I85PREP
⌘ K
ORELA Mathematics (NT304) study materials
ORELA Mathematics (NT304) study resources

ORELA Mathematics (NT304) practice questions

One question at a time. Build your ORELA Mathematics (NT304) understanding.

First 50 of 200 questions. Each one lists the choices, the correct answer, and an explanation. The checker at the top of this page saves progress in this browser when it is available.

Continue in the practice tool above to load more questions, 50 at a time.

Question 1Mathematics

A school buys 24 boxes of markers. Each box contains 18 markers. The markers are then divided equally among 12 classrooms. How many markers does each classroom receive?

  1. 36 Correct answer.
  2. 18
  3. 24
  4. 216

Explanation

First find the total number of markers by multiplying 24 boxes by 18 markers per box, which gives 432 markers. Dividing 432 markers equally among 12 classrooms yields 36 markers per classroom.

Question 2Mathematics

Which number is equivalent to 3/8 expressed as a decimal?

  1. 0.38
  2. 0.375 Correct answer.
  3. 0.267
  4. 0.83

Explanation

Dividing the numerator 3 by the denominator 8 gives 0.375 exactly, because 8 divides 3.000 with no remainder. This terminating decimal is the standard decimal form of the fraction 3/8.

Question 3Mathematics

Two interior angles of a triangle measure 37° and 58°. What is the exterior angle adjacent to the third interior angle?

  1. 143°
  2. 122°
  3. 95° Correct answer.
  4. 85°

Explanation

A triangle's exterior angle equals the sum of the two nonadjacent interior angles. Adding 37 and 58 gives 95 degrees; the adjacent interior angle is its supplement, 85 degrees.

Question 4Mathematics

Which expression represents the perimeter of a rectangle whose length is 3 more than twice its width w?

  1. 2w + 3
  2. 6w + 6 Correct answer.
  3. 4w + 3
  4. 6w + 3

Explanation

The length is 2w + 3, and perimeter equals twice the sum of length and width. That gives 2(w + 2w + 3) = 2(3w + 3) = 6w + 6.

Question 5Mathematics

What is the greatest common factor of 84 and 126?

  1. 6
  2. 14
  3. 42 Correct answer.
  4. 21

Explanation

The prime factorizations are 84 = 2²·3·7 and 126 = 2·3²·7. Taking the lowest power of each shared prime gives 2·3·7 = 42, which divides both numbers.

Question 6Mathematics

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. One marble is drawn at random. What is the probability that it is blue?

  1. 3/7
  2. 3/10 Correct answer.
  3. 1/10
  4. 1/3

Explanation

There are 5 + 3 + 2 = 10 marbles total, and 3 of them are blue. The probability of drawing blue is therefore 3 out of 10, or 3/10.

Question 7Mathematics

Which of the following describes the slope of the line passing through the points (2, 5) and (6, 13)?

  1. 2 Correct answer.
  2. 8
  3. 1/2
  4. 4

Explanation

Slope equals the change in y divided by the change in x, so (13 − 5)/(6 − 2) = 8/4 = 2. The line rises two units for every one unit to the right.

Question 8Mathematics

A store discounts a $60 item by 25%. What is the sale price?

  1. $15
  2. $45 Correct answer.
  3. $35
  4. $75

Explanation

A 25% discount removes 0.25 × $60 = $15 from the original price. Subtracting the discount from $60 gives a sale price of $45.

Question 9Mathematics

What is the value of 4 + 3 × (8 − 5)²?

  1. 85
  2. 63
  3. 31 Correct answer.
  4. 13

Explanation

Following order of operations, evaluate the parentheses first to get 3, then square it to get 9. Multiply 3 × 9 = 27, and finally add 4 to obtain 31.

Question 10Mathematics

Solve for x: 5(x − 3) = 2x + 9.

  1. x = 6
  2. x = 8 Correct answer.
  3. x = 12
  4. x = 2

Explanation

Distribute to get 5x − 15 = 2x + 9. Subtract 2x from both sides to get 3x − 15 = 9, then add 15 to get 3x = 24, so x = 8. Substituting 8 back confirms both sides equal 25.

Question 11Mathematics

A rectangular field is 8 m wide and 15 m long. A straight path joins opposite corners. What is the path's length?

  1. 13 m
  2. 17 m Correct answer.
  3. 23 m
  4. 120 m

Explanation

The path is the hypotenuse of a right triangle with legs eight and fifteen. Its squared length is 64 plus 225, or 289, giving a length of seventeen metres.

