Mathwise Academy | Grade 10 Mathematics Paper 1 - Preparatory Paper 1
M

MATHWISE ACADEMY

Grade 10 Mathematics: Preparatory Paper 1 • Paper 1 (Algebra, Patterns, Functions, Finance, Probability)

INSTRUCTIONS AND INFORMATION

  • This question paper consists of 5 questions totaling 100 marks.
  • Answer ALL questions.
  • Clearly show ALL calculations, diagrams, and graphs used in determining your answers. Full marks will not necessarily be awarded for answers only.
  • You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise.
  • Round off final answers to TWO decimal places where necessary, unless stated otherwise.
  • To save a printable worksheet, tap the green "Download / Print PDF" button above and select "Save as PDF".

QUESTION 1: ALGEBRA [30]

1.1 Simplify the following expressions fully:

  • 1.1.1 \( (2x - 1)(x^2 + 3x - 2) \) (3)
  • 1.1.2 \( \dfrac{x^2 - 4}{x^2 - x - 6} \div \dfrac{x^2 + 2x}{x - 3} \) (4)
  • 1.1.3 \( \dfrac{2^{n+1} \cdot 4^{n-1}}{8^n} \) (3)

1.2 Factorise the following expressions fully:

  • 1.2.1 \( 3x^2 - 27 \) (2)
  • 1.2.2 \( 2x^2 - 5x - 12 \) (2)
  • 1.2.3 \( ax - bx + ay - by \) (2)

1.3 Solve for \( x \):

  • 1.3.1 \( 2x - 5 = 4(x + 1) \) (2)
  • 1.3.2 \( x^2 - 8x + 15 = 0 \) (3)
  • 1.3.3 \( 3^x = 81 \) (2)
  • 1.3.4 \( -3 \le 2x - 1 < 5 \) (3)

1.4 Solve simultaneously for \( x \) and \( y \):

\( y = 2x - 3 \quad \text{and} \quad 3x + 2y = 8 \)
[4]

QUESTION 2: PATTERNS [15]

2.1 Consider the linear pattern:

5   ;   9   ;   13   ;   17   ;   \dots
  • 2.1.1 Write down the next two terms of the pattern. (2)
  • 2.1.2 Determine the general formula for the \( n^{\text{th}} \) term, \( T_n \). (2)
  • 2.1.3 Calculate the value of the \( 50^{\text{th}} \) term. (2)
  • 2.1.4 Which term in the pattern is equal to \( 121 \)? (3)

2.2 A linear pattern has \( T_3 = 14 \) and \( T_8 = 34 \).

  • 2.2.1 Determine the constant difference. (3)
  • 2.2.2 Determine the first term of the sequence. (3)

QUESTION 3: FUNCTIONS [30]

3.1 Given the functions \( f(x) = -x^2 + 4 \) and \( g(x) = x + 2 \).

  • 3.1.1 Determine the \( x \)-intercepts of \( f \). (3)
  • 3.1.2 Write down the coordinates of the turning point of \( f \). (2)
  • 3.1.3 Determine the \( x \)- and \( y \)-intercepts of \( g \). (2)
  • 3.1.4 Determine the coordinates of the points of intersection of \( f \) and \( g \). (5)
  • 3.1.5 Sketch the graphs of \( f \) and \( g \) on the provided Cartesian grid below. Clearly indicate all intercepts with the axes, turning points, and intersection coordinates. (4)
x y -6 -4 -2 2 4 6 6 4 2 -2 -4 -6
  • 3.1.6 Use your graph to determine the values of \( x \) for which \( f(x) \ge 0 \). (2)

3.2 Sketched conceptually are the functions \( h(x) = \dfrac{a}{x} + q \) and \( k(x) = b^x - 2 \). The horizontal asymptote of \( h \) is \( y = 1 \) and \( h \) passes through the point \( (2 ; 3) \). The function \( k \) passes through \( (1 ; 0) \).

