (7 x + 3) - x = 6 x + 3$
  Width $= (5 x + 2) - x = 4 x + 2$
  1 mark · Set up an expression or equation
2. ✓
  Calculate AreaArea $= (6 x + 3) (4 x + 2)$
  1 mark · Calculate area or perimeter
3. ✓
  Simplify $24 x^{2} + 12 x + 12 x + 6 = 24 x^{2} + 24 x + 6$
  1 mark · Collect like terms

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