Grade 8 Mathematics Paper June 2025 Mock Marking Guideline

Question 1

• Multiple choice questions: Circle the letter for the correct answer.

• 1.1 $a(b - c) = ac - ac$ is the distributive property of whole numbers. (C)

• 1.2 0.3 (with 3 recurring) is a rational number. (D)

• 1.3 Simplify $3(-20 + 5) = -45$. (C)

• 1.4 $(3)^3 - 4 = 23$. (A)

• 1.5 The expression $-x^4 + 3x^2 - 2x^4 - x + 10$ is of the fourth degree. (B)

• 1.6 A computer game costs R750 excluding VAT. VAT will be R105. (C)

• 1.7 $(5x^3y^5)^0 = 1$. (D)

• 1.8 An item that costs R2500 is reduced by 30%, the new price is R1750. (D)

• 1.9 The temperature of $-10°C$ decreased by $3°C$, the new temperature will be $-13°C$. (C)

• 1.10 The output of $y = \frac{3}{2}x - 3$ if $x = 4$ will be 3. (C)

Question 2

• 2.1 $\frac{30}{0} = undefined/NA$

• 2.2 Peter jumped 3.8 meters. James jumped $\frac{4}{3}$ of this distance. How far did James jump?
  $\frac{4}{3} \times 3.8 m = 5.06 m \approx 5.1m$

• 2.3 Determine the prime factors of 275 and 160.

  • Factors of 275: 5, 5, 11
  • Factors of 160: 2, 2, 2, 2, 2, 5

• 2.4 Determine the LCM and HCF of 275 and 160.

  • $LCM = 2^5 \times 5^2 \times 11 = 8800$
  • $HCF = 5$

• 2.5 Decrease 783 in the ratio 5:2.
  $783 \times \frac{2}{5} = 313.2$

• 2.6 Calculate the value of $1.25 \times 0.42$ without the use of a calculator.

  $1.25 = \frac{5}{4}$, $0.42 = \frac{21}{50}$
  $\frac{5}{4} \times \frac{21}{50} = \frac{21}{40} = 0.525$

Question 3

• Simplify the following without the use of a calculator. Show all steps.

• 3.1 $(17) - (-5) = 17 + 5 = 22$

• 3.2 $\sqrt{0.25} - \sqrt{\frac{8}{3}} + (-3)^2$
  $\frac{5}{10} - 2 + 9 = \frac{75}{10}$

• 3.3 $4 \frac{1}{2} + (2)^2 \frac{1}{3} - \sqrt{36}$

  $\frac{9}{2} + \frac{4}{3} - 6$
  $\frac{27 + 8 - 36}{6} = -\frac{1}{6}$

• 3.4 $\frac{(-4) + (-16)}{2(-3)} = \frac{-4 - 16}{-6} = \frac{-20}{-6} = \frac{10}{3}$

Question 4

• Simplify the following, showing all working out where necessary.

• 4.1 $3a^3 + a^3 - a^3 = 3a^3$

• 4.2 $-2x - 8x + 4x = -6x$

• 4.3 $3y^3 . y^2 = 3y^{3+2} = 3y^5$

• 4.4 $3(x - 2y) + 3(x - y) - 3x = 3x - 6y + 3x - 3y - 3x = 3x - 9y$

• 4.5 $\frac{(2a^3 . 3ab^0)}{(-3a^2b)^{-2}} = (6a^4) \times \frac{1}{(-3a^2b)^2} = \frac{6a^4}{9a^4b^2} = \frac{2}{3b^2}$

• 4.6 $\frac{36a^2 - 6a}{6a} = \frac{6a(6a - 1)}{6a} = 6a - 1$

Question 5

• Consider the expression $8 - 4x^2 + 3x^3 - 5x$

• 5.1 Rewrite the expression in ascending order form of x.

  $8 - 5x - 4x^2 + 3x^3$

• 5.2 How many terms are there in the expression?

  4 terms

• 5.3 What is the coefficient of $x^2$?

  -4

• 5.4 If $x = 3$, determine the value of the given expression.

$3(3)^3 - 4(3)^2 - 5(3) + 8 = 81 - 36 - 15 + 8 = 38$

Question 6

• Solve for x in the following equations.

• 6.1.1 $4x + 5 = 65$

  $4x + 5 - 5 = 65 - 5$
  $4x = 60$
  $x = 15$

• 6.1.2 $5x - 7 = -2x - 28$

  $5x + 2x = 7 - 28$
  $7x = -21$
  $x = -3$

• 6.1.3 $5(x - 2) = 2(2 - x)$

  $5x - 10 = 4 - 2x$
  $7x = 14$
  $x = 2$

• 6.1.4 $\frac{2x + 3}{5} = -3$

  $2x + 3 = -15$
  $x = -9$

• 6.1.5 $3 . 2x = 192$

  $2x = 64$
  $2x = 2^6$
  $x = 6$

• 6.2 Themba is 15 years older than Elsie. After 4 years Themba will be two times as old as Elsie. How old is Elsie now?

  • Let Elsie's current age = x

  • Themba's current age = x + 15

  • After 4 years:

    • Elsie's age = x + 4
    • Themba's age = x + 15 + 4 = x + 19

  • After 4 years:
    $x + 19 = 2(x + 4)$
    $x + 19 = 2x + 8$

  • $x = 11$

  • Elsie will be 11 years old

Question 7

• Simplify and leave answer as a positive exponent.

• 7.1.1 $a^5 \times a^{-5} = \frac{1}{1}$

• 7.1.2 $-(-2x^2y^6)^4 = -16x^8y^{24}$

• 7.1.3 $\frac{\sqrt{36m^{14}}}{6(m^4)(m^3)} = \frac{6m^7}{6m^7} = 1$

• 7.1.4 $\frac{(-3a^3 . 2a^7)}{((-2a^3)(a^2))^4} = (\frac{-6a^{10}}{-2a^5})^4 = (3a^5)^4 = 81a^{20}$

• 7.2 Determine the value of P and Q if $(x^P . y^4)^3 = x^{24} . y^Q$

  • $(x^P . y^4)^3 = x^{24} . y^Q$
  • $x^{3P} . y^{12} = x^{24} . y^Q$
  • $3P = 24 and Q = 12$
  • $\therefore Q = 12 and P = 8$

Question 8

• Fill in the missing values for Question 8.1.1 and 8.1.2 in the flow diagram below (input is x and the output is y).

• $y = -2x - 4$

• 8.1.1 y = 4

  $4 = -2x - 4$
  $2x = -8$
  $x = -4$

• 8.1.2 x = -3

  $y = -2(-3) - 4$
  $y = 2$

• 8.2 Given the table below:

  • x: -2, -1, 0, 1, 2, -3, b
  • y: 4, 3, 2, 1, 0, a, -8

• 8.2.1 Determine the rule for finding y in the given table

  $y = -x + c$
  when x = 2 then y = 0

  $y = -x + 2$

• 8.2.2 Find the value of a in the given table.

  $a = -(-3) + 2$

  $a = 5$

• 8.2.3 Find the value of b in the table above.

  $-8 = -(b) + 2$
  $-8 - 2 = -(b)$
  $10 = b$