  • 3.2.1 Write down the value of \( q \). (1)
  • 3.2.2 Determine the value of \( a \). (3)
  • 3.2.3 Write down the equations of the asymptotes of \( h \). (2)
  • 3.2.4 Determine the value of \( b \). (3)
  • 3.2.5 Write down the domain of \( h \) and the range of \( k \). (3)

QUESTION 4: FINANCE [10]

4.1 Sarah invests \( \text{R } 15\,000 \) for \( 5\text{ years} \) at a simple interest rate of \( 8,5\% \) p.a.

  • 4.1.1 Calculate the total interest earned over the \( 5\text{ years} \). (2)
  • 4.1.2 Calculate the accumulated amount at the end of the period. (2)

4.2 A television set currently costs \( \text{R } 8\,999 \). The average inflation rate is \( 5,2\% \) p.a. compound interest. Calculate the expected cost of the television in \( 3\text{ years'} \) time.

[3]

4.3 Convert \( £450 \) (British Pounds) to South African Rands if the current exchange rate is \( £1 = \text{R } 23,45 \).

[3]

QUESTION 5: PROBABILITY [15]

5.1 In a class of \( 40 \) learners, \( 24 \) play soccer (\( S \)), \( 18 \) play rugby (\( R \)), and \( 6 \) play neither.

  • 5.1.1 Draw a neat Venn diagram to represent this information. Let \( x \) be the number of learners who play both sports. (5)
  • 5.1.2 Calculate the value of \( x \). (3)
  • 5.1.3 Find the probability that a randomly chosen learner plays soccer only. (2)

5.2 Two events \( A \) and \( B \) are mutually exclusive. It is given that \( P(A) = 0,4 \) and \( P(B) = 0,3 \).

  • 5.2.1 Write down \( P(A \text{ and } B) \). (1)
  • 5.2.2 Calculate \( P(A \text{ or } B) \). (2)
  • 5.2.3 Are events \( A \) and \( B \) exhaustive? Motivate your answer with a mathematical reason. (2)
--- END OF PAPER ---
Mathwise Academy | Grade 10 Mathematics Paper 1 - Preparatory Paper 2
M

MATHWISE ACADEMY

Grade 10 Mathematics: Preparatory Paper 2 • Paper 1 (Algebra, Patterns, Functions, Finance, Probability)

INSTRUCTIONS AND INFORMATION

  • This question paper consists of 5 questions totaling 100 marks.
  • Answer ALL questions.
  • Clearly show ALL calculations, diagrams, and graphs used in determining your answers. Full marks will not necessarily be awarded for answers only.
  • You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise.
  • Round off final answers to TWO decimal places where necessary, unless stated otherwise.
  • To save a printable worksheet, tap the green "Download / Print PDF" button above and select "Save as PDF".

QUESTION 1: ALGEBRA [30]

1.1 Simplify fully:

  • 1.1.1 \( (3x - 2)^2 - (x - 4)(x + 4) \) (4)
  • 1.1.2 \( \dfrac{x^2 - 5x + 6}{x^2 - 9} \times \dfrac{x^2 + 3x}{2x - 4} \) (4)
  • 1.1.3 \( \dfrac{3^{x+1} \cdot 9^x}{27^x} \) (3)

1.2 Factorise fully:

  • 1.2.1 \( 2x^3 - 18x \) (3)
  • 1.2.2 \( 3x^2 - 10x + 8 \) (2)

1.3 Solve for \( x \):

  • 1.3.1 \( x(x - 5) = 14 \) (4)
  • 1.3.2 \( 5^{2x - 1} = 125 \) (3)
  • 1.3.3 \( \dfrac{2}{x} + \dfrac{1}{3} = \dfrac{5}{x} \) (3)

1.4 Solve for \( x \) and \( y \) simultaneously:

\( 3x - y = 5 \quad \text{and} \quad 2x + 3y = 7 \)
[4]

QUESTION 2: PATTERNS [15]

2.1 Consider the pattern:

18   ;   15   ;   12   ;   9   ;   \dots
  • 2.1.1 Determine the general term \( T_n \). (2)
  • 2.1.2 Which term is equal to \( -42 \)? (3)
  • 2.1.3 Determine the value of the \( 30^{\text{th}} \) term. (2)

2.2 A pattern is formed by placing matches in squares. Pattern 1 uses \( 4 \) matches. Pattern 2 uses \( 7 \) matches. Pattern 3 uses \( 10 \) matches.