Question 12Mathematics

A data set consists of the values 4, 7, 7, 9, 12, 15. Which statement about its measures of center is true?

  1. The mean is 9 and the median is 8. Correct answer.
  2. The mean is 8 and the median is 9.
  3. The mean is 9 and the mode is 9.
  4. The mean and median are both 9.

Explanation

The mean is (4 + 7 + 7 + 9 + 12 + 15)/6 = 54/6 = 9. With six ordered values, the median is the average of the third and fourth values, (7 + 9)/2 = 8.

Question 13Mathematics

Which expression is equivalent to (2x³y²)(3x²y⁵)?

  1. 6x⁶y¹⁰
  2. 6x⁵y¹⁰
  3. 6x⁵y⁷ Correct answer.
  4. 5x⁵y⁷

Explanation

Multiply the coefficients 2 × 3 = 6, then add exponents of like bases: x³·x² = x⁵ and y²·y⁵ = y⁷. The simplified product is 6x⁵y⁷.

Question 14Mathematics

A cylinder has a radius of 3 cm and a height of 10 cm. Using π ≈ 3.14, what is its volume?

  1. 565.2 cm³
  2. 94.2 cm³
  3. 188.4 cm³
  4. 282.6 cm³ Correct answer.

Explanation

The volume of a cylinder is πr²h, so substitute to get 3.14 × 9 × 10 = 282.6 cm³. Squaring the radius before multiplying by height is essential.

Question 15Mathematics

The function f(x) = 2x − 5 is defined for all real numbers. What is f⁻¹(7)?

  1. 1
  2. 6 Correct answer.
  3. 9
  4. −19

Explanation

Set 2x − 5 = 7 and solve: 2x = 12, so x = 6. Equivalently, the inverse function is f⁻¹(y) = (y + 5)/2, which gives (7 + 5)/2 = 6.

Question 16Mathematics

A sequence begins 3, 7, 11, 15, ... and continues with a constant common difference. What is the 20th term?

  1. 76
  2. 83
  3. 79 Correct answer.
  4. 80

Explanation

This is an arithmetic sequence with first term 3 and common difference 4. The nth term is a₁ + (n − 1)d, so a₂₀ = 3 + 19(4) = 3 + 76 = 79.

Question 17Mathematics

In a coordinate plane, the line 3x + 4y = 12 intersects the x-axis and y-axis. What is the area of the triangle formed with the origin?

  1. 7 square units
  2. 24 square units
  3. 6 square units Correct answer.
  4. 12 square units

Explanation

Setting y = 0 gives x = 4, and setting x = 0 gives y = 3, so the intercepts are (4, 0) and (0, 3). The right triangle has legs 4 and 3, so its area is ½ × 4 × 3 = 6 square units.

Question 18Mathematics

A fair six-sided die is rolled twice. What is the probability that the sum of the two rolls is 7?

  1. 7/36
  2. 1/6 Correct answer.
  3. 1/12
  4. 1/36

Explanation

There are 36 equally likely ordered outcomes. Six of them sum to 7: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1), giving 6/36 = 1/6.

Question 19Mathematics

Which of the following is a counterexample to the statement "If a number is prime, then it is odd"?

  1. 1
  2. 15
  3. 9
  4. 2 Correct answer.

Explanation

A counterexample must make the hypothesis true and the conclusion false, so it must be an even prime. The number 2 is prime and even, which disproves the statement.

Question 20Mathematics

The expression x² − 7x + 12 factors as which product?

  1. (x − 2)(x − 6)
  2. (x − 1)(x − 12)
  3. (x + 3)(x + 4)
  4. (x − 3)(x − 4) Correct answer.

Explanation

We need two numbers that multiply to 12 and add to −7, namely −3 and −4. Therefore x² − 7x + 12 = (x − 3)(x − 4).

Question 21Mathematics

A right triangle has a hypotenuse of 13 and one leg of 5. What is the tangent of the angle opposite the leg of length 5?

  1. 12/13
  2. 5/13
  3. 5/12 Correct answer.
  4. 12/5

Explanation

The other leg is √(13² − 5²) = √144 = 12. The tangent of an angle equals the opposite leg over the adjacent leg, which is 5/12 for the angle opposite the side of length 5.

Question 22Mathematics

Consider the quadratic function f(x) = x² − 6x + 5. What are the coordinates of its vertex?

