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ATAR Maths

1.1 Exam Papers (Level 01)

1. Exam Paper 01

The paper will consist of different sections, including

  • algebra
  • geometry
  • trigonometry
  • probability and statistics.

Year 10 Mathematics Exam

Time Allowed: 2 Hours
Total Marks: 100
Instructions:

  1. Write all your answers in the space provided.
  2. Show all working for full marks.
  3. Calculators are allowed.
  4. Check your answers carefully.

Section A: Multiple Choice (20 marks)

  1. Simplify the expression: .

    a)
    b)
    c)
    d)
    (1 mark)

  2. Solve for in the equation: .

    a)
    b)
    c)
    d)
    (1 mark)

  3. What is the area of a triangle with a base of 8 cm and a height of 5 cm?

    a) 20 cm²
    b) 40 cm²
    c) 10 cm²
    d) 30 cm²
    (1 mark)

  4. If , what is ?

    a) 7
    b) 5
    c) 9
    d) 1
    (1 mark)

  5. The probability of flipping a coin and getting heads is:

    a) 0.5
    b) 0.25
    c) 1
    d) 0.75
    (1 mark)

Section B: Short Answer (40 marks)

  1. Expand and simplify:
    (4 marks)

  2. Solve the simultaneous equations:
    (6 marks)

  3. A right-angled triangle has legs of lengths 6 cm and 8 cm. Find the length of the hypotenuse.
    (4 marks)

  4. Calculate the gradient of the line passing through the points and .
    (4 marks)

  5. The sum of the angles in a quadrilateral is 360°. If three angles are 90°, 85°, and 95°, find the fourth angle.
    (4 marks)

Section C: Extended Response (40 marks)

  1. A rectangle has a length of cm and a width of cm.

    a) Express the area of the rectangle as a polynomial in terms of .
    b) If the area of the rectangle is 30 cm², find the value of .
    (10 marks)

  2. A student scores 72%, 85%, 90%, and 76% on four tests.

    a) Find the mean percentage score.
    b) If the student wants to have an average of 80% after five tests, what must they score on the fifth test?
    (10 marks)

  3. The following data shows the number of hours students spent studying for a test: 2, 4, 4, 6, 7, 8, 9, 10.

    a) Calculate the mean, median, and mode of the data.
    b) If a student who studied for 1 hour is added to the data, how does the mean change?
    (10 marks)

  4. A cylindrical tank has a radius of 5 m and a height of 12 m.

    a) Calculate the volume of the tank.
    b) If the tank is filled to 75% of its capacity, how much water does it contain?
    (10 marks)

End of Paper

2. Exam Paper 02

Year 10 Mathematics Examination Paper

Time Allowed: 2 hours

Instructions:

  1. Answer all questions.
  2. Write your answers in the space provided.
  3. Use a calculator where necessary.
  4. Show all working out.

Section A: Algebra and Functions

  1. Solve the quadratic equation .

  2. Expand and simplify:

  3. Factorise the following expression completely:

  4. Solve the simultaneous equations:

Section B: Geometry

  1. In a right-angled triangle, one angle is 30 degrees, and the hypotenuse is 10 cm. Find the length of the opposite side to the 30-degree angle.

  2. Calculate the area of a trapezium with bases 8 cm and 5 cm, and a height of 4 cm.

  3. The diameter of a circle is 12 cm. Find the circumference of the circle.
    (Use )

  4. Given a rectangle with a length of 12 cm and a width of 5 cm, find the length of the diagonal.
    (Use the Pythagorean theorem)

Section C: Statistics and Probability

  1. Find the mean of the following set of numbers:
    4, 7, 9, 10, 12

  2. A die is rolled once. What is the probability of rolling a number greater than 4?

  3. The following data represents the number of books read by a group of students in a month: 3, 5, 7, 5, 8, 6, 7, 8, 7, 5. Construct a frequency table for this data.

  4. If the probability of raining tomorrow is 0.3, what is the probability that it will not rain tomorrow?

Section D: Measurement and Calculation

  1. Convert 3.5 liters to milliliters.

  2. A car travels 150 km in 2 hours. What is its average speed in km/h?

  3. If a recipe requires 250 grams of sugar to make 4 servings, how much sugar is needed to make 10 servings?

  4. Calculate the volume of a rectangular prism with a length of 5 cm, width of 4 cm, and height of 3 cm.

End of Paper

3. Exam Paper 03

Year 10 Mathematics Examination Paper

Time Allowed: 2 hours

Instructions:

  1. Answer all questions.
  2. Write your answers in the space provided.
  3. Use a calculator where necessary.
  4. Show all working out.

Section A: Algebra and Functions

  1. Solve the following linear equation for :

  2. Solve the quadratic equation using the quadratic formula:

  3. Simplify the following algebraic expression:

  4. Given , find .

  5. Find the inverse of the function .

Section B: Geometry

  1. In triangle ABC, angle A is 45 degrees, angle B is 65 degrees. Find angle C.

  2. Calculate the surface area of a cylinder with a radius of 3 cm and a height of 10 cm.
    (Use )

  3. The base of a cone is a circle with a radius of 4 cm, and its height is 9 cm. Find the volume of the cone.
    (Use )

  4. Find the length of the hypotenuse of a right-angled triangle with sides of lengths 6 cm and 8 cm.

Section C: Statistics and Probability

  1. Calculate the median of the following data set:
    12, 7, 10, 5, 8

  2. A bag contains 4 red, 3 blue, and 5 green balls. What is the probability of drawing a blue ball from the bag?

  3. The following data represents the number of hours studied by a group of students: 2, 4, 6, 4, 8, 6, 5, 4. Construct a frequency distribution table.

  4. If the probability of an event happening is 0.75, what is the probability of the event not happening?

Section D: Measurement and Calculation

  1. Convert 4500 milliliters to liters.

  2. A tank is filled with water at a rate of 3 liters per minute. How many minutes will it take to fill the tank if it holds 150 liters?

  3. If a rectangular garden is 20 meters long and 15 meters wide, find its area.

  4. Calculate the perimeter of a triangle with sides of lengths 7 cm, 10 cm, and 5 cm.

Section E: Number and Algebra

  1. Find the value of if .

  2. Simplify the following expression:

  3. Solve for :

  4. Determine the value of if .

Section F: Financial Mathematics

  1. If you invest $1000 at an annual interest rate of 5% compounded annually, how much will you have after 3 years?

  2. A shop offers a 20% discount on a jacket that originally costs $80. What is the discounted price?

  3. If you save $50 each month into a savings account with no interest, how much will you have saved after 1 year?

End of Paper