BECE 2026 MATHEMATICS HEAT QUESTIONS ✅ SOLVE Q1. A student scored 45 marks in a test which is 60%. a) Find the total marks b) How many more marks are needed to reach 80%? Q2. A sum of GH₵360 is shared among Kofi, Ama, and Yaw in the ratio 2 : 3 : 4. Find: a) Kofi’s share b) Ama’s share c) Yaw’s share Q3. A rectangular garden is 20 m long and 15 m wide. a) Find the perimeter b) Find the area c) Find the cost of fencing it at GH₵5 per metre Q4. Two angles on a straight line Find(x+10)°and (3x-20) ° a) Find x b) If one of the angles is part of a triangle, find the third angle if the other two are 50° and that angle. Q5. A shirt was sold for GH₵180 after a 10% discount. What was the original price? b) A shopkeeper bought goods for GH₵450 and sold them for GH₵540. Find the profit percentage. Q6. The marks of 12 students are: 42, 55, 50, 48, 55, 62, 38, 50, 55, 60, 45, 48 i. Find the mode ii. Find the range b) A bag contains 4 red, 3 blue and 3 green balls. One ball is drawn at random. Find the probability that it is: i. Blue ii. Not green Q7. a) A taxi company charges a fixed fee of GH₵10 plus GH₵1.20 per kilometer. How much will a passenger pay for a trip of 15 km? b) A rectangular field is 85 m long and 60 m wide. A farmer wants to put a fence around the field and also divide the field into 5 equal smaller plots by lines parallel to the shorter side. i. What is the perimeter of the field? ii. How many metres of fencing will be needed altogether?

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Asked on April 29, 2026Business/Management

This business/management problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.