  1. (3, −4) Correct answer.
  2. (−3, −4)
  3. (3, 4)
  4. (6, 5)

Explanation

The vertex x-coordinate is −b/(2a) = 6/2 = 3. Evaluating f(3) = 9 − 18 + 5 = −4, so the vertex is (3, −4), which is also the minimum point.

Question 23Mathematics

A geometric sequence has first term 5 and common ratio 3. What is the sum of the first 4 terms?

  1. 200 Correct answer.
  2. 135
  3. 405
  4. 180

Explanation

The first four terms are 5, 15, 45, and 135. Their sum is 5 + 15 + 45 + 135 = 200, which also matches the formula a(1 − rⁿ)/(1 − r) = 5(1 − 81)/(1 − 3).

Question 24Mathematics

A circle is inscribed in a square with side length 10. What is the area of the region inside the square but outside the circle?

  1. 100 − 25π Correct answer.
  2. 100 − 100π
  3. 100 − 50π
  4. 25π

Explanation

The square's area is 100, and the inscribed circle has radius 5, so its area is π·5² = 25π. Subtracting the circle's area from the square's area gives 100 − 25π.

Question 25Mathematics

If log₂(x) + log₂(x − 2) = 3, what is the value of x?

  1. −2
  2. 8
  3. 4 Correct answer.
  4. 2

Explanation

Combining the logs gives log₂(x(x − 2)) = 3, so x² − 2x = 8, or x² − 2x − 8 = 0. Factoring gives (x − 4)(x + 2) = 0; x = −2 is rejected because the logarithm's argument must be positive, leaving x = 4.

Question 26Mathematics

A rectangular garden measures 14 meters by 9 meters. A walkway of uniform width 2 meters is added around all four sides. What is the area of the walkway alone?

  1. 108 square meters Correct answer.
  2. 126 square meters
  3. 92 square meters
  4. 46 square meters

Explanation

The enlarged rectangle measures 18 by 13, giving area 234 square meters, while the garden itself is 14 × 9 = 126 square meters. The walkway area is the difference, 234 − 126 = 108 square meters.

Question 27Mathematics

Which set of numbers is closed under subtraction?

  1. The set of natural numbers
  2. The set of integers Correct answer.
  3. The set of whole numbers
  4. The set of positive integers

Explanation

A set is closed under subtraction when the difference of any two members is again in the set. Subtracting any integer from another integer always yields an integer, so the integers are closed.

Question 28Mathematics

A student claims that the sum of any two odd integers is even. Which reasoning establishes this claim for all odd integers?

  1. Noting that an even number between two odd numbers is always present
  2. Writing odd integers as 2m + 1 and 2n + 1, so the sum is 2(m + n + 1) Correct answer.
  3. Testing several pairs of odd integers and finding each sum even
  4. Observing that odd plus odd differs from odd plus even

Explanation

Every odd integer has the form 2m + 1 for some integer m. Adding two such expressions gives 2m + 2n + 2, which factors as 2(m + n + 1), an even number, so the statement holds in general.

Question 29Mathematics

A jacket originally priced at $80 is marked down 15%, and then an additional 10% is taken off the reduced price. What is the final price?

  1. $72.00
  2. $61.20 Correct answer.
  3. $60.00
  4. $68.00

Explanation

Successive percent discounts multiply: 80 × 0.85 = 68, then 68 × 0.90 = 61.20. The combined factor is 0.85 × 0.90 = 0.765, so the final price is $61.20.

Question 30Mathematics

The line through the points (1, 4) and (5, 12) is parallel to a second line that passes through (0, −3). What is the equation of the second line?

  1. y = 2x − 3 Correct answer.
  2. y = 2x + 3
  3. y = −2x − 3
  4. y = (1/2)x − 3

Explanation

The slope of the first line is (12 − 4)/(5 − 1) = 2, and parallel lines share the same slope. With slope 2 and y-intercept −3, the second line is y = 2x − 3.

Question 31Mathematics

A function g is defined by g(x) = x² + 2x. What is g(x + 1) − g(x)?

  1. 2x + 1
  2. 2x + 3 Correct answer.
  3. x² + 2x + 1
  4. 2x + 2

Explanation

Compute g(x + 1) = (x + 1)² + 2(x + 1) = x² + 4x + 3, and subtract g(x) = x² + 2x. The difference is 2x + 3.

Question 32Mathematics

The system 2x + 3y = 12 and 4x + 6y = 20 is presented in a coordinate plane. Which statement about the system is accurate?

