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Kankor 14-Pass study materials
Kankor 14-Pass study resources

Kankor 14-Pass practice questions

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Question 1Mathematics

What is the value of 7 + 5 × 3 − 4?

  1. 12
  2. 32
  3. 18 Correct answer.
  4. 19

Explanation

Order of operations requires multiplication before addition and subtraction, so 5 × 3 = 15 first. Then 7 + 15 − 4 = 18.

Question 2Mathematics

Which number is the additive identity in the set of integers?

  1. 1
  2. −1
  3. 0 Correct answer.
  4. 10

Explanation

The additive identity is the number that leaves any integer unchanged when added to it. Since a + 0 = a for every integer a, the additive identity is 0.

Question 3Mathematics

A shirt costs 800 Afghani and is sold at a 15% discount. What is the selling price?

  1. 760 Afghani
  2. 720 Afghani
  3. 700 Afghani
  4. 680 Afghani Correct answer.

Explanation

The discount amount is 15% of 800, which equals 120. Subtracting the discount from the original price gives 800 − 120 = 680 Afghani.

Question 4Mathematics

Simplify the expression 3x + 5x − 2x.

  1. 4x
  2. 10x
  3. 6x²
  4. 6x Correct answer.

Explanation

Like terms with the same variable can be combined by adding their coefficients: 3 + 5 − 2 = 6. The result is therefore 6x.

Question 5Mathematics

What is the slope of the line passing through the points (1, 2) and (4, 11)?

  1. 1/3
  2. 9
  3. 3 Correct answer.
  4. −3

Explanation

Slope equals the change in y divided by the change in x: (11 − 2)/(4 − 1) = 9/3 = 3.

Question 6Mathematics

What is the value of 2⁵?

  1. 25
  2. 32 Correct answer.
  3. 10
  4. 64

Explanation

The expression 2⁵ means multiplying 2 by itself five times: 2 × 2 × 2 × 2 × 2 = 32.

Question 7Mathematics

What is the value of sin 30°?

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

Explanation

For the standard angle 30°, the sine ratio equals the opposite side over the hypotenuse of a 30-60-90 triangle, giving 1/2.

Question 8Mathematics

What is the mean of the numbers 4, 8, 6, 10, and 12?

  1. 10
  2. 7
  3. 8 Correct answer.
  4. 9

Explanation

The mean is the sum of the values divided by how many there are: (4 + 8 + 6 + 10 + 12)/5 = 40/5 = 8.

Question 9Mathematics

Solve the equation 4x − 7 = 21.

  1. x = 6
  2. x = 7 Correct answer.
  3. x = 8
  4. x = 5

Explanation

Add 7 to both sides to obtain 4x = 28, then divide both sides by 4 to get x = 7.

Question 10Mathematics

Factor the expression x² − 9.

  1. (x − 9)(x + 1)
  2. (x − 3)(x + 3) Correct answer.
  3. (x − 3)(x − 3)
  4. (x + 3)(x + 3)

Explanation

The expression is a difference of squares, a² − b² = (a − b)(a + b). With a = x and b = 3, it factors as (x − 3)(x + 3).

Question 11Mathematics

A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?

  1. 14
  2. 12
  3. 10 Correct answer.
  4. 48

Explanation

By the Pythagorean theorem, the hypotenuse c satisfies c² = 6² + 8² = 36 + 64 = 100. Taking the positive square root gives c = 10.

Question 12Mathematics

What is the next term in the arithmetic sequence 3, 7, 11, 15, ...?

  1. 23
  2. 19 Correct answer.
  3. 18
  4. 20

Explanation

An arithmetic sequence adds a constant difference each step; here the difference is 4. Adding 4 to the last term 15 gives 19.

Question 13Mathematics

If log₁₀(1000) = x, what is the value of x?

  1. 100
  2. 10
  3. 2
  4. 3 Correct answer.

Explanation

The logarithm asks for the exponent to which the base 10 must be raised to give 1000. Since 10³ = 1000, x = 3.

Question 14Mathematics

The sum of two numbers is 20 and their difference is 4. What is the larger number?

  1. 10
  2. 8
  3. 16
  4. 12 Correct answer.