Pattern 1 (4 matches)
Pattern 2 (7 matches)
Pattern 3 (10 matches)
  • 2.2.1 Find the formula for the number of matches in pattern \( n \). (3)
  • 2.2.2 How many matches are needed for pattern \( 20 \)? (2)
  • 2.2.3 If you have \( 100 \) matches, what is the largest pattern number you can build completely? (3)

QUESTION 3: FUNCTIONS [30]

3.1 Given \( f(x) = x^2 - 9 \) and \( g(x) = -2x - 6 \).

  • 3.1.1 Find the \( x \)- and \( y \)-intercepts of \( f \). (3)
  • 3.1.2 Find the \( x \)- and \( y \)-intercepts of \( g \). (2)
  • 3.1.3 Calculate the coordinates of the points of intersection of \( f \) and \( g \). (5)
  • 3.1.4 Sketch \( f \) and \( g \) on the grid below. Clearly show all intercepts and turning points. (4)
x y -6 -4 -2 2 4 6 6 4 2 -2 -4 -6
  • 3.1.5 Write down the range of \( f \). (2)

3.2 Given \( h(x) = \dfrac{-4}{x} + 2 \) and \( p(x) = 3^x - 1 \).

  • 3.2.1 Write down the equations of the asymptotes of \( h \). (2)
  • 3.2.2 Write down the equation of the asymptote of \( p \). (1)
  • 3.2.3 Calculate the \( x \)-intercept of \( h \). (3)
  • 3.2.4 Calculate the \( y \)-intercept of \( p \). (2)
  • 3.2.5 Draw a rough sketch of \( h(x) \) on the grid below, clearly showing asymptotes and intercepts. (4)
x y -6 -4 -2 2 4 6 6 4 2 -2 -4 -6
  • 3.2.6 State the domain of \( p \). (2)

QUESTION 4: FINANCE [10]

4.1 You invest \( \text{R } 12\,000 \) for \( 4\text{ years} \) at \( 9\% \) p.a. compound interest.

  • 4.1.1 Calculate the final amount. (3)
  • 4.1.2 How much interest was earned? (1)

4.2 A car depreciates on a straight-line basis at \( 12\% \) p.a. If its original value was \( \text{R } 150\,000 \), calculate its value after \( 5\text{ years} \).

[3]

4.3 An American tourist buys a curio for \( \text{R } 450 \). The exchange rate is \( \$1 = \text{R } 18,80 \). Calculate the price of the curio in US Dollars.

[3]

QUESTION 5: PROBABILITY [15]

5.1 A spinner has \( 8 \) equal sectors numbered \( 1 \) to \( 8 \). It is spun once.

  • 5.1.1 Write down the sample space. (2)
  • 5.1.2 Find the probability of spinning an odd number. (2)
  • 5.1.3 Find the probability of spinning a prime number. (2)

5.2 Given \( P(A) = 0,5 \), \( P(B) = 0,4 \), and \( P(A \text{ or } B) = 0,7 \).

  • 5.2.1 Calculate \( P(A \text{ and } B) \). (3)
  • 5.2.2 Are events \( A \) and \( B \) mutually exclusive? Give a reason. (2)

5.3 A bag contains \( 5 \) red balls and \( 3 \) green balls. A ball is chosen at random. What is the probability that the ball is NOT green?