  1. It has exactly one solution at (3, 2)
  2. It has infinitely many solutions
  3. It has exactly two solutions
  4. It has no solution because the lines are parallel Correct answer.

Explanation

The second equation is twice the left side of the first but with a different constant, so the lines have equal slope and different intercepts. Parallel distinct lines never meet, so the system has no solution.

Question 33Mathematics

A quadratic function has zeros at x = −3 and x = 5 and opens upward. Over which interval is the function negative?

  1. x < 5
  2. x > −3
  3. −3 < x < 5 Correct answer.
  4. x < −3 or x > 5

Explanation

An upward-opening parabola is below the x-axis between its zeros. Since the zeros are −3 and 5, the function is negative for values strictly between them.

Question 34Mathematics

The polynomial p(x) = x³ − 4x² + x + 6 has x = 2 as a zero. Which factorization of p(x) is correct?

  1. (x − 2)(x − 3)(x + 1) Correct answer.
  2. (x − 2)(x − 1)(x − 3)
  3. (x − 2)(x + 3)(x + 1)
  4. (x + 2)(x − 3)(x − 1)

Explanation

Dividing p(x) by (x − 2) gives x² − 2x − 3, which factors as (x − 3)(x + 1). Thus p(x) = (x − 2)(x − 3)(x + 1), and the zeros are 2, 3, and −1.

Question 35Mathematics

If f(x) = 3x + 1 and g(x) = x², what is f(g(−2))?

  1. 36
  2. −11
  3. 13 Correct answer.
  4. 49

Explanation

Evaluate the inner function first: g(−2) = (−2)² = 4. Then f(4) = 3(4) + 1 = 13.

Question 36Mathematics

An exponential function is written as h(t) = 250(0.8)^t, where t is measured in years. Which description matches this model?

  1. A quantity starting at 250 that grows 80% each year
  2. A quantity starting at 80 that decreases 25% each year
  3. A quantity starting at 250 that decreases 20% each year Correct answer.
  4. A quantity starting at 250 that decreases 80% each year

Explanation

In h(t) = a·b^t, the value a = 250 is the initial amount and b = 0.8 is the yearly multiplier. A multiplier of 0.8 means each year's value is 80% of the previous, a 20% decrease.

Question 37Mathematics

A right triangle has an angle measuring 30°, and the side opposite that angle is 7 units long. What is the length of the hypotenuse?

  1. 7√2 units
  2. 3.5 units
  3. 14 units Correct answer.
  4. 7√3 units

Explanation

The sine ratio gives sin 30° = opposite/hypotenuse. Since sin 30° = 1/2, the hypotenuse is 7 ÷ (1/2) = 14 units.

Question 38Mathematics

In a circle of radius 9, a central angle measures 40°. What is the length of the arc intercepted by this angle, expressed in terms of π?

  1. 2π Correct answer.
  2. 4π
  3. 9π
  4. 18π

Explanation

Arc length equals rθ with θ in radians, and 40° = 40π/180 = 2π/9 radians. Multiplying by radius 9 gives 9 × (2π/9) = 2π.

Question 39Mathematics

A rectangular prism has a length of 6 cm, a width of 4 cm, and a height of 5 cm. If all three dimensions are doubled, what happens to the volume?

  1. It increases by a factor of 6
  2. It increases by a factor of 4
  3. It increases by a factor of 8 Correct answer.
  4. It doubles

Explanation

Original volume is 6 × 4 × 5 = 120 cm³. Doubling each dimension gives 12 × 8 × 10 = 960 cm³, which is 8 times larger, consistent with volume scaling by the cube of the linear scale factor.

Question 40Mathematics

Two similar triangles have corresponding side lengths in the ratio 3:5. If the area of the smaller triangle is 27 square units, what is the area of the larger triangle?

  1. 45 square units
  2. 75 square units Correct answer.
  3. 81 square units
  4. 135 square units

Explanation

For similar figures, areas scale as the square of the side ratio, so the area ratio is 3²:5² = 9:25. Setting 27/x = 9/25 gives x = 27 × 25/9 = 75 square units.

Question 41Mathematics

A box contains 6 black pens and 4 red pens. Two pens are drawn without replacement. What is the probability that both pens are red?

  1. 2/15 Correct answer.
  2. 8/45
  3. 1/5
  4. 4/25

Explanation

The probability the first pen is red is 4/10, and given that, the second is 3/9. Multiplying gives (4/10)(3/9) = 12/90 = 2/15.

Question 42Mathematics

A data set of 20 test scores has a mean of 72. A new score of 92 is added to the set. What is the mean of the 21 scores?

