Grade 10 Maths · Analytical Geometry · Paper 2

Coordinate Geometry Grade 10

Real Coordinate Geometry past paper questions and answers from 2024 to 2025, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

past paper questions: 23 past paper questions
skills: 10 skills
videos: 10 videos

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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)

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

Coordinate Geometry skills

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More Coordinate Geometry Grade 10 questions and answers

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4. Question 3.1 · November 2024 · Paper 2 · Provincial · 2 marks
In the figure, $Δ A BC$ has vertices $A (- 11; 2)$ , $B (3; - 5)$ and $C (6; 1)$ .
3.1 Calculate the length of BC. Leave the answer in surd form.(2)
Show the memo (2 ticks)Memo
1. ✓
  Apply distance formula $BC = (6 - 3)^{2} + (1 - (- 5))^{2}$
  $BC = 3^{2} + 6^{2}$
  $BC = 9 + 36$
  1 mark · Calculate distance between two points
2. ✓
  Final answer in surd form $BC = 45 = 35$
  1 mark · Simplify and combine surds
5. Question 8.1 · November 2024 · Paper 2 · Provincial · 3 marks
In the diagram, a lid with a hemispherical form seals an open cone. The slanted height of the cone is 13 cm, the diameter of the cone and hemisphere is 10 cm, the height of the cone $h$ cm.

Formulae:
$V = \frac{2}{3} π r^{3}$ ; $V = \frac{1}{3} π r^{2} h$ ; Surface Area $= π r^{2} + π rs$ ; Surface Area $= 2 π r^{2}$ $Diagram for this question$
8.1 Determine the height of the cone.(3)
Show the memo (3 ticks)Memo
1. ✓
  Correct formula $(h_{s})^{2} = r^{2} + h^{2}$
  1 mark · Use the theorem of Pythagoras
2. ✓
  Substitution $(13)^{2} = (5)^{2} + h^{2}$
  1 mark · Use the theorem of Pythagoras
3. ✓
  Answer $h^{2} = 169 - 25 = 144$
  $h = 12$ cm
  1 mark · Use the theorem of Pythagoras
6. Question 10.2.5 · November 2024 · Paper 2 · Provincial · 3 marks
10.2 In the diagram, PAT is the common tangent of the smaller and larger circles at A. AMB is the diameter of the larger circle with M on the circumference of the smaller circle. ASC and BC are chords of the larger circle and MS chord of the smaller circle. M is the centre of the larger circle.

It is also given that, the length of AM $= p$ units, AS $= (p - 1)$ units and BC $= 6$ units.

Answer the questions that follow. $Diagram for question 10.2$
10.2.5 Calculate the value of $p$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Apply Pyth theorem $p^{2} = (p - 1)^{2} + 3^{2}$ [Pyth. theorem]
  1 mark · Use the theorem of Pythagoras
2. ✓
  Simplification $p^{2} = p^{2} - 2 p + 1 + 9$
  $2 p = 10$
  1 mark · Square a binomial
3. ✓
  Answer $p = 5$
  1 mark · Use the theorem of Pythagoras
7. Question 8.1 · November 2024 · Paper 2 · Provincial · 3 marks
A mine dumps its waste at a landfill site where it takes the shape of a cone shown in the diagram below. The radius of the circular base is $r$ meters, the height is $h$ meters and the angle between the slant height and the base of the cone is $50°$ .
The circumference of the landfill site is 245 meters.

Volume of cone $= \frac{1}{3} π r^{2} h$

Total surface area of cone $= π r^{2} + π rs$ $Diagram for this question$
8.1 Determine the height of the mine waste, correct to ONE decimal place.(3)
Show the memo (3 ticks)Memo
1. ✓
  $r = 39$ m $2 π r = 245$
  $∴ r = \frac{245}{2 π}$
  $r = 39$ m
  1 mark · Calculate area or perimeter
2. ✓
  $\frac{h}{r} = tan 50°$ In $Δ A BC$ : $\frac{h}{r} = tan 50°$
  1 mark · Calculate a side using trig
3. ✓
  Answer $∴ h = 39. tan 50°$
  $∴ h = 46, 5$ m
  1 mark · Calculate a side using trig
8. Question WE23.3 · Siyavula Grade 8 Mathematics, 23 Graphs, The Cartesian plane, Worked example 23.3 · 2 marks
$Diagram for this question$
WE23.3 The graph below shows the Cartesian plane and four points. The points are labelled $A$ , $B$ , $C$ and $D$ . Which point has the coordinates $(5; 1)$ ?(2)
Show the memo (2 ticks)Memo
1. ✓
  Use the coordinatesIn $(5; 1)$ , $x = 5$ and $y = 1$ .
  From the origin, move $5$ units to the right (the $x$ -coordinate is positive), then $1$ unit upwards (the $y$ -coordinate is positive).
  1 mark · Plot and read points
2. ✓
  AnswerThe point that has the coordinates $(5; 1)$ is point $D$ .
  1 mark · Plot and read points
9. Question WE23.4 · Siyavula Grade 8 Mathematics, 23 Graphs, The Cartesian plane, Worked example 23.4 · 2 marks
$Diagram for this question$
WE23.4 The diagram shows the Cartesian plane and two points. The points are labelled $A$ and $B$ . Write down the coordinates of $A$ and $B$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Coordinates of B $B$ is $6$ units to the right of the origin and $5$ units above it.
  $B (6; 5)$
  1 mark · Plot and read points
2. ✓
  Coordinates of A $A$ lies on the $y$ -axis, so its $x$ -coordinate is $0$ . It is $6$ units below the origin.
  $A (0; - 6)$
  1 mark · Plot and read points
10. Question b · Siyavula Grade 8 Mathematics, 23 Graphs, Drawing global graphs, Worked example 23.2 · 2 marks
Forty learners completed a physical fitness test consisting of different exercises. $5$ learners completed the test in $10$ minutes, $7$ learners completed the test in $15$ minutes, $8$ learners completed the test in $20$ minutes, $11$ learners completed the test in $25$ minutes, $6$ learners completed the test in $30$ minutes and $3$ learners completed the test in $35$ minutes.
Use the information provided to answer the questions.
b Use the information provided to draw a suitable graph.(2)
Show the memo (2 ticks)Memo
1. ✓
  Plot the pointsPlot the points $(10; 5)$ , $(15; 7)$ , $(20; 8)$ , $(25; 11)$ , $(30; 6)$ and $(35; 3)$ with time (minutes) on the horizontal axis and number of learners on the vertical axis.
  1 mark · Plot and read points
2. ✓
  Points not joinedThe data is discrete, so the points are not joined by a line (see the graph). $Memo diagram$
  1 mark · Interpret or draw a global graph

Coordinate Geometry Grade 10 videos

Short lessons from South African teachers first. Videos load only when you tap play, to save your data.

Plotting Points on a Coordinate Plane | All 4 QuadrantsMath with Mr. J

Introduction to TRANSFORMATION in Mathematics - Grade 8SHFT - Your Learning

Gr 8 Mathematics QuadrilateralsMrs Townsend Mathematics - South Africa

Area and Perimeter Grade 9: Square, rhombus, parallelogram, rectangleKevinmathscience

Pythagoras Theorem grade 9Kevinmathscience

Straight line graphs grade 9: Gradient Part 1Kevinmathscience

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