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S1 Mathematics Paper: Directed Numbers, Algebraic Expressions, Linear Equations, Percentages, Area and Statistics (100 marks)
S1 Maths – number, algebra and mensuration
S1 Maths paper: 6 questions, 24 parts, 100 marks on directed numbers, algebra, linear equations, percentages, mensuration and statistics. Values computed in python.
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Paper details S1 Mathematics practice paper with 6 questions and 24 parts on directed numbers, algebraic expressions, linear equations, percentages, area and simple statistics.
Section A: Operations with Directed Numbers (16 marks)
Evaluate the following expressions and show your working (no calculator needed).
| # | Question | Answer and marking notes |
|---|---|---|
| 1 | Evaluate 7 – 12 + 3. | Answer: 7 – 12 = -5, then -5 + 3 = -2. (Marking: first step 2, answer 2) |
| 2 | Evaluate (-6) x (-4). | Answer: the product of two negative numbers is positive, so 6 x 4 = 24. (Marking: sign rule 2, answer 2) |
| 3 | Evaluate (-45) / 9. | Answer: a negative divided by a positive is negative, 45 / 9 = 5, so the answer is -5. (Marking: sign 2, answer 2) |
| 4 | Evaluate the sum of the absolute value of -18 and (-7). | Answer: |-18| = 18, and 18 + (-7) = 11. (Marking: absolute value 2, answer 2) |
Section B: Simplifying, Evaluating and Expanding Algebraic Expressions (16 marks)
Given a = 4 and b = -3, answer the following.
| # | Question | Answer and marking notes |
|---|---|---|
| 5 | Simplify 3x + 5y – x + 2y. | Answer: collect like terms, 3x – x = 2x and 5y + 2y = 7y, giving 2x + 7y. (Marking: x terms 2, y terms 2) |
| 6 | Find the value of 2a^2 – b. | Answer: 2 x 4^2 – (-3) = 2 x 16 + 3 = 35. (Marking: square 2, sign handling 2) |
| 7 | Expand 4(2m – 3). | Answer: 4 x 2m – 4 x 3 = 8m – 12. (Marking: distributive law 2, answer 2) |
| 8 | Simplify 6p / 3 + 2p x 4. | Answer: 6p / 3 = 2p and 2p x 4 = 8p, giving 10p in total. (Marking: division 2, collecting 2) |
Section C: Linear Equations in One Unknown (16 marks)
Solve the following equations and show your steps.
| # | Question | Answer and marking notes |
|---|---|---|
| 9 | Solve 3x + 7 = 22. | Answer: 3x = 22 – 7 = 15, so x = 5. (Marking: transposition 2, answer 2) |
| 10 | Solve 4(x – 3) = 2x + 6. | Answer: 4x – 12 = 2x + 6, so 2x = 18 and x = 9. (Marking: expansion 2, answer 2) |
| 11 | Solve x / 4 + 3 = 7. | Answer: x / 4 = 4, so x = 16. (Marking: transposition 2, answer 2) |
| 12 | Solve 2(3x + 1) = 5x + 9. | Answer: 6x + 2 = 5x + 9, so 6x – 5x = 9 – 2 and x = 7. (Marking: expansion 2, answer 2) |
Section D: Percentages and Discounts (16 marks)
A product has a marked price of $250 and is now sold at 80% of the marked price.
| # | Question | Answer and marking notes |
|---|---|---|
| 13 | Find the selling price after the discount. | Answer: 250 x 80% = $200. (Marking: percentage 2, answer 2) |
| 14 | Find the percentage discount. | Answer: (250 – 200) / 250 x 100% = 20%. (Marking: difference 2, percentage 2) |
| 15 | Another number becomes 92 after increasing by 15%%. Find its original value. | Answer: 92 / 1.15 = 80. (Marking: setting up 2, answer 2) |
| 16 | A class has 40 students and 35% of them are boys. Find the number of girls and their percentage of the class. | Answer: boys 40 x 35% = 14, girls 40 – 14 = 26, that is 65%. (Marking: boys 1, girls 2, percentage 1) |
Section E: Perimeter and Area (16 marks)
Give units in your answers unless stated otherwise. Use pi = 22 / 7 for circles.
| # | Question | Answer and marking notes |
|---|---|---|
| 17 | A rectangle is 12 cm long and 7 cm wide. Find its perimeter and area. | Answer: perimeter = 2 x (12 + 7) = 38 cm; area = 12 x 7 = 84 cm2. (Marking: perimeter 2, area 2) |
| 18 | A triangle has base 15 cm and height 8 cm. Find its area. | Answer: 15 x 8 / 2 = 60 cm2. (Marking: formula 2, answer 2) |
| 19 | A circle has radius 7 cm. Find its area and circumference (take pi = 22 / 7). | Answer: area = 22 / 7 x 7^2 = 154 cm2; circumference = 2 x 22 / 7 x 7 = 44 cm. (Marking: area 2, circumference 2) |
| 20 | A trapezium has parallel sides 6 cm and 10 cm and height 5 cm. Find its area. | Answer: (6 + 10) x 5 / 2 = 40 cm2. (Marking: sum 1, formula 2, answer 1) |
Section F: Mean, Median, Mode and Range (20 marks)
The numbers of books read in one week by five students are: 4, 7, 7, 9, 13.
| # | Question | Answer and marking notes |
|---|---|---|
| 21 | Find the mean of the data. | Answer: (4 + 7 + 7 + 9 + 13) / 5 = 8 books. (Marking: total 3, answer 2) |
| 22 | Find the median. | Answer: in ascending order 4, 7, 7, 9, 13, the middle value is 7. (Marking: ordering 3, answer 2) |
| 23 | Find the mode and state whether the data set has only one mode. | Answer: the mode is 7, it appears twice while every other value appears once, so there is only one mode. (Marking: mode 3, explanation 2) |
| 24 | Find the range and explain which feature of the data the range shows better than the median. | Answer: range = 13 – 4 = 9; the range shows the spread of the data (how far the largest is from the smallest), while the median only shows the middle value, so the range better shows the gap. (Marking: range 3, explanation 2) |
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