Accepted Answer · 2026-04-29T03:53:19.377Z

Hey Omar, good to see you again. Q1. a) Step 1: Let the total marks be T. We are given that 45 marks represent 60% of the total marks. 0.60 × T = 45 Step 2: Divide both sides by 0.60 to find T. T = (45)/(0.60) T = 75 The total marks are 75. b) Step 1: Calculate 80% of the total marks. 80\% of 75 = 0.80 × 75 = 60 Step 2: Find the difference between 80% of the total marks and the student's current score. Marks needed = 60 - 45 = 15 The student needs 15 more marks to reach 80%. Q2. Step 1: Find the total number of ratio parts. Total ratio parts = 2 + 3 + 4 = 9 Step 2: Find the value of one ratio part. Value per part = GH₵3609 = GH₵40 a) Step 3: Calculate Kofi's share. Kofi's share = 2 × GH₵40 = GH₵80 Kofi's share is GH₵80. b) Step 4: Calculate Ama's share. Ama's share = 3 × GH₵40 = GH₵120 Ama's share is GH₵120. c) Step 5: Calculate Yaw's share. Yaw's share = 4 × GH₵40 = GH₵160 Yaw's share is GH₵160. Q3. Given: Length (L) = 20 m, Width (W) = 15 m. a) Step 1: Use the formula for the perimeter of a rectangle. P = 2(L + W) P = 2(20 m + 15 m) P = 2(35 m) P = 70 m The perimeter is 70 m. b) Step 1: Use the formula for the area of a rectangle. A = L × W A = 20 m × 15 m A = 300 m^2 The area is 300 m^2. c) Step 1: Calculate the cost of fencing using the perimeter and the cost per metre. Cost = Perimeter × Cost per metre Cost = 70 m × GH₵5/m Cost = GH₵350 The cost of fencing is GH₵350. Q4. Given: Two angles on a straight line are (x+10)^ and (3x-20)^. a) Step 1: Angles on a straight line sum to 180^. (x+10) + (3x-20) = 180 Step 2: Combine like terms. 4x - 10 = 180 Step 3: Add 10 to both sides. 4x = 190 Step 4: Divide by 4. x = (190)/(4) x = 47.5 The value of x is 47.5. b) Step 1: Calculate the values of the two angles using x=47.5. First angle = (x+10)^ = (47.5+10)^ = 57.5^ Second angle = (3x-20)^ = (3 × 47.5 - 20)^ = (142.5 - 20)^ = 122.5^ Step 2: Assume "that angle" refers to the first angle, 57.5^. The sum of angles in a triangle is 180^. Third angle = 180^ - 50^ - 57.5^ Third angle = 130^ - 57.5^ Third angle = 72.5^ The third angle is 72.5^. Q5. a) Step 1: Let the original price be P. A 10% discount means the selling price is 90% of the original price. 0.90 × P = GH₵180 Step 2: Divide by 0.90 to find P. P = GH₵1800.90 P = GH₵200 The original price was GH₵200. b) Step 1: Calculate the profit. Profit = Selling Price - Cost Price Profit = GH₵540 - GH₵450 = GH₵90 Step 2: Calculate the profit percentage. Profit Percentage = ProfitCost Price × 100\% Profit Percentage = GH₵90GH₵450 × 100\% Profit Percentage = 0.2 × 100\% Profit Percentage = 20\% The profit percentage is 20%. Q6. Given marks: 42, 55, 50, 48, 55, 62, 38, 50, 55, 60, 45, 48. i. Step 1: Identify the frequency of each mark. • 38: 1 • 42: 1 • 45: 1 • 48: 2 • 50: 2 • 55: 3 • 60: 1 • 62: 1 The mark that appears most frequently is 55. The mode is 55. ii. Step 1: Identify the highest and lowest marks. Highest mark = 62 Lowest mark = 38 Step 2: Calculate the range. Range = Highest mark - Lowest mark Range = 62 - 38 = 24 The range is 24. b) Given: 4 red, 3 blue, 3 green balls. Step 1: Calculate the total number of balls. Total balls = 4 + 3 + 3 = 10 i. Step 2: Calculate the probability of drawing a blue ball. P(Blue) = Number of blue ballsTotal number of balls P(Blue) = (3)/(10) The probability of drawing a blue ball is (3)/(10). ii. Step 3: Calculate the probability of drawing a ball that is not green. Number of non-green balls = Number of red balls + Number of blue balls Number of non-green balls = 4 + 3 = 7 P(Not green) = Number of non-green ballsTotal number of balls P(Not green) = (7)/(10) The probability of drawing a ball that is not green is (7)/(10). Q7. a) Step 1: Identify the fixed fee and the cost per kilometer. Fixed fee = GH₵10 Cost per km = GH₵1.20 Distance = 15 km Step 2: Calculate the total cost. Total cost = Fixed fee + (Cost per km × Distance) Total cost = GH₵10 + (GH₵1.20/km × 15 km) Total cost = GH₵10 + GH₵18 Total cost = GH₵28 A passenger will pay GH₵28 for a trip of 15 km. b) Given: Length (L) = 85 m, Width (W) = 60 m. i. Step 1: Use the formula for the perimeter of a rectangle. P = 2(L + W) P = 2(85 m + 60 m) P = 2(145 m) P = 290 m The perimeter of the field is 290 m. ii. Step 1: The fencing around the field is its perimeter. Perimeter fencing = 290 m Step 2: To divide the field into 5 equal smaller plots by lines parallel to the shorter side (60 m), 4 internal fences are needed. Number of internal fences = 5 - 1 = 4 Step 3: Each internal fence will have the length of the shorter side. Length of each internal fence = 60 m Step 4: Calculate the total length of internal fencing. Total internal fencing = 4 × 60 m = 240 m Step 5: Calculate the total fencing needed. Total fencing = Perimeter fencing + Total internal fencing Total fencing = 290 m + 240 m = 530 m A total of 530 m of