  1. 76
  2. 74
  3. 72.95 Correct answer.
  4. 73

Explanation

The original total is 20 × 72 = 1440. Adding 92 gives 1532, and dividing by 21 scores gives approximately 72.95.

Question 43Mathematics

A set of quiz scores is displayed in a frequency table: score 1 appears 2 times, score 2 appears 5 times, score 3 appears 8 times, and score 4 appears 1 time. What is the median score?

  1. 2.5
  2. 4
  3. 2
  4. 3 Correct answer.

Explanation

There are 16 scores total, so the median is the average of the 8th and 9th values in order. Both the 8th and 9th values fall in the group of 3s, since the first 7 scores are 1s and 2s and scores 8 through 15 are 3s, making the median 3.

Question 44Mathematics

A spinner has 5 equal sectors numbered 1 through 5. What is the probability of spinning a number greater than 3 on two consecutive spins?

  1. 4/25 Correct answer.
  2. 2/5
  3. 1/5
  4. 3/5

Explanation

The numbers greater than 3 are 4 and 5, so each spin has probability 2/5. Because the spins are independent, the probability of both is (2/5)(2/5) = 4/25.

Question 45Mathematics

A right circular cone has a radius of 5 cm and a height of 12 cm. What is its slant height, and what is its lateral surface area in terms of π?

  1. Slant height 13 cm; lateral area 65π cm² Correct answer.
  2. Slant height 17 cm; lateral area 85π cm²
  3. Slant height 13 cm; lateral area 30π cm²
  4. Slant height 12 cm; lateral area 60π cm²

Explanation

The slant height is the hypotenuse of a right triangle with legs 5 and 12, so it is 13 cm. Lateral surface area of a cone is πrl = π(5)(13) = 65π cm².

Question 46Mathematics

A transformation maps the point (x, y) to (x + 4, y − 3). Which statement describes this transformation?

  1. A rotation of 90° clockwise about the origin
  2. A translation 4 units right and 3 units down Correct answer.
  3. A dilation by a factor of 4
  4. A reflection across the line y = x

Explanation

Adding a constant to x shifts points horizontally and subtracting from y shifts them vertically. The rule (x + 4, y − 3) moves every point 4 units right and 3 units down, which is a translation.

Question 47Mathematics

A sequence is defined by a₁ = 4 and aₙ = 2aₙ₋₁ − 3 for n ≥ 2. What is a₄?

  1. 11 Correct answer.
  2. 7
  3. 19
  4. 5

Explanation

Apply the recurrence step by step: a₂ = 2(4) − 3 = 5, a₃ = 2(5) − 3 = 7, and a₄ = 2(7) − 3 = 11.

Question 48Mathematics

The complex numbers z = 3 + 2i and w = 1 − 4i are given. What is the product zw?

  1. 11 − 10i Correct answer.
  2. 3 − 8i
  3. 11 + 10i
  4. −5 − 10i

Explanation

Distribute: (3)(1) + (3)(−4i) + (2i)(1) + (2i)(−4i) = 3 − 12i + 2i − 8i². Since i² = −1, the constant becomes 3 + 8 = 11, and the imaginary part is −10i, giving 11 − 10i.

Question 49Mathematics

A logarithmic function is defined as f(x) = log₃(x − 2). What are the domain and the vertical asymptote of f?

  1. Domain x > 3; asymptote x = 3
  2. Domain x > 2; asymptote x = 2 Correct answer.
  3. Domain x ≥ 2; asymptote x = −2
  4. Domain x > 0; asymptote x = 0

Explanation

A logarithm requires a positive argument, so x − 2 > 0, giving x > 2. As x approaches 2 from the right, the argument approaches 0 and the logarithm decreases without bound, so x = 2 is a vertical asymptote.

Question 50Mathematics

A statement is given: "If a quadrilateral is a square, then its diagonals are perpendicular." Which statement is the converse of this statement?

  1. If the diagonals of a quadrilateral are perpendicular, then it is a square Correct answer.
  2. If a quadrilateral is not a square, then its diagonals are not perpendicular
  3. If the diagonals of a quadrilateral are not perpendicular, then it is not a square
  4. If a quadrilateral is a square, then its diagonals bisect each other

Explanation

The converse of "If P, then Q" is "If Q, then P." Here P is "quadrilateral is a square" and Q is "diagonals are perpendicular," so the converse swaps these, giving the statement about perpendicular diagonals implying a square.