Explanation

Let the numbers be a and b with a + b = 20 and a − b = 4. Adding the equations gives 2a = 24, so a = 12.

Question 15Mathematics

What is the area of a circle with radius 7? (Use π ≈ 22/7)

  1. 44
  2. 308
  3. 154 Correct answer.
  4. 49

Explanation

The area of a circle is πr². Substituting r = 7 and π ≈ 22/7 gives (22/7) × 49 = 22 × 7 = 154.

Question 16Mathematics

Solve the inequality 3x + 2 < 11.

  1. x < 3 Correct answer.
  2. x > 3
  3. x > 9
  4. x < 9

Explanation

Subtract 2 from both sides to get 3x < 9, then divide by the positive number 3, which keeps the inequality direction, giving x < 3.

Question 17Mathematics

Two dice are rolled. What is the probability that the sum of the two numbers is 7?

  1. 7/36
  2. 1/12
  3. 5/36
  4. 1/6 Correct answer.

Explanation

There are 36 equally likely outcomes. The sums equal to 7 occur in 6 ways: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). Thus the probability is 6/36 = 1/6.

Question 18Mathematics

What is the value of the expression |−9| + |4|?

  1. 5
  2. 13 Correct answer.
  3. −13
  4. −5

Explanation

Absolute value gives the distance from zero, so |−9| = 9 and |4| = 4. Their sum is 9 + 4 = 13.

Question 19Mathematics

The quadratic equation x² − 5x + 6 = 0 has roots:

  1. 1 and 6
  2. 2 and 3 Correct answer.
  3. −2 and −3
  4. −1 and −6

Explanation

We need two numbers whose product is 6 and whose sum is 5; these are 2 and 3. So x² − 5x + 6 = (x − 2)(x − 3) = 0, giving x = 2 or x = 3.

Question 20Mathematics

In a triangle, two angles measure 45° and 65°. What is the measure of the third angle?

  1. 110°
  2. 80°
  3. 70° Correct answer.
  4. 60°

Explanation

The angles of a triangle sum to 180°. The third angle is 180° − 45° − 65° = 70°.

Question 21Mathematics

What is the 10th term of the geometric sequence 2, 6, 18, 54, ...?

  1. 3 × 2⁹
  2. 2 × 10³
  3. 2 × 3⁹ Correct answer.
  4. 2 × 3¹⁰

Explanation

A geometric sequence has nth term a·r^(n−1), where a = 2 is the first term and r = 3 is the common ratio. For n = 10, the term is 2 × 3⁹.

Question 22Mathematics

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

  1. −1
  2. 11
  3. 3
  4. 15 Correct answer.

Explanation

Substitute x = −2: 2(−2)² − 3(−2) + 1 = 2(4) + 6 + 1 = 8 + 6 + 1 = 15.

Question 23Mathematics

A cone has radius 3 and height 4. What is its volume? (Use π in the answer)

  1. 16π
  2. 48π
  3. 36π
  4. 12π Correct answer.

Explanation

The volume of a cone is (1/3)πr²h. Substituting r = 3 and h = 4 gives (1/3)π(9)(4) = 12π.

Question 24Mathematics

Simplify (x³ · x⁴) / x².

  1. x⁵ Correct answer.
  2. x⁶
  3. x²
  4. x⁹

Explanation

When multiplying powers with the same base, add the exponents: x³ · x⁴ = x⁷. When dividing, subtract the exponents: x⁷ / x² = x⁵.

Question 25Mathematics

The roots of x² + bx + 8 = 0 are both positive integers. What is the value of b?

  1. −8
  2. 8
  3. −6 Correct answer.
  4. 6

Explanation

If the roots are positive integers with product 8, the possible pairs are (1,8), (2,4). Their sums are 9 and 6, so b = −(sum) equals −9 or −6. Since the options include −6, that is the valid value.

Question 26Mathematics

What is the value of 3⁴?

  1. 64
  2. 12
  3. 81 Correct answer.
  4. 27

Explanation

A power means repeated multiplication: 3⁴ = 3 × 3 × 3 × 3. Multiplying gives 9 × 9 = 81.

Question 27Mathematics

What is the value of cos 60°?