Accepted Answer · 2026-04-29T03:53:19.377Z

Hey Omar, good to see you again. Q1. a) Step 1: Let the total marks be T. We are given that 45 marks represent 60% of the total marks. 0.60 × T = 45 Step 2: Divide both sides by 0.60 to find T. T = (45)/(0.60) T = 75 The total marks are 75. b) Step 1: Calculate 80% of the total marks. 80\% of 75 = 0.80 × 75 = 60 Step 2: Find the difference between 80% of the total marks and the student's current score. Marks needed = 60 - 45 = 15 The student needs 15 more marks to reach 80%. Q2. Step 1: Find the total number of ratio parts. Total ratio parts = 2 + 3 + 4 = 9 Step 2: Find the value of one ratio part. Value per part = GH₵3609 = GH₵40 a) Step 3: Calculate Kofi's share. Kofi's share = 2 × GH₵40 = GH₵80 Kofi's share is GH₵80. b) Step 4: Calculate Ama's share. Ama's share = 3 × GH₵40 = GH₵120 Ama's share is GH₵120. c) Step 5: Calculate Yaw's share. Yaw's share = 4 × GH₵40 = GH₵160 Yaw's share is GH₵160. Q3. Given: Length (L) = 20 m, Width (W) = 15 m. a) Step 1: Use the formula for the perimeter of a rectangle. P = 2(L + W) P = 2(20 m + 15 m) P = 2(35 m) P = 70 m The perimeter is 70 m. b) Step 1: Use the formula for the area of a rectangle. A = L × W A = 20 m × 15 m A = 300 m^2 The area is 300 m^2. c) Step 1: Calculate the cost of fencing using the perimeter and the cost per metre. Cost = Perimeter × Cost per metre Cost = 70 m × GH₵5/m Cost = GH₵350 The cost of fencing is GH₵350. Q4. Given: Two angles on a straight line are (x+10)^ and (3x-20)^. a) Step 1: Angles on a straight line sum to 180^. (x+10) + (3x-20) = 180 Step 2: Combine like terms. 4x - 10 = 180 Step 3: Add 10 to both sides. 4x = 190 Step 4: Divide by 4. x = (190)/(4) x = 47.5 The value of x is 47.5. b) Step 1: Calculate the values of the two angles using x=47.5. First angle = (x+10)^ = (47.5+10)^ = 57.5^ Second angle = (3x-20)^ = (3 × 47.5 - 20)^ = (142.5 - 20)^ = 122.5^ Step 2: Assume "that angle" refers to the first angle, 57.5^. The sum of angles in a triangle is 180^. Third angle = 180^ - 50^ - 57.5^ Third angle = 130^ - 57.5^ Third angle = 72.5^ The third angle is 72.5^. Q5. a) Step 1: Let the original price be P. A 10% discount means the selling price is 90% of the original price. 0.90 × P = GH₵180 Step 2: Divide by 0.90 to find P. P = GH₵1800.90 P = GH₵200 The original price was GH₵200. b) Step 1: Calculate the profit. Profit = Selling Price - Cost Price Profit = GH₵540 - GH₵450 = GH₵90 Step 2: Calculate the profit percentage. Profit Percentage = ProfitCost Price × 100\% Profit Percentage = GH₵90GH₵450 × 100\% Profit Percentage = 0.2 × 100\% Profit Percentage = 20\% The profit percentage is 20%. Q6. Given marks: 42, 55, 50, 48, 55, 62, 38, 50, 55, 60, 45, 48. i. Step 1: Identify the frequency of each mark. • 38: 1 • 42: 1 • 45: 1 • 48: 2 • 50: 2 • 55: 3 • 60: 1 • 62: 1 The mark that appears most frequently is 55. The mode is 55. ii. Step 1: Identify the highest and lowest marks. Highest mark = 62 Lowest mark = 38 Step 2: Calculate the range. Range = Highest mark - Lowest mark Range = 62 - 38 = 24 The range is 24. b) Given: 4 red, 3 blue, 3 green balls. Step 1: Calculate the total number of balls. Total balls = 4 + 3 + 3 = 10 i. Step 2: Calculate the probability of drawing a blue ball. P(Blue) = Number of blue ballsTotal number of balls P(Blue) = (3)/(10) The probability of drawing a blue ball is (3)/(10). ii. Step 3: Calculate the probability of drawing a ball that is not green. Number of non-green balls = Number of red balls + Number of blue balls Number of non-green balls = 4 + 3 = 7 P(Not green) = Number of non-green ballsTotal number of balls P(Not green) = (7)/(10) The probability of drawing a ball that is not green is (7)/(10). Q7. a) Step 1: Identify the fixed fee and the cost per kilometer. Fixed fee = GH₵10 Cost per km = GH₵1.20 Distance = 15 km Step 2: Calculate the total cost. Total cost = Fixed fee + (Cost per km × Distance) Total cost = GH₵10 + (GH₵1.20/km × 15 km) Total cost = GH₵10 + GH₵18 Total cost = GH₵28 A passenger will pay GH₵28 for a trip of 15 km. b) Given: Length (L) = 85 m, Width (W) = 60 m. i. Step 1: Use the formula for the perimeter of a rectangle. P = 2(L + W) P = 2(85 m + 60 m) P = 2(145 m) P = 290 m The perimeter of the field is 290 m. ii. Step 1: The fencing around the field is its perimeter. Perimeter fencing = 290 m Step 2: To divide the field into 5 equal smaller plots by lines parallel to the shorter side (60 m), 4 internal fences are needed. Number of internal fences = 5 - 1 = 4 Step 3: Each internal fence will have the length of the shorter side. Length of each internal fence = 60 m Step 4: Calculate the total length of internal fencing. Total internal fencing = 4 × 60 m = 240 m Step 5: Calculate the total fencing needed. Total fencing = Perimeter fencing + Total internal fencing Total fencing = 290 m + 240 m = 530 m A total of 530 m of

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