[4]
--- END OF PAPER ---
Mathwise Academy | Grade 10 Mathematics Paper 1 - Preparatory Paper 3
M

MATHWISE ACADEMY

Grade 10 Mathematics: Preparatory Paper 3 • Paper 1 (Algebra, Patterns, Functions, Finance, Probability)

INSTRUCTIONS AND INFORMATION

  • This question paper consists of 5 questions totaling 100 marks.
  • Answer ALL questions.
  • Clearly show ALL calculations, diagrams, and graphs used in determining your answers. Full marks will not necessarily be awarded for answers only.
  • You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise.
  • Round off final answers to TWO decimal places where necessary, unless stated otherwise.
  • To save a printable worksheet, tap the green "Download / Print PDF" button above and select "Save as PDF".

QUESTION 1: ALGEBRA [30]

1.1 Simplify fully:

  • 1.1.1 \( (x - 3)(x^2 + 3x + 9) \) (3)
  • 1.1.2 \( \dfrac{2}{x - 1} + \dfrac{3}{x + 1} \) (4)
  • 1.1.3 \( \dfrac{5^{x+1} \cdot 25^x}{125^x} \) (3)

1.2 Factorise fully:

  • 1.2.1 \( 4x^2 - 100 \) (3)
  • 1.2.2 \( x^2 - 7x + 12 \) (2)

1.3 Solve for \( x \):

  • 1.3.1 \( 3(x - 2) + 4 = 2(x + 1) \) (3)
  • 1.3.2 \( (x - 1)(x + 2) = 4 \) (4)
  • 1.3.3 \( -2 \le \dfrac{x}{2} + 1 \le 3 \) (4)

1.4 Given \( 2x + y = 6 \) and \( x - y = 3 \). Solve for \( x \) and \( y \) simultaneously.

[4]

QUESTION 2: PATTERNS [15]

2.1 The first three terms of a linear sequence are:

\( 2x - 1 \quad ; \quad x + 3 \quad ; \quad 3x - 1 \)
  • 2.1.1 Calculate the value of \( x \). (4)
  • 2.1.2 Write down the numerical values of the first three terms. (2)
  • 2.1.3 Determine the \( n^{\text{th}} \) term, \( T_n \). (2)
  • 2.1.4 Calculate the \( 25^{\text{th}} \) term. (2)

2.2 A sequence is defined by \( T_n = -5n + 22 \).

  • 2.2.1 Find the first term that is negative. (3)
  • 2.2.2 Is \( -128 \) a term in this sequence? Show all working. (2)

QUESTION 3: FUNCTIONS [30]

3.1 Sketched conceptually are the graphs of \( f(x) = ax^2 + q \) and \( g(x) = mx + c \). The graph of \( f \) passes through \( (0 ; 8) \) and \( (2 ; 0) \). The line \( g \) passes through \( (0 ; 4) \) and intersects \( f \) at \( (2 ; 0) \).

  • 3.1.1 Show that \( a = -2 \) and \( q = 8 \). (4)
  • 3.1.2 Determine the equation of \( g(x) \). (3)
  • 3.1.3 Determine the coordinates of the other point of intersection of \( f \) and \( g \). (4)
  • 3.1.4 For which values of \( x \) is \( f(x) > g(x) \)? (2)
  • 3.1.5 Write down the range of \( f \). (2)

3.2 Given \( h(x) = \left(\dfrac{1}{2}\right)^x - 4 \).

  • 3.2.1 Write down the equation of the asymptote of \( h \). (1)
  • 3.2.2 Calculate the \( x \)- and \( y \)-intercepts of \( h \). (4)
  • 3.2.3 Sketch the graph of \( h(x) \) on the grid below. (4)
x y -6 -4 -2 2 4 6 6 4 2 -2 -4 -6
  • 3.3 State the domain of \( k(x) = \dfrac{5}{x - 2} + 1 \). (2)
  • 3.4 Write down the equation of \( h(x) \) if it is shifted \( 2 \) units upwards. (4)

QUESTION 4: FINANCE [10]

4.1 You borrow \( \text{R } 20\,000 \) from a bank at a simple interest rate of \( 11\% \) p.a. for \( 3\text{ years} \).