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

Explanation

For the standard angle 60°, the cosine equals the adjacent side over the hypotenuse in a 30-60-90 triangle, giving 1/2. This is one of the exact values worth memorizing.

Question 28Mathematics

What is the median of the data set 3, 7, 8, 12, 15, 20?

  1. 12
  2. 10 Correct answer.
  3. 9.5
  4. 8

Explanation

With six values already in order, the median is the average of the two middle values, 8 and 12. Their average is (8 + 12)/2 = 10.

Question 29Mathematics

Solve for x: 5x + 9 = 34.

  1. x = 7
  2. x = 8.6
  3. x = 25
  4. x = 5 Correct answer.

Explanation

Subtract 9 from both sides to get 5x = 25, then divide both sides by 5 to obtain x = 5.

Question 30Mathematics

Factor x² + 7x + 12.

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

Explanation

We need two numbers whose product is 12 and whose sum is 7; those numbers are 3 and 4. Hence x² + 7x + 12 = (x + 3)(x + 4).

Question 31Mathematics

A rectangle has length 12 cm and width 5 cm. What is the length of its diagonal?

  1. 17 cm
  2. 13 cm Correct answer.
  3. 7 cm
  4. 60 cm

Explanation

The diagonal of a rectangle forms a right triangle with the two sides, so by the Pythagorean theorem d² = 12² + 5² = 144 + 25 = 169. Thus d = 13 cm.

Question 32Mathematics

What is the next term in the geometric sequence 5, 15, 45, 135, ...?

  1. 675
  2. 270
  3. 180
  4. 405 Correct answer.

Explanation

Each term is obtained by multiplying the previous term by the common ratio 3. Therefore the next term is 135 × 3 = 405.

Question 33Mathematics

If log₂(32) = y, what is the value of y?

  1. 5 Correct answer.
  2. 16
  3. 6
  4. 4

Explanation

The equation log₂(32) = y means 2^y = 32. Since 2⁵ = 32, we get y = 5.

Question 34Mathematics

The sum of two numbers is 30 and their difference is 8. What is the smaller number?

  1. 15
  2. 11 Correct answer.
  3. 22
  4. 19

Explanation

Let the numbers be a and b with a + b = 30 and a − b = 8. Adding the equations gives 2a = 38, so a = 19 and b = 30 − 19 = 11.

Question 35Mathematics

What is the circumference of a circle with diameter 14 cm? (Use π ≈ 22/7)

  1. 44 cm Correct answer.
  2. 22 cm
  3. 88 cm
  4. 154 cm

Explanation

Circumference equals π times the diameter: C = πd = (22/7) × 14 = 44 cm.

Question 36Mathematics

Solve the inequality 4x − 5 ≥ 15.

  1. x ≤ 2.5
  2. x ≥ 5 Correct answer.
  3. x ≥ 2.5
  4. x ≤ 5

Explanation

Add 5 to both sides to get 4x ≥ 20, then divide both sides by the positive number 4, which keeps the inequality direction, giving x ≥ 5.

Question 37Mathematics

A bag contains 5 red balls and 7 blue balls. Two balls are drawn one after the other without replacement. What is the probability that both are red?

  1. 5/33 Correct answer.
  2. 1/6
  3. 25/144
  4. 5/22

Explanation

The probability the first ball is red is 5/12; given that, 4 red remain out of 11 balls, so the second is red with probability 4/11. Multiplying gives (5/12)(4/11) = 20/132 = 5/33.

Question 38Mathematics

What is the value of |−13| − |−5|?

  1. −8
  2. 18
  3. −18
  4. 8 Correct answer.

Explanation

Absolute value gives distance from zero, so |−13| = 13 and |−5| = 5. Subtracting gives 13 − 5 = 8.

Question 39Mathematics

The quadratic equation x² + 2x − 15 = 0 has roots:

  1. 1 and −15
  2. 3 and −5 Correct answer.
  3. −3 and −5
  4. −3 and 5

Explanation

We need two numbers whose product is −15 and whose sum is 2; these are 3 and −5. Hence (x − 3)(x + 5) = 0, giving x = 3 or x = −5.

