Grade 10 Math Test – 30 Questions in 30 Minutes

Solve these questions in 30 minutes

  1. Write the formula for the volume of a cone
  2. What will be the sum of P(E) and P(Not E)?
  3. What will be Sec2A if TanA = 1
  4. Write the formula for the sum of an Arithmetic Progression
  5. Calculate the probability of getting a number less than 4 when a card is drawn from a deck of well shuffled cards
  6. A die is rolled three times in a row. What is the theoretical probability the number 2 will occur each time.
  7. For the two lines with equations area as below, the slopes will be equal True or False
    y = 2x – 3, and y = 5x – 3
  8. A polynomial of degree two will always have which of the following?
    (a) only two terms (b) the term with the highest degree will be a square term (c) two unknowns (x and y) without the square term (d) a y intercept that is a square of a natural number
  9. A triangle has corners at: A (0, 10), B (0, 5), and C (5, 5). Therefore, it must be (select one from the following): (a) Acute angled triangle (b) Right angled triangle (c) Obtuse angled triangle (d) Equilateral triangle.
  10. Calculate the area and perimeter for the triangle in question 9
  11. If an insect is crawling from point C to point A, how much distance will it have to cover to reach A in the triangle of question 9?
  12. From a starting point A – I walk 5 km to the East then turn right and walk 3 km to the South. Then I turn right and walk 5 km again. What are my coordinates (x, y) if A is the origin, and the Y axis represents North / South.
  13. Write a formula or equation to calculate the white space in the figure below (no calculations needed)

14. You are given a circle with center C, and radius R. A tangent to the circle touches it at point P. Another point Q is on the tangent 5 cm away from point P. Therefore in triangle CPQ which of the following is true?
(a) Angle at Q is a right angle
(b) Angle at C is a right angle
(c) Angle Q is obtuse
(d) None of the above

15. Two concentric circles A and B are drawn, with diameters equal to 15 cm and 30 cm respectively. A tangent is drawn to the circle A. This line will be which of the following?
(a) A tangent to the outer circle B also
(b) It could be a chord for the inner circle A
(c) It could be a chord for the outer circle B
(d) None of the above

16. A sure event can have a probability as: 0<P(E)<1 True / False
17. What will be the angle between the minute hand and hour hand of a clock when the time is 4.30?
18. A pair of dice is rolled, what is the probability the product of the numbers on the faces will be 6?
19. What is the median score for a class of 10 students? Their scores are as below:
45, 44, 59, 90, 78 88, 89, 34, 28, 66

20. For the equation 2y = 4x – 10 which one is the correct y intercept from the ones below?
(a) 2 (b) -10 (c) 4 (d) -5
21. What will be the zero for the equation in question 20?
22. Write the formula to find the slope for a line passing through two points (2, 6) and (-2, 4)
23. Which of the following is true?
a) The shortest line drawn inside a circle is the diameter
b) The longest line drawn inside a circle is the radius
c) The longest line drawn inside a circle is the diameter
d) The longest line drawn inside the circle is a tangent

24. Write the general equation for a circle
25. A triangle lies inside a circle with point A on the circumference, B at one end of a diameter, and C at the other end. Angle A will be which of the following?
(a) 90o (b) 60o (c) 30o (d) none of these
26. What is the formula for the curved surface area of a hollow hemisphere?
27. Which of the following are similar?
(a) Isosceles triangles (b) Circles (c) Squares (d) all of these

28. Triangles ABC and ADE would be similar if:
(a) all their angles are equal
(b) both have one right angle
(c) both are inside a circle with the diameter as the base
(d) both have all acute angles

29. Find the zeros for this polynomial: 4x2 – 16x + 12
30. Find the common difference “d” if the first term of a series is 15 and the fifth term is -5.

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31. Calculate 1/2 Sin 60 – 1/4 Cos 60 + (2/32) Tan 60
32. In an isosceles triangle, the two equal angles add up to 60o; if the base is 20 cm what is the area of the triangle?
33. If the area of a square of side 7 cm is the same as the area of a quadrant of a circle, what is the radius of the circle?
34. For the figure below what will be the length of CD if the radius of the circle is 7 cm, and the triangle ABC is inside the quadrant.

35. What are the two equations used for arithmetic series (one for sum and one for finding the value of the nth. number?

36. What are the formulas used for a right angled triangle (all trigonometric formulas)

37. What are the formulas used for finding volumes of cone, hemisphere, cylinder?

38. What are the formulas for areas of different shapes and objects: circle, rhombus, parallelogram, sector, hemisphere, cone, cylinder, etc.

39 What are the formulas for linear equations



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