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Maths Grade 8 Term 3 2023 Question Paper

June 25, 2025
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Category: Mathematics Notes

In this page we will access a video and written walkthrough of the Mathematics Grade 8 Term 3 2024 Question Paper, to prepare for the Term 3 2025 Exam.

2024 Maths Term 3 Grade 8 Revision For 2025 Term 3 Exam

The scope for this Term 3 2024 paper is 100% aligned with the Term 3 2025 exam that you are going to write.

2025 Scope Similarity 100%

2025 Maths Grade 8 Term 3 CAPS Scope:

-GEOMETRY OF STRAIGHT LINES

-GEOMETRY OF 2D SHAPES

-THEOREM OF PYTHAGORAS

-AREA AND PERIMETER OF 2-D SHAPES

Being able to answer questions on this question paper will enable you to answer the Term 3 2025 exam questions. Click the button below to read more about the Mathematics 2025 scope and predictions.
👇

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QUESTION 1: (12 MARKS)

FOR EACH QUESTION, CHOOSE THE CORRECT LETTER OF THE CORRECT ANSWER.

1.1 Simplify: $$\mathsf{Simplify:~}1x^2+2x^2+3x^2$$

$$\begin{aligned}
& \mathrm{A.}6x^6 \\
& \mathrm{B.}6x^2 \\
& \mathrm{C.}6x^8 \\
& \mathrm{D.}6x
\end{aligned}$$

1.2 $$\begin{aligned}
& \text{The equation}y=2x-1\text{ is given. Which table representing the} \\
& \mathrm{equation.}
\end{aligned}$$

x	-1	0	1	4
y	3	-1	-1	-7

x	-1	0	1	4
y	-3	1	1	7

x	-1	0	1	4
y	-3	-1	1	7

x	-1	0	1	4
y	3	1	-1	-7

1.3 What is the size of m?

A. 80°
B. 60°
C. 100°
D. 160°

1.4 Which one of the following triangles is an equilateral triangle?

Maths Grade 8 Term 3 2023 Question Paper 1

1.5 $$\Delta ACB\equiv\Delta ECD,\mathrm{~because}$$

A. A,A,S
B. R,H,S
C. S,A,S
D. S,S,S

Question 1 : Explained Answers By CAPS AI

ⓘ CAPS AI is the first reliable and trusted academic AI that you can ask questions as you go through your textbooks, question papers, and notes, it is programmed with the fundamental CAPS curriculum guidelines and content which allows it to give the prompter relevant answers that are aligned with the South African CAPS curriculum and it can further your understanding about any subject topic in general.

ⓘ Below are Question 1 explained answers by CAPS AI (supervised by Maths Teachers)

1.1

Let’s simplify the given expression:

Step 1: Combine like terms

All the terms have the same variable and exponent:

$$x^2$$

So, we just add their coefficients:

$$1+2+3=6$$

Step 2: Write the final simplified term

$$6x^2$$

Final Answer:

$$6x^2$$

1.2

Let’s test each table against the given equation until we find the matching one:

Check Table C:

When x =−1:

$y = -3$
When x = 0:

$y = -1$
When x = 1:

$y = 1$
When x = 4

$y = 2(4) – 1 = 8 – 1 = 7$

Table C matches the equation perfectly.

Correct answer: C

1.3

Let’s solve this:

The angles shown are vertically opposite angles, so they are equal:
$$m+20^\circ=100^\circ$$

Now, solve for m:
$$m=100^\circ-20^\circ=80^\circ$$

Correct answer: A. 80°

1.4

The correct answer is B.

The sum of the interior angles of any triangle is always 180 degrees.

An equilateral triangle has:

All three sides equal in length, and
All three angles equal to 60°.

In option B, all three angles are 60°, which confirms that it’s an equilateral triangle.

Here’s why the others are incorrect:

A: Angles are 80°, 65°, and 35° — not equal.
B: Angles are 60°, 60°, and (180°-60-60=60°) — therefore equal.
C: Two angles are 68°, and two sides are marked equal — it’s isosceles, not equilateral.
D: One angle is 90° (a right angle), and another is 60° — cannot be equilateral.

Answer: B.

1.5

The triangles △ACB ≡ △ECD are congruent because of the SAS (Side-Angle-Side) rule.