Question 40Mathematics

In a triangle, two angles measure 50° and 60°. What is the measure of the exterior angle at the third vertex?

  1. 110° Correct answer.
  2. 130°
  3. 120°
  4. 70°

Explanation

The third interior angle is 180° − 50° − 60° = 70°. The exterior angle is supplementary to it, so it equals 180° − 70° = 110°, which also equals the sum of the two remote interior angles.

Question 41Mathematics

What is the 8th term of the geometric sequence 3, 6, 12, 24, ...?

  1. 768
  2. 96
  3. 192
  4. 384 Correct answer.

Explanation

The first term is a = 3 and the common ratio is r = 2. The nth term is a·r^(n−1), so the 8th term is 3 × 2⁷ = 3 × 128 = 384.

Question 42Mathematics

If f(x) = x² + 4x − 2, what is f(3)?

  1. 19 Correct answer.
  2. 7
  3. 23
  4. 13

Explanation

Substitute x = 3: f(3) = 3² + 4(3) − 2 = 9 + 12 − 2 = 19.

Question 43Mathematics

A cylinder has radius 2 cm and height 9 cm. What is its volume? (Leave the answer in terms of π)

  1. 12π cm³
  2. 18π cm³
  3. 36π cm³ Correct answer.
  4. 72π cm³

Explanation

The volume of a cylinder is V = πr²h. Substituting r = 2 and h = 9 gives V = π(4)(9) = 36π cm³.

Question 44Mathematics

Simplify (x⁵ · x³) / x⁶, assuming x ≠ 0.

  1. x² Correct answer.
  2. x⁸
  3. x⁴
  4. x⁻²

Explanation

When multiplying powers with the same base, add the exponents: x⁵ · x³ = x⁸. When dividing, subtract the exponents: x⁸ / x⁶ = x².

Question 45Mathematics

A right triangle has an angle of 30° and a hypotenuse of 10 cm. What is the length of the side opposite the 30° angle?

  1. 5 cm Correct answer.
  2. 20 cm
  3. 5√3 cm
  4. 10√3 cm

Explanation

In a right triangle, sin 30° = opposite / hypotenuse. Since sin 30° = 1/2, the opposite side is 10 × 1/2 = 5 cm, which also matches the 30-60-90 side ratio.

Question 46Mathematics

The roots of x² + bx + 10 = 0 are both positive integers. What is the value of b?

  1. 7
  2. 10
  3. −7 Correct answer.
  4. 11

Explanation

If the roots are positive integers with product 10, the possible pairs are (1, 10) and (2, 5). Since the sum of the roots equals −b and the sum must be positive, b = −(sum), giving b = −11 or b = −7. Of the listed choices, only −7 is possible.

Question 47Mathematics

If 2^(x+1) = 8^(x−1), what is the value of x?

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

Explanation

Write both sides with base 2: 8^(x−1) = (2³)^(x−1) = 2^(3x−3). Equating exponents gives x + 1 = 3x − 3, so 4 = 2x and x = 2.

Question 48Mathematics

A cone has radius 6 cm and slant height 10 cm. What is its total surface area? (Leave the answer in terms of π)

  1. 36π cm²
  2. 60π cm²
  3. 96π cm² Correct answer.
  4. 160π cm²

Explanation

Total surface area of a cone is πr² + πrl. With r = 6 and l = 10, this is π(36) + π(60) = 96π cm².

Question 49Mathematics

For what value of k does the equation x² + kx + 9 = 0 have exactly one real solution?

  1. k = 3
  2. k = 0
  3. k = 6 Correct answer.
  4. k = 9

Explanation

A quadratic has exactly one real solution when its discriminant b² − 4ac equals zero. Here that means k² − 4(1)(9) = 0, so k² = 36 and k = ±6; among the choices, k = 6 works.

Question 50Mathematics

The sum of the first n terms of an arithmetic sequence is Sₙ = n² + 3n. What is the 10th term of the sequence?

  1. 20
  2. 22 Correct answer.
  3. 24
  4. 130

Explanation

The nth term equals Sₙ − Sₙ₋₁. Here S₁₀ = 100 + 30 = 130 and S₉ = 81 + 27 = 108, so the 10th term is 130 − 108 = 22.