  • 4.1.1 Calculate the total amount to be repaid. (3)
  • 4.1.2 If you repay the loan in equal monthly instalments over \( 3\text{ years} \), calculate the monthly instalment. (2)

4.2 A population of a town is currently \( 50\,000 \). It is growing at a rate of \( 4,5\% \) p.a. compound growth. Estimate the population in \( 5\text{ years} \).

[3]

4.3 Convert \( \text{R } 5\,000 \) to Euros if the exchange rate is \( \text{€}1 = \text{R } 20,50 \).

[2]

QUESTION 5: PROBABILITY [15]

5.1 A bag contains \( 4 \) blue marbles, \( 5 \) red marbles, and \( 1 \) yellow marble.

  • 5.1.1 What is the probability of drawing a blue marble? (2)
  • 5.1.2 What is the probability of drawing a red or yellow marble? (3)

5.2 Let \( S \) be a sample space where \( n(S) = 50 \). \( A \) and \( B \) are events such that \( n(A) = 20 \), \( n(B) = 15 \), and \( n(A \text{ and } B) = 5 \).

  • 5.2.1 Draw a Venn diagram in the space below to represent this information. (5)
  • 5.2.2 Calculate \( P(A \text{ or } B) \). (3)
  • 5.2.3 Calculate the probability of neither \( A \) nor \( B \) occurring. (2)
--- END OF PAPER ---
Mathwise Academy | Grade 10 Mathematics Paper 1 - Preparatory Paper 4
M

MATHWISE ACADEMY

Grade 10 Mathematics: Preparatory Paper 4 • Paper 1 (Algebra, Patterns, Functions, Finance, Probability)

INSTRUCTIONS AND INFORMATION

  • This question paper consists of 5 questions totaling 100 marks.
  • Answer ALL questions.
  • Clearly show ALL calculations, diagrams, and graphs used in determining your answers. Full marks will not necessarily be awarded for answers only.
  • You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise.
  • Round off final answers to TWO decimal places where necessary, unless stated otherwise.
  • To save a printable worksheet, tap the green "Download / Print PDF" button above and select "Save as PDF".

QUESTION 1: ALGEBRA [30]

1.1 Simplify fully:

  • 1.1.1 \( \dfrac{x^2 - 16}{x^2 + 4x} \) (3)
  • 1.1.2 \( (x - 1)(x^2 + x + 1) \) (3)
  • 1.1.3 \( \dfrac{2^{x+2} + 2^x}{2^x} \) (4)

1.2 Factorise:

  • 1.2.1 \( x^2 - x - 30 \) (2)
  • 1.2.2 \( 3x^2 - 12xy \) (2)

1.3 Solve for \( x \):

  • 1.3.1 \( x^2 + 2x = 8 \) (4)
  • 1.3.2 \( 4^{x-1} = 64 \) (3)
  • 1.3.3 \( 2(x - 3) \ge 4x + 2 \) (4)

1.4 The sum of two numbers is \( 15 \) and their difference is \( 3 \). Set up equations and determine the two numbers.

[5]

QUESTION 2: PATTERNS [15]

2.1 Consider the pattern:

\( -5 \quad ; \quad -1 \quad ; \quad 3 \quad ; \quad 7 \quad ; \quad \dots \)
  • 2.1.1 Determine the \( n^{\text{th}} \) term. (3)
  • 2.1.2 Calculate the \( 40^{\text{th}} \) term. (2)
  • 2.1.3 Is \( 103 \) a term in this pattern? Show your calculations. (3)

2.2 A water tank currently holds \( 200\text{ litres} \). Water is being pumped in at a constant rate of \( 15\text{ litres} \) per minute.