Here’s why:

AC ≡ EC (marked equal)
CB ≡ CD (marked equal)
∠ACB ≡ ∠ECD (vertically opposite angles, which are always equal)

This matches the SAS condition: two sides and the included angle are equal.

Correct answer: C. S, A, S

1.6

The triangles △ACB ≡ △ECD are congruent because of the SAS (Side-Angle-Side) rule.

Here’s why:

AC ≡ EC (marked equal)
CB ≡ CD (marked equal)
∠ACB ≡ ∠ECD (vertically opposite angles, which are always equal)

This matches the SAS condition: two sides and the included angle are equal.

Correct answer: C. S, A, S

Questions from Maths Term 3 200+ Questions and Answers:

1. In the diagram below, the value of x = 55°. The reason for this is:

Maths Grade 8 Term 3 2024 Question Paper

a) Alternating angles BA || CD

b) Corresponding angles BA || CD

c) Co-interior angles BA || CD

d) Opposite angles are equal.

QUESTION 2

2.1 Simplify the expression: $$2x^2+4^2-3x^2-2$$

2.2 Simplify: $$\frac{2x^4y\times3x^2y}{12x^6y^2}$$

2.3 Simplify: $$\frac{-12x-6}{6}$$

2.4 Simplify: $$2p+2p\times(3q-5q)+4q\times(-3p)$$

2.5 $$\mathrm{If}\quad x=2\quad\mathrm{and}\quad y=-5$$

determine the value of: $$4x^2y+y^3$$

Question 2 : Explained Answers By CAPS AI

ⓘ Below are Question 2 explained answers by CAPS AI (supervised by Maths Teachers)

2.1

$$2x^2+4^2-3x^2-2\\=2x^2+16-3x^2-2\\=-x^2+14$$

Step 1: Expand known powers

$$4^2=16$$

So substitute that in:

$$2x^2+16-3x^2-2$$

Step 2: Combine like terms

$$\quad\text{Combine the }x^2\mathrm{~terms:}\\2x^2-3x^2=-x^2$$

$$\begin{aligned}
& \text{Combine the constants:} \\
& 16-2=14
\end{aligned}$$

Final Answer:

$$-x^2+14$$

2.2

$$\frac{2x^4y\times3x^2y}{12x^6y^2}\\=\frac{6x^6y^2}{12x^6y^2}\\=\frac{1}{2}$$

Step 1: Multiply the numerators

Multiply coefficients and like variables:

$$\begin{aligned}
& 2\times3=6 \\
& x^4\times x^2=x^{4+2}=x^6 \\
& y\times y=y^2
\end{aligned}$$

So the numerator becomes:

$$6x^6y^2$$

Step 2: Simplify the whole fraction

$$\frac{6x^6y^2}{12x^6y^2}$$

Now cancel out common terms:

$$\begin{aligned}& x^6\text{ cancels with }x^6 \\& y^2\text{ cancels with }y^2\end{aligned}$$

$$\begin{aligned} \frac{6}{12} & =\frac{1}{2} \end{aligned} \\$$

Final Answer:

$$\frac{1}{2}$$

2.3

$$\frac{-12x-6}{6}\\=\frac{-12x}{6}+\frac{-6}{6}\\=-2x-1$$

Step 1: Split the fraction

$$\frac{-12x}{6}+\frac{-6}{6}$$

Step 2: Simplify each term

$$\begin{aligned}
& \frac{-12x}{6}=-2x
\end{aligned}$$

$$\begin{aligned}
& \frac{-6}{6}=-1
\end{aligned}$$

Final Answer:

$$-2x-1$$

2.4

$$2p+2p(3q-5q)+4q(-3p)\\=2p+2p(-2q)+(-12pq)\\=2p-4pq-12pq\\=2p-16pq$$

Step 1: Simplify inside the brackets

$$3q-5q=-2q$$

Now the expression becomes:

$$2p+2p\times(-2q)+4q\times(-3p)$$

Step 2: Multiply the terms

$$2p\times(-2q)=-4pq$$

$$4q\times(-3p)=-12pq$$

Now the expression is:

$$2p-4pq-12pq$$

Step 3: Combine like terms

Combine the two like terms involving $pq$ :

$$-4pq-12pq=-16pq$$

So, the final simplified expression is:

$$2p-16pq$$

Final Answer:

$$2p-16pq$$

2.5

$$4x^2y+y^3\\=4(2)^2(-5)+(-5)^3\\=4(4)(-5)+(-125)\\=-80-125\\=-205$$

Step 1: Substitute the values into the expression

$$4(2)^2(-5)+(-5)^3$$

Step 2: Simplify powers

$$(2)^2=4\\(-5)^3=-125$$

Now substitute those results back in:

$$4\times4\times(-5)+(-125)$$

Step 3: Multiply values

$$4\times4=16\\16\times(-5)=-80$$

Now the expression is:

$$-80+(-125)$$

Step 4: Add the values

$$-80-125=-205$$

Final Answer:

$$=-205$$

Questions from Maths Term 3 200+ Questions and Answers:

1. Simplify the expression fully:

$$\frac{4x^5y^3\times6x^2y}{8x^3y^4}$$

2. Factorise and simplify the expression:

$$\frac{4x^5y^3\times6x^2y}{8x^3y^4}$$

3. Simplify the following:

$$3x^2-5x+2-(4x^2-x-6)$$

QUESTION 3

Solve the following equations

3.1 $$-3-(x+2)=x+8$$

3.2 $$4+\frac{x-2}{4}=-2$$

3.3 $$3^{x-1}=81$$

Question 3 : Explained Answers By CAPS AI

ⓘ Below are Question 3 explained answers by CAPS AI (supervised by Maths Teachers)

3.1

Solve: $$-3-(x+2)=x+8$$

Step 1: Expand the left-hand side

$$-3-x-2=x+8\\\Rightarrow-x-5=x+8$$

Step 2: Move all terms to one side

$$-5=2x+8$$

$$-13=2x$$

Step 3: Solve for x

$$-13=2x\\\Rightarrow x=\frac{-13}{2}$$

3.2

Solve: $$4+\frac{x-2}{4}=x+8$$

Step 1: Subtract 4 from both sides

$$\frac{x-2}{4}=x+4$$

Step 2: Multiply both sides by 4 to eliminate the denominator

$$x-2=4(x+4)\\\Rightarrow x-2=4x+16$$

Step 3: Solve for x

$$x-2=4x+16\\\Rightarrow-2-16=4x-x\\\Rightarrow-18=3x\\\Rightarrow x=-6$$

3.3

$$3^{x-1}=3^4\\\Rightarrow x-1=4\\\Rightarrow x=5$$

Step 1: Rewrite 81 as a power of 3

So: $$3^{x-1}=3^4$$

Step 2: If the bases are the same, the exponents must be equal

$$x-1=4$$

Step 3: Solve for $x$

$$x=4+1=5$$

Final Answer:

$$x=5$$

QUESTION 4

4.1 Are the following statements true or false? Give a reason for your answer.

4.1.1 When two lines intersect and extended, vertically opposite angles are equal.

4.1.2

$$x+y=180^\circ$$

4.1.3

$$AB//CD$$

4.2 Given: $$AC//DE,A\widehat{B}D=D\widehat{B}E,B\widehat{D}E=63^{\circ}$$

4.2.1 Calculate the value of 𝑥, provide reasons.

4.2.2 Calculate the value of 𝑦, provide reason.

Question 4 : Explained Answers By CAPS AI

ⓘ Below are Question 4 explained answers by CAPS AI (supervised by Maths Teachers)

4.1.1

Statement: “When two lines intersect and extended, vertically opposite angles are equal.”
Answer: True
Reason: Vertically opposite angles are always equal when two straight lines intersect.

4.1.2

From the diagram, angle x and angle y are on a straight line.
Answer: True
Reason: Angles on a straight line add up to 180°, so $x + y = 18 0^{\circ}$

4.1.3

Given: $A B ∥ C D$
The marked angles are corresponding angles.

Answer: True
Reason: Corresponding angles are equal when parallel lines are cut by a transversal.

4.2.1

Calculate the value of x, provide reasons.

From the diagram and given info:

Lines $A C ∥ D E$
$x = ∠ D BE$ and it lies between parallel lines

Reason: Corresponding angles are equal when a transversal crosses parallel lines.

63∘

4.2.2

Calculate the value of y, provide reasons.

