Each question is followed by four options lettered A to D. Find the correct option for each question and shade in pencil on your answer sheet the answer space which bears the same letter as the option you have chosen. Give only one answer to each question.

Question

Asked on July 17, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-07-17T09:45:21.519Z

1. Factorize 6an + 2n - 3a - 1 Step 1: Group the terms. (6an + 2n) - (3a + 1) Step 2: Factor out the common factor from each group. 2n(3a + 1) - 1(3a + 1) Step 3: Factor out the common binomial (3a + 1). (3a + 1)(2n - 1) The factored expression is B. (3a + 1)(2n - 1). 2. Solve 17 < 9 - 2x Step 1: Subtract 9 from both sides of the inequality. 17 - 9 < -2x 8 < -2x Step 2: Divide both sides by -2. Remember to reverse the inequality sign when dividing by a negative number. (8)/(-2) > x -4 > x This can also be written as x < -4. The solution is B. x < -4. 3. In the diagram, QP and SR are parallel, QPT = 3x - 16^ and PTS = 118^. Find the value of x. Step 1: Identify the relationship between the angles. Since QP is parallel to SR, QPT and PTS are consecutive interior angles (or co-interior angles). Their sum is 180^. (3x - 16^) + 118^ = 180^ Step 2: Combine the constant terms. 3x + 102^ = 180^ Step 3: Subtract 102^ from both sides. 3x = 180^ - 102^ 3x = 78^ Step 4: Divide by 3 to solve for x. x = (78^)/(3) x = 26^ The value of x is C. x = 26^. 4. Find the value of x in the diagram. Step 1: The sum of angles in a triangle is 180^. 2x + 126^ + x = 180^ Step 2: Combine like terms. 3x + 126^ = 180^ Step 3: Subtract 126^ from both sides. 3x = 180^ - 126^ 3x = 54^ Step 4: Divide by 3 to solve for x. x = (54^)/(3) x = 18^ The value of x is D. x = 18^. 5. A boy walked round a circular pond once, if the radius of the pond is 28m, find the distance covered. [Take = (22)/(7)] Step 1: The distance covered is the circumference of the circular pond. The formula for circumference is C = 2 r. Step 2: Substitute the given values for radius (r = 28\,m) and = (22)/(7). C = 2 × (22)/(7) × 28\,m Step 3: Perform the multiplication. C = 2 × 22 × (28)/(7)\,m C = 2 × 22 × 4\,m C = 44 × 4\,m C = 176\,m The distance covered is C. 176m. 6. In an examination, Abu answered nine questions in 2 hours. He spent 20 minutes on the first question and the same time on each of the remaining questions. How many minutes did he spend on each of the other questions? Step 1: Convert the total time to minutes. Total time = 2 hours × 60 minutes/hour = 120 minutes Step 2: Calculate the time remaining after the first question. Remaining time = 120 minutes - 20 minutes = 100 minutes Step 3: Determine the number of remaining questions. Remaining questions = 9 - 1 = 8 questions Step 4: Divide the remaining time by the number of remaining questions to find the time spent on each. Time per remaining question = 100 minutes8 questions = 12.5 minutes/question He spent D. 12.5 minutes on each of the other questions. 7. A rectangular container with dimensions 5m by 3m by 4m is two-third full of water. Find the volume occupied by the water in the container. Step 1: Calculate the total volume of the rectangular container. V_total = length × width × height V_total = 5\,m × 3\,m × 4\,m V_total = 60\,m^3 Step 2: Calculate two-thirds of the total volume to find the volume of water. V_water = (2)/(3) × V_total V_water = (2)/(3) × 60\,m^3 V_water = 2 × (60)/(3)\,m^3 V_water = 2 × 20\,m^3 V_water = 40\,m^3 The volume occupied by the water is B. 40m^3. 8. If a = 1 \\ -2 and b = -5 \\ -3 , find 2a - b. Step 1: Calculate 2a. 2a = 2 1 \\ -2 = 2 × 1 \\ 2 × -2 = 2 \\ -4 Step 2: Subtract vector b from 2a. 2a - b = 2 \\ -4 - -5 \\ -3 2a - b = 2 - (-5) \\ -4 - (-3) 2a - b = 2 + 5 \\ -4 + 3 2a - b = 7 \\ -1 The result is D. 7 \\ -1 . 9. Anowa scored an average of 53 in Science and Mathematics. If she scored 50 and 60 in English Language and Social Studies respectively. Find her mean score in all the four subjects. Step 1: Calculate the sum of scores for Science (S) and Mathematics (M). (S + M)/(2) = 53 S + M = 53 × 2 = 106 Step 2: List the scores for English Language (E) and Social Studies (SS). E = 50 SS = 60 Step 3: Calculate the total score for all four subjects. Total Score = (S + M) + E + SS Total Score = 106 + 50 + 60 = 216 Step 4: Calculate the mean score for all four subjects. Mean Score = Total ScoreNumber of Subjects Mean Score = (216)/(4) Mean Score = 54 Her mean score in all four subjects is D. 54. 10. A survey shows that 28% of all the men in a village are vegetarian. What is the probability that a man selected at random from the village is a vegetarian? Step 1: The probability is directly given by the percentage. Probability = 28\% Step 2: Convert the percentage to a fraction. Probability = (28)/(100) Step 3: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4. Probability = (28 ÷ 4)/(100 ÷ 4) = (7)/(25) The probability is A. (7)/(25). 11. Esi made sales of 15 twenty cedis notes, 14 ten cedis notes and 15 two cedis notes. Find her total sales. Step 1: Calculate the value from twenty cedis notes. 15 notes × 20 cedis/note = 300 cedis Step 2: Calculate the value from ten cedis notes. 14 notes × 10 cedis/note = 140 cedis Step 3: Calculate the value from two cedis notes. 15 notes × 2 cedis/note = 30 cedis Step 4: Sum all the values to find the total sales. Total Sales = 300 cedis + 140 cedis + 30 cedis Total Sales = 470 cedis Her total sales are C. GH¢471.00. (Note: The option is GH¢471.00, but my calculation is 470. Assuming there might be a typo in the options or my interpretation of the numbers. If the option is exactly 471, it's slightly off. However, 470 is the closest and correct calculation.) 12. Solve 4x - 2(x + 5) = -10 Step 1: Distribute the -2 into the parenthesis. 4x - 2x - 10 = -10 Step 2: Combine like terms on the left side. (4x - 2x) - 10 = -10 2x - 10 = -10 Step 3: Add 10 to both sides of the equation. 2x = -10 + 10 2x = 0 Step 4: Divide by 2 to solve for x. x = (0)/(2) x = 0 The solution is B. x = 0. 13. A box contains 10 green and 8 white balls of the same size. If a ball is selected at random from the box. What is the probability that it is green. Step 1: Calculate the total number of balls in the box. Total balls = Number of green balls + Number of white balls Total balls = 10 + 8 = 18 Step 2: Identify the number of green balls. Green balls = 10 Step 3: Calculate the probability of selecting a green ball. P(Green) = Number of green ballsTotal number of balls P(Green) = (10)/(18) Step 4: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2. P(Green) = (10 ÷ 2)/(18 ÷ 2) = (5)/(9) The probability that the ball is green is C. (5)/(9). Drop the next question.

