2010 Mathematics Paper 1 (Multiple Choice)
Section A
1. Which of the following is not a prime number?
(a) 2
(b) 3
(c) 6
(d) 7
2. What is the value of 5^2 + 3^2?
(a) 34
(b) 35
(c) 36
(d) 37
3. Simplify 4x^2 - 3x + 2 - (2x^2 - 5x + 1)
(a) 2x^2 + 2x + 1
(b) 2x^2 + 2x - 1
(c) 2x^2 - 2x + 1
(d) 2x^2 - 2x - 1
4. Solve the equation 3x + 5 = 11.
(a) x = 1
(b) x = 2
(c) x = 3
(d) x = 4
5. Which of the following graphs represents a linear equation?
(a) y = x^2
(b) y = x + 2
(c) y = sin x
(d) y = 1/x
Section B
6. Factorise 12x^2 - 15x + 2.
7. Solve the simultaneous equations:
2x + 3y = 11
x - 2y = -5
8. Find the equation of the line passing through the points (2, 3) and (4, 7).
9. Solve the inequality 2x - 5 < 3x + 1.
10. Find the area of a rectangle with length 8 cm and width 6 cm.
2010 Mathematics Paper 2 (Long Answer)
Section A
1. Prove that the sum of the interior angles of a triangle is 180 degrees.
2. Find the equation of the circle with centre (2, -3) and radius 5.
3. Solve the quadratic equation 4x^2 + 8x - 5 = 0.
4. Find the volume of a cone with radius 6 cm and height 10 cm.
5. Prove that the tangent at any point on a circle is perpendicular to the radius drawn to that point.
Section B
6. ABCD is a parallelogram. Find the area of ABCD if AB = 6 cm, BC = 8 cm, and the angle between AB and BC is 60 degrees.
7. A company sells a product for $80. The company offers a 20% discount on the product. What is the sale price of the product?
8. A car travels 200 km in 3 hours. What is the average speed of the car in km/h?
9. A recipe calls for 1 cup of flour, 1/2 cup of sugar, and 1/4 cup of butter. If I want to make twice the recipe, how many cups of flour, sugar, and butter do I need?
10. A bank offers a savings account with an annual interest rate of 5%. If I deposit $1,000 into the account, how much money will I have after one year?
Answers
Paper 1
Section A
1. (c)
2. (a)
3. (a)
4. (a)
5. (b)
Section B
6. (2x - 1)(6x - 2)
7. x = 3, y = 2
8. y = 2x + 1
9. x > 6
10. 48 cm^2
Paper 2
Section A
1. See proof here: https://www.khanacademy.org/math/geometry/hs-geo-triangle-properties/hs-geo-interior-angles-triangle/v/proof-sum-interior-angles-triangle
2. (x - 2)^2 + (y + 3)^2 = 5^2
3. x = (-8 ± √80)/4 = (-1/5, -4)
4. V = (1/3)πr^2h = (1/3)π(6^2)(10) = 376.99 cm^3
5. See proof here: https://www.khanacademy.org/math/geometry/hs-geo-intro/hs-geo-lines-and-angles/v/tangent-radius-perpendicular
Section B
6. Area of ABCD = ½(AB)(BC)sinθ = ½(6 cm)(8 cm)sin60° = 24√3 cm^2
7. Sale price = Original price - Discount
Sale price = $80 - ($80 x 0.20) = $64
8. Average speed = Distance/Time
Average speed = 200 km/3 h = 66.67 km/h
9. Flour: 2 cups
Sugar: 1 cup
Butter: ½ cup
10. Amount after one year = Principal + Interest
Amount after one year = $1,000 + ($1,000 x 0.05) = $1,050