أسئلة الرياضيات الصف التاسع مع الحل

15 سؤالاً تدريبياً في الرياضيات – الصف التاسع

1. الفصل: Rational and Irrational Numbers; the Set of Real Numbers · سهل

   1. The number 0.475 is:

   • A. a negative integer
   • B. a rational number that is not an integer
   • C. a natural number
   • D. an irrational number
   أظهر الجواب ▾

   Answer: a rational number that is not an integer

   Explanation: It can be written a/b with integers a, b (finite or periodic decimal) but it is not an integer.

2. الفصل: Rational and Irrational Numbers; the Set of Real Numbers · سهل

   2. The number √100 is:

   • A. a rational number that is not an integer
   • B. an irrational number
   • C. a negative integer
   • D. a natural number
   أظهر الجواب ▾

   Answer: a natural number

   Explanation: It is a natural number (0, 1, 2, 3…), so it is also an integer, a rational and a real.

3. الفصل: Calculation on Real Numbers: Simplifying Square Roots · سهل

   3. 5√2 + 9√2 = ?

   • A. 45√2
   • B. 14
   • C. 14√2
   • D. 14√4
   أظهر الجواب ▾

   Answer: 14√2

   Explanation: Like radicals: (5 + 9)√2 = 14√2.

4. الفصل: Calculation on Real Numbers: Simplifying Square Roots · سهل

   4. √32 / √2 = ?

   • A. 2
   • B. 17
   • C. 4
   • D. 16
   أظهر الجواب ▾

   Answer: 4

   Explanation: √32 / √2 = √(32/2) = √16 = 4.

5. الفصل: Rationalizing the Denominator of a Numerical Fraction · سهل

   5. What is the conjugate of 2 + √10?

   • A. −2 + √10
   • B. 2 + √100
   • C. 2 − √10
   • D. −2 − √10
   أظهر الجواب ▾

   Answer: 2 − √10

   Explanation: The conjugate changes the sign between the two terms: 2 − √10. Their product is 2² − 10 = -6.

6. الفصل: Rationalizing the Denominator of a Numerical Fraction · سهل

   6. (9 − √7)(9 + √7) = ?

   • A. 88
   • B. 18
   • C. 2
   • D. 74
   أظهر الجواب ▾

   Answer: 74

   Explanation: (x − y)(x + y) = x² − y²: 9² − (√7)² = 81 − 7 = 74.

7. الفصل: Linear Functions and Proportionality · سهل

   7. The graph of f(x) = 0.5x is:

   • A. a straight line that does not pass through O
   • B. a straight line through O rising from left to right
   • C. a straight line through O falling from left to right
   • D. the x-axis itself (horizontal line through O)
   أظهر الجواب ▾

   Answer: a straight line through O rising from left to right

   Explanation: Every linear function passes through O; a = 0.5 > 0 → rising.

8. الفصل: Linear Functions and Proportionality · سهل

   8. Apples cost 5 $ per kg. Cost of 3 kg? (f(x) = 5x)

   • A. 8
   • B. 15
   • C. 30
   • D. 24
   أظهر الجواب ▾

   Answer: 15

   Explanation: f(3) = 5 × 3 = 15 $.

9. الفصل: Algebraic Expressions Having Radicals · سهل

   9. (√7 − √6)(√7 + √6) = ?

   • A. -1
   • B. 42
   • C. 13
   • D. 1
   أظهر الجواب ▾

   Answer: 1

   Explanation: (√7)² − (√6)² = 7 − 6 = 1.

10. الفصل: Algebraic Expressions Having Radicals · سهل

    10. (√11 − 6)(√11 + 6) = ?

    • A. -1
    • B. 5
    • C. -25
    • D. 47
    أظهر الجواب ▾

    Answer: -25

    Explanation: (√11)² − 6² = 11 − 36 = −25.

11. الفصل: Polynomial in One Variable · سهل

    11. P(x) = 3x³ − 3x² − 8x + 1. What is the coefficient of x?

    • A. 3
    • B. 1
    • C. -8
    • D. -3
    أظهر الجواب ▾

    Answer: -8

    Explanation: Reading the coefficients of 3x³ − 3x² − 8x + 1: x³ → 3, x² → −3, x → −8, constant → 1.

12. الفصل: Polynomial in One Variable · سهل

    12. What is the degree of P(x) = x⁴ + 4x²?

    • A. 4
    • B. 3
    • C. 1
    • D. 2
    أظهر الجواب ▾

    Answer: 4

    Explanation: The degree is the highest exponent of x: 4.

13. الفصل: Fractional Expressions · سهل

    13. Value of (x + 6)/(x + 7) for x = 6:

    • A. 12/13
    • B. 13/12
    • C. 12/7
    • D. −12/13
    أظهر الجواب ▾

    Answer: 12/13

    Explanation: (6 + 6)/(6 + 7) = 12/13 = 12/13.

14. الفصل: Fractional Expressions · صعب

    14. Solve: 4/x = 6/(x + 4)

    • A. x = 8/5
    • B. x = −8
    • C. x = 8
    • D. x = 4
    أظهر الجواب ▾

    Answer: x = 8

    Explanation: Conditions x ≠ 0, x ≠ −4. Cross-multiply: 4(x + 4) = 6x → 16 = 2x → x = 8.

15. الفصل: Equations of the Form x² = a and Product Equations · سهل

    15. Solve: x² = 100.

    • A. x = 10
    • B. x = 100 or x = −100
    • C. x = 10 or x = −10
    • D. x = 50
    أظهر الجواب ▾

    Answer: x = 10 or x = −10

    Explanation: x² = 100 > 0 has two solutions: √100 = 10 and −10.

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