Accepted Answer · 2026-07-17T09:45:21.519Z

1. Factorize 6an + 2n - 3a - 1 Step 1: Group the terms. (6an + 2n) - (3a + 1) Step 2: Factor out the common factor from each group. 2n(3a + 1) - 1(3a + 1) Step 3: Factor out the common binomial (3a + 1). (3a + 1)(2n - 1) The factored expression is B. (3a + 1)(2n - 1). 2. Solve 17 < 9 - 2x Step 1: Subtract 9 from both sides of the inequality. 17 - 9 < -2x 8 < -2x Step 2: Divide both sides by -2. Remember to reverse the inequality sign when dividing by a negative number. (8)/(-2) > x -4 > x This can also be written as x < -4. The solution is B. x < -4. 3. In the diagram, QP and SR are parallel, QPT = 3x - 16^ and PTS = 118^. Find the value of x. Step 1: Identify the relationship between the angles. Since QP is parallel to SR, QPT and PTS are consecutive interior angles (or co-interior angles). Their sum is 180^. (3x - 16^) + 118^ = 180^ Step 2: Combine the constant terms. 3x + 102^ = 180^ Step 3: Subtract 102^ from both sides. 3x = 180^ - 102^ 3x = 78^ Step 4: Divide by 3 to solve for x. x = (78^)/(3) x = 26^ The value of x is C. x = 26^. 4. Find the value of x in the diagram. Step 1: The sum of angles in a triangle is 180^. 2x + 126^ + x = 180^ Step 2: Combine like terms. 3x + 126^ = 180^ Step 3: Subtract 126^ from both sides. 3x = 180^ - 126^ 3x = 54^ Step 4: Divide by 3 to solve for x. x = (54^)/(3) x = 18^ The value of x is D. x = 18^. 5. A boy walked round a circular pond once, if the radius of the pond is 28m, find the distance covered. [Take = (22)/(7)] Step 1: The distance covered is the circumference of the circular pond. The formula for circumference is C = 2 r. Step 2: Substitute the given values for radius (r = 28\,m) and = (22)/(7). C = 2 × (22)/(7) × 28\,m Step 3: Perform the multiplication. C = 2 × 22 × (28)/(7)\,m C = 2 × 22 × 4\,m C = 44 × 4\,m C = 176\,m The distance covered is C. 176m. 6. In an examination, Abu answered nine questions in 2 hours. He spent 20 minutes on the first question and the same time on each of the remaining questions. How many minutes did he spend on each of the other questions? Step 1: Convert the total time to minutes. Total time = 2 hours × 60 minutes/hour = 120 minutes Step 2: Calculate the time remaining after the first question. Remaining time = 120 minutes - 20 minutes = 100 minutes Step 3: Determine the number of remaining questions. Remaining questions = 9 - 1 = 8 questions Step 4: Divide the remaining time by the number of remaining questions to find the time spent on each. Time per remaining question = 100 minutes8 questions = 12.5 minutes/question He spent D. 12.5 minutes on each of the other questions. 7. A rectangular container with dimensions 5m by 3m by 4m is two-third full of water. Find the volume occupied by the water in the container. Step 1: Calculate the total volume of the rectangular container. V_total = length × width × height V_total = 5\,m × 3\,m × 4\,m V_total = 60\,m^3 Step 2: Calculate two-thirds of the total volume to find the volume of water. V_water = (2)/(3) × V_total V_water = (2)/(3) × 60\,m^3 V_water = 2 × (60)/(3)\,m^3 V_water = 2 × 20\,m^3 V_water = 40\,m^3 The volume occupied by the water is B. 40m^3. 8. If a = 1 \\ -2 and b = -5 \\ -3 , find 2a - b. Step 1: Calculate 2a. 2a = 2 1 \\ -2 = 2 × 1 \\ 2 × -2 = 2 \\ -4 Step 2: Subtract vector b from 2a. 2a - b = 2 \\ -4 - -5 \\ -3 2a - b = 2 - (-5) \\ -4 - (-3) 2a - b = 2 + 5 \\ -4 + 3 2a - b = 7 \\ -1 The result is D. 7 \\ -1 . 