Grade 10 Maths · Functions

Substitute into a formula

Replace the letters in a formula or expression with the given numbers and work out the value (for example if x = 3, then 2x + 1 = 7).

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Algebra Grade 9: SubstitutionKevinmathscience

Grade 8 Algebra: SubstitutionMaths Monkey

Substitution with negative numbersKhan Academy

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Question 8.3 · May/June 2025 · Paper 2 · National (DBE) · 2 marks

In the diagram, A, B and C lie in the same horizontal plane with

A B = A C

. D is directly above A such that

2 A D = BC

. Also,

A D = p

A \hat{B} C = x

and

D \hat{B} A = y

8.3 If

x = 6 0^{\circ}

, calculate the size of y.(2)

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

More past paper questions: substitute into a formula

Work each one out first, then open the memo and check every tick.

3. Question 1.1.1 · March 2025 · Provincial · 2 marks
1.1 Given: The sum to $n$ terms of an arithmetic sequence is $S_{n} = 3 n^{2} - 5 n$ .
1.1.1 Calculate the sum of the first 21 terms of this sequence.(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitute $n = 21$ into the formula $S_{21} = 3 (21)^{2} - 5 (21)$
  1 mark · Substitute into a formula
2. ✓
  Calculate final answer $S_{21} = 1218$
  1 mark · Substitute into a formula
4. Question 4.4 · November 2024 · Paper 1 · National (DBE) · 3 marks
Given: $f (x) = a^{x} - 1$ for $a > 0$ . $B (2; \frac{- 5}{9})$ is a point on $f$ .
4.4 It is further given that $C$ is a point on $f$ at $y = \frac{19}{8}$ . Determine the coordinates of $C^{'}$ , the image of $C$ , when $C$ is reflected about the line $y = x$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Substitute y-value to find x $\frac{19}{8} = (\frac{2}{3})^{x} - 1$
  $\frac{27}{8} = (\frac{2}{3})^{x}$
  1 mark · Substitute into a formula
2. ✓
  Solve for x $(\frac{3}{2})^{3} = (\frac{3}{2})^{- x}$
  $3 = - x ⟹ x = - 3$
  Coordinates of C are $(- 3; \frac{19}{8})$
  1 mark · Solve an exponential equation
3. ✓
  Reflect point across y=xSwap x and y coordinates.
  $C^{'} (\frac{19}{8}; - 3)$
  1 mark · Find the equation of an inverse
5. Question 5.3 · June 2025 · Paper 1 · Provincial · 3 marks
Given: $f (x) = - x + 1$ and $g (x) = \frac{- 2}{x} + 2$ , which are not drawn to scale. R and S are points of intersection of the graphs.

DBQ is a line perpendicular to the x-axis with D and B on $g$ and $f$ respectively. The coordinates of Q are $(- 1; 0)$ .
5.3 Determine the length of DB.(3)
Show the memo (3 ticks)Memo
1. ✓
  Find the y-coordinate of DD lies on $g (x)$ at $x = - 1$ (since DBQ is perpendicular to the x-axis at Q(-1; 0)).
  $y_{D} = g (- 1) = \frac{- 2}{- 1} + 2$
  $y_{D} = 2 + 2 = 4$
  1 mark · Substitute into a formula
2. ✓
  Find the y-coordinate of BB lies on $f (x)$ at $x = - 1$ .
  $y_{B} = f (- 1) = - (- 1) + 1$
  $y_{B} = 1 + 1 = 2$
  1 mark · Substitute into a formula
3. ✓
  Calculate the length of DB $D B = y_{D} - y_{B}$
  $D B = 4 - 2$
  $D B = 2$ units
  1 mark · Find a horizontal or vertical length
6. Question 1.3.2 · March 2025 · Provincial · 3 marks
1.3 Given the expression: $2 x^{2} + 8 x + 10$
1.3.2 Hence, determine the minimum value of $1 6^{4^{2 x^{2} + 8 x + 10}}$ (3)
Show the memo (2 ticks)Memo
1. ✓
  Identify minimum of exponentMinimum value of $2 x^{2} + 8 x + 10$ is $2$
  1 mark · Find turning point of a parabola
2. ✓
  Substitute minimum valueMinimum value = $1 6^{4^{2}}$
  $= 1 6^{16}$
  2 marks · Substitute into a formula

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