From the diagram:

$∠ B D E =$ 63∘
$y and$ 63∘ lie on a straight line

Reason: Angles on a straight line add up to $180^{\circ}$

$$y=180^\circ-63^\circ=117^\circ$$

$$$I=\frac{V}{R}=\frac{56}{8}=7\mathbf{A}$$$$I=\frac{V}{R}=\frac{56}{8}=7\mathbf{A}$$180^\circ$

QUESTION 5

5.1 Match (a, (b, (c and (d with (i, (ii, (iii and (iv

a) Scalene Triangle

b) Equilateral Triangle

c) Right Angled Triangle

d) Isosceles Triangle

ii)

iii)

iv)

5.2

5.2.1 ABCD is a_________

5.2.2 Calculate C , giving reason.

5.3

5.3.1 Calculate a and b. Provide reasons.

5.3.2 What can you conclude about the two triangles and why?

Question 5 : Explained Answers By CAPS AI

ⓘ Below are Question 5 explained answers by CAPS AI (supervised by Maths Teachers)

Column A	Column B
5.1.1. Scalene Triangle	(ii)
5.1.2. Equilateral Triangle	(iii)
5.1.3. Right-Angled Triangle	(iv)
5.1.4. Isosceles Triangle	(i)

Explanations:

(i) has two equal sides → Isosceles Triangle
(ii) has all sides different → Scalene Triangle
(iii) has three equal sides and angles → Equilateral Triangle
(iv) has a right angle marked → Right-Angled Triangle

5.2.1 ABCD is a trapezium (or trapezoid)

It has one pair of parallel sides (AB || CD) with different lengths

5.2.2 Calculate Ĉ, giving reason.

In a trapezium, co-interior angles on the same side are supplementary (add up to 180°).

Angles A and C are co-interior angles, so:

Â + Ĉ = 180°

110° + Ĉ = 180°

Ĉ = 180° – 110°

= 70°

Reason: Co-interior angles are supplementary

5.3.1

$$\begin{gathered}
\angle A+\angle B+\angle C=180^\circ \\
86^\circ+59^\circ+b=180^\circ \\
145^\circ+b=180^\circ \\
b=180^\circ-145^\circ\\=35^\circ
\end{gathered}$$

In any triangle, the sum of the three interior angles is always 180°.

You’re given:

$∠ A = 8 6^{\circ}$
$∠ B = 5 9^{\circ}$
$∠ C = b$

To find b use the rule: ∠A+∠B+∠C=180∘

Substitute the known values:

$86^{\circ} + 59^{\circ} + b = 180^{\circ}$

Add the two known angles:

$145^{\circ} + b = 180^{\circ}$

Now isolate b

$b = 180^{\circ} - 145^{\circ} = 35^{\circ}$

Answer: ∠C=b=35∘

Why this works?

This is a basic geometric rule that applies to all triangles, no matter their side lengths. The side lengths given (AB = 3, AC = 2, BC = 3.5) are not needed here because you are only asked to find the missing angle using known angle values.

Step 1: Calculate angle D

$\angle D = 180^\circ – 59^\circ – 35^\circ = 86^\circ$

So the angles in triangle DEF are:

$∠ D = 8 6^{\circ}$ ,
$∠ E = 5 9^{\circ}$ ,
$∠ F = 3 5^{\circ}$

Same as triangle ABC.

Step 2: Compare side lengths

Triangle ABC sides:

2, 3, 3.5

Triangle DEF sides:

4, 6, 7

These are proportional:

$2 : 4 = 1 : 2$
$3 : 6 = 1 : 2$
$3.5 : 7 = 1 : 2$

5.3.2

The two triangles are similar, because:

All three angles are equal (AAA),
All sides are in the same ratio (1:2)

Why?

Because two triangles are similar if:

Their corresponding angles are equal, and
Their corresponding sides are in proportion.

Maths Grade 8 Term 3 2023 Question Paper

2024 Maths Term 3 Grade 8 Revision For 2025 Term 3 Exam

2025 Maths Grade 8 Term 3 CAPS Scope:

Practice over 200 Maths Exam Questions

Or get an online tutor from R50 per month?

QUESTION 1: (12 MARKS)

Question 1 : Explained Answers By CAPS AI

Questions from Maths Term 3 200+ Questions and Answers:

QUESTION 2

Question 2 : Explained Answers By CAPS AI

Questions from Maths Term 3 200+ Questions and Answers:

QUESTION 3

Question 3 : Explained Answers By CAPS AI

QUESTION 4

Question 4 : Explained Answers By CAPS AI

QUESTION 5

Question 5 : Explained Answers By CAPS AI

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