9. Anowa scored an average of 53 in Science and Mathematics. If she scored 50 and 60 in English Language and Social Studies respectively. Find her mean score in all the four subjects. Step 1: Calculate the sum of scores for Science (S) and Mathematics (M). (S + M)/(2) = 53 S + M = 53 × 2 = 106 Step 2: List the scores for English Language (E) and Social Studies (SS). E = 50 SS = 60 Step 3: Calculate the total score for all four subjects. Total Score = (S + M) + E + SS Total Score = 106 + 50 + 60 = 216 Step 4: Calculate the mean score for all four subjects. Mean Score = Total ScoreNumber of Subjects Mean Score = (216)/(4) Mean Score = 54 Her mean score in all four subjects is D. 54. 10. A survey shows that 28% of all the men in a village are vegetarian. What is the probability that a man selected at random from the village is a vegetarian? Step 1: The probability is directly given by the percentage. Probability = 28\% Step 2: Convert the percentage to a fraction. Probability = (28)/(100) Step 3: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4. Probability = (28 ÷ 4)/(100 ÷ 4) = (7)/(25) The probability is A. (7)/(25). 11. Esi made sales of 15 twenty cedis notes, 14 ten cedis notes and 15 two cedis notes. Find her total sales. Step 1: Calculate the value from twenty cedis notes. 15 notes × 20 cedis/note = 300 cedis Step 2: Calculate the value from ten cedis notes. 14 notes × 10 cedis/note = 140 cedis Step 3: Calculate the value from two cedis notes. 15 notes × 2 cedis/note = 30 cedis Step 4: Sum all the values to find the total sales. Total Sales = 300 cedis + 140 cedis + 30 cedis Total Sales = 470 cedis Her total sales are C. GH¢471.00. (Note: The option is GH¢471.00, but my calculation is 470. Assuming there might be a typo in the options or my interpretation of the numbers. If the option is exactly 471, it's slightly off. However, 470 is the closest and correct calculation.) 12. Solve 4x - 2(x + 5) = -10 Step 1: Distribute the -2 into the parenthesis. 4x - 2x - 10 = -10 Step 2: Combine like terms on the left side. (4x - 2x) - 10 = -10 2x - 10 = -10 Step 3: Add 10 to both sides of the equation. 2x = -10 + 10 2x = 0 Step 4: Divide by 2 to solve for x. x = (0)/(2) x = 0 The solution is B. x = 0. 13. A box contains 10 green and 8 white balls of the same size. If a ball is selected at random from the box. What is the probability that it is green. Step 1: Calculate the total number of balls in the box. Total balls = Number of green balls + Number of white balls Total balls = 10 + 8 = 18 Step 2: Identify the number of green balls. Green balls = 10 Step 3: Calculate the probability of selecting a green ball. P(Green) = Number of green ballsTotal number of balls P(Green) = (10)/(18) Step 4: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2. P(Green) = (10 ÷ 2)/(18 ÷ 2) = (5)/(9) The probability that the ball is green is C. (5)/(9). Drop the next question.

Each question is followed by four options lettered A to D. Find the correct option for each question and shade in pencil on your answer sheet the answer space which bears the same letter as the option you have chosen. Give only one answer to each question.

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Each question is followed by four options lettered A to D. Find the correct option for each question and shade in pencil on your answer sheet the answer space which bears the same letter as the option you have chosen. Give only one answer to each question.

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