  • 2.2.1 Write a sequence for the volume of water after \( 1 \), \( 2 \), and \( 3\text{ minutes} \). (3)
  • 2.2.2 Write a formula for the volume after \( n\text{ minutes} \). (2)
  • 2.2.3 How long will it take for the tank to hold \( 500\text{ litres} \)? (2)

QUESTION 3: FUNCTIONS [30]

3.1 Given \( f(x) = \dfrac{6}{x} + 2 \).

  • 3.1.1 Write down the asymptotes of \( f \). (2)
  • 3.1.2 Calculate the \( x \)-intercept of \( f \). (3)
  • 3.1.3 Sketch the graph of \( f \) on the grid below, showing intercepts and asymptotes. (4)
x y -6 -4 -2 2 4 6 6 4 2 -2 -4 -6
  • 3.1.4 In which quadrants is the hyperbola drawn relative to its asymptotes? (2)

3.2 Given \( g(x) = 2x^2 - 8 \) and \( h(x) = -2x - 4 \).

  • 3.2.1 Determine the \( x \)- and \( y \)-intercepts of \( g \). (4)
  • 3.2.2 Write down the turning point of \( g \). (2)
  • 3.2.3 Determine the points of intersection of \( g \) and \( h \). (5)
  • 3.2.4 Write down the range of \( g \). (2)
  • 3.3 Given \( k(x) = 3^x \). Determine the value of \( x \) for which \( k(x) = \dfrac{1}{9} \). (6)

QUESTION 4: FINANCE [10]

4.1 Compare two investments of \( \text{R } 10\,000 \) over \( 3\text{ years} \):
• Option A: \( 8,5\% \) p.a. simple interest.
• Option B: \( 7,8\% \) p.a. compound interest.

  • 4.1.1 Calculate the final amount for Option A. (3)
  • 4.1.2 Calculate the final amount for Option B. (3)
  • 4.1.3 Which option is better, and by how much? (2)

4.2 If \( 1\text{ Euro} = \text{R } 20,50 \) and \( 1\text{ US Dollar} = \text{R } 18,80 \), how many US Dollars is equivalent to \( 100\text{ Euros} \)?

[2]

QUESTION 5: PROBABILITY [15]

5.1 In a class of \( 30 \) students, \( 12 \) study History (\( H \)), \( 15 \) study Geography (\( G \)), and \( 5 \) study neither.

  • 5.1.1 Draw a Venn diagram in the space below. Let \( x \) be the students studying both. (5)
  • 5.1.2 Solve for \( x \). (3)
  • 5.1.3 Find \( P(\text{History only}) \). (2)

5.2 A card is drawn from a standard deck of \( 52 \) cards.

  • 5.2.1 What is the probability of drawing a King? (2)
  • 5.2.2 What is the probability of drawing a Red card? (1)
  • 5.2.3 What is the probability of drawing the King of Hearts? (2)
--- END OF PAPER ---
Mathwise Academy | Grade 10 Mathematics Paper 1 - Preparatory Paper 5
M

MATHWISE ACADEMY

Grade 10 Mathematics: Preparatory Paper 5 • Paper 1 (Algebra, Patterns, Functions, Finance, Probability)

INSTRUCTIONS AND INFORMATION

  • This question paper consists of 5 questions totaling 100 marks.
  • Answer ALL questions.
  • Clearly show ALL calculations, diagrams, and graphs used in determining your answers. Full marks will not necessarily be awarded for answers only.
  • You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise.
  • Round off final answers to TWO decimal places where necessary, unless stated otherwise.
  • To save a printable worksheet, tap the green "Download / Print PDF" button above and select "Save as PDF".

