Grade 10 Maths · Financial Maths · Calculate with percentages

Percentages Grade 10

Find a percentage of an amount, or increase or decrease an amount by a percentage (for example 15% of R200 is R30).

past paper questions use it: 8 past paper questions use it
videos: 4 videos

Learn it: calculate with percentages

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Grade 8 Mathematics: PercentagesMrs Townsend Mathematics - South Africa

Finding a Percent of a Number | Calculating PercentagesMath with Mr. J

GCSE Maths - Percentage Increase and Decrease (Multiplier Method) (2026/27 exams)Cognito

Expressing one quantity as a percentage of anothercorbettmaths

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Question 1.4 · May/June 2025 · Paper 2 · National (DBE) · 4 marks

An insurance broker signed contracts with 15 people. The monthly premium (in rands) payable on each contract is given below.

134, 215, 325, 326, 362, 429, 515, 531, 598, 610, 624, 728, 923, 1034, 1200

1.4 The insurance company decided to increase the monthly premiums.

Monthly premiums that were less than R500 increased by

18%

Monthly premiums that were equal to or more than R500 increased by

k %

After these increases were applied to the above data, the new mean monthly premium was R686,44.

Calculate the value of

k

.(4)

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

More past paper questions: calculate with percentages

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3. Question 10.2 · May/June 2025 · Paper 1 · National (DBE) · 6 marks
10.2 A game at a fun park requires a player to roll a six-sided dice and pick a card from a deck of 52 cards. A player wins if an odd number appears on the uppermost face of the dice and the player also draws a picture card from the deck. A deck of cards has 4 suites (hearts, diamonds, spades and clubs). There are 4 picture cards (king, queen, jack and ace) in every suite. A player pays R10 to play a game and in an hour, 260 people can each play one game. If the owner wants to make a 70% profit per hour, calculate the maximum amount that the owner must pay out to each winner.(6)
Show the memo (6 ticks)Memo
1. ✓
  Determine total revenue collected in one hour [cite: 272]People pay: $260 \times R 10 = R 2600$
  1 mark · Use a ratio, rate or proportion
2. ✓
  Calculate total amount available for pay-outs based on profit margin [cite: 272]If the owner keeps $70%$ profit, $30%$ is available for pay-outs.
  Total value of pay-outs $= 0, 3 \times R 2600 = R 780$
  1 mark · Calculate with percentages
3. ✓
  Calculate the probability of drawing a picture card [cite: 272]There are $4$ picture cards per suite and $4$ suites.
  Total picture cards $= 16$
  $P (picture card) = \frac{16}{52}$
  1 mark · Calculate a simple probability
4. ✓
  Calculate the combined probability of someone winning [cite: 272]Probability of odd number $= \frac{1}{2}$
  $P (someone to win) = \frac{16}{52} \times \frac{1}{2} = \frac{2}{13}$
  1 mark · Use the product rule for independence
5. ✓
  Determine the total expected number of winners [cite: 272]Total number of people winning $= \frac{2}{13} \times 260 = 40$
  1 mark · Use relative frequency
6. ✓
  Calculate maximum pay-out per winner [cite: 272] $Pay-out = \frac{R 780}{40} = R 19, 50$ per person winning
  1 mark · Use a ratio, rate or proportion
4. Question 3.2.4 · September 2024 · Provincial · 3 marks
3.2 In a school of 70 Grade 10 learners, 32 learners take Economics (E), 43 take Mathematics (M) and 15 learners take neither of these two subjects. Let the number of learners who take both subjects be $x$ .
3.2.4 The probability that a Mathematics learner is also a Physical Sciences learner is $79%$ . Determine the number of learners that take Physical Sciences.(3)
Show the memo (2 ticks)Memo
1. ✓
  $43 \times 79%$ (double tick) $Number = 43 \times 79%$
  $= 33, 97$
  2 marks · Calculate with percentages
2. ✓
  Round to nearest whole number $\approx 34$ learners
  1 mark · Round off to required accuracy
5. Question 5.4 · September 2024 · Provincial · 2 marks
The following Life Sciences marks, for a test out of 50, were recorded from 15 grade 10 learners at a certain school.
5.4 The pass mark for the Life Sciences test was 30%. How many learners passed?(2)
Show the memo (2 ticks)Memo
1. ✓
  Pass mark $30% of 50 = 15$
  1 mark · Calculate with percentages
2. ✓
  AnswerLearners with marks $\geq 15$ : $13$ learners passed
  1 mark · Read and complete a frequency table
6. Question a · Siyavula Grade 12 Mathematics, 3.4 Present value annuities, Worked example 10 · 4 marks
For calculations, assume the prime lending rate is $8, 5%$ per annum.
A school sells its old bus and uses the proceeds as a $15%$ deposit for the purchase of the new bus, which costs R330 000. To finance the balance of the purchase, the school takes out a loan that is subject to an interest rate of prime $+ 1%$ compounded monthly. The repayment period of the loan is $3$ years.
a Calculate the monthly repayments.(4)
Show the memo (4 ticks)Memo
1. ✓
  Loan amount $P = R 330000 - (\frac{15}{100} \times R 330000) = R 330000 - R 49500 = R 280500$
  1 mark · Calculate with percentages
2. ✓
  Formula and values $x = \frac{P \times i}{[ 1 - ( 1 + i ) ^{- n} ]}$
  $i = \frac{0 , 095}{12}$ (prime $8, 5% + 1% = 9, 5%$ ); $n = 3 \times 12 = 36$
  1 mark · Use the present value formula
3. ✓
  Substitution $x = \frac{280 500 \times \frac{0 , 095}{12}}{[ 1 - ( 1 + \frac{0 , 095}{12} ) ^{- 36} ]}$
  1 mark · Use the present value formula
4. ✓
  Answer $x = R 8985, 24$
  The school must pay R8 985,24 per month.
  1 mark · Use the present value formula

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