QUESTION 1: ALGEBRA [30]

1.1 Simplify fully:

  • 1.1.1 \( \dfrac{x^2 - 25}{x^2 - 5x} \) (3)
  • 1.1.2 \( (2x - 3y)^2 \) (3)
  • 1.1.3 \( \dfrac{3^{n+1} \cdot 6^n}{2^n \cdot 9^n} \) (4)

1.2 Factorise:

  • 1.2.1 \( x^2 + 8x + 15 \) (2)
  • 1.2.2 \( 2x^2 + 5x - 3 \) (3)

1.3 Solve for \( x \):

  • 1.3.1 \( x^2 = 5x \) (3)
  • 1.3.2 \( 2 \cdot 5^x = 250 \) (3)
  • 1.3.3 \( -5 < 2x + 1 \le 7 \) (4)

1.4 Solve for \( x \) and \( y \):
\( y = x^2 - 4 \) \quad \text{and} \quad \( y = x - 2 \)

[5]

QUESTION 2: PATTERNS [15]

2.1 The \( n^{\text{th}} \) term of a sequence is \( T_n = 4n - 3 \).

  • 2.1.1 Write down the first 3 terms. (3)
  • 2.1.2 Calculate \( T_{15} \). (2)
  • 2.1.3 Determine which term is equal to \( 97 \). (3)

2.2 Consider the pattern:

\( 10 \quad ; \quad 4 \quad ; \quad -2 \quad ; \quad -8 \quad ; \quad \dots \)
  • 2.2.1 Determine the formula for \( T_n \). (3)
  • 2.2.2 Calculate the \( 50^{\text{th}} \) term. (2)
  • 2.2.3 Find \( n \) if \( T_n = -110 \). (2)

QUESTION 3: FUNCTIONS [30]

3.1 The graph of \( f(x) = a^x + q \) passes through \( (0 ; 0) \) and \( (1 ; 3) \).

  • 3.1.1 Show that \( q = -1 \) and \( a = 4 \). (4)
  • 3.1.2 Write down the asymptote of \( f \). (1)
  • 3.1.3 Sketch \( f(x) \) on the grid below, showing intercepts and asymptote. (4)
x y -6 -4 -2 2 4 6 6 4 2 -2 -4 -6
  • 3.1.4 Write down the range of \( f \). (2)

3.2 Given \( g(x) = \dfrac{-2}{x} - 2 \) and \( h(x) = -x - 2 \).

  • 3.2.1 Write down the equations of the asymptotes of \( g \). (2)
  • 3.2.2 Determine the \( x \)-intercept of \( g \). (3)
  • 3.2.3 Sketch \( g \) and \( h \) on the same axes on the grid below. (5)
x y -6 -4 -2 2 4 6 6 4 2 -2 -4 -6
  • 3.2.4 Find the points of intersection of \( g \) and \( h \). (5)
  • 3.2.5 Give the domain of \( g \). (2)
  • 3.2.6 Determine the values of \( x \) for which \( h(x) \ge 0 \). (2)

QUESTION 4: FINANCE [10]

4.1 Sipho wants to buy a sound system for \( \text{R } 6\,500 \) on hire purchase. He pays a \( 10\% \) deposit and the balance over \( 2\text{ years} \) at a simple interest rate of \( 15\% \) p.a.

  • 4.1.1 Calculate the deposit amount. (1)
  • 4.1.2 Calculate the total amount paid on the loan. (4)
  • 4.1.3 Calculate the monthly instalment. (2)

4.2 A house is valued at \( \text{R } 800\,000 \). Its value appreciates at \( 8\% \) p.a. compound growth. Calculate its value after \( 4\text{ years} \).

[3]

QUESTION 5: PROBABILITY [15]

5.1 Let \( P(A) = 0,6 \) and \( P(B) = 0,3 \).

  • 5.1.1 If \( A \) and \( B \) are mutually exclusive, calculate \( P(A \text{ or } B) \). (2)
  • 5.1.2 If \( A \) and \( B \) are independent, calculate \( P(A \text{ and } B) \). (3)

5.2 In a survey of \( 60 \) people, \( 35 \) like tea, \( 25 \) like coffee, and \( 10 \) like both.

  • 5.2.1 Draw a Venn diagram in the space below to represent this information. (5)
  • 5.2.2 How many people like neither? (2)
  • 5.2.3 Find the probability that a person chosen at random likes ONLY tea. (3)
--- END OF PAPER ---