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The exam covers the fundamental concepts of numbers: types of numbers (natural, whole, integers, rational, irrational, real), their properties, and operations. Focus on the number line, absolute value, and basic arithmet…
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Explain the difference between rational and irrational numbers with examples, and show how to locate √2 on a number line.
Rational: p/q (e.g., 1/2); Irrational: non-terminating non-repeating (e.g., √2); √2 is located by constructing a right triangle with legs 1 and 1.
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Describe the real number system and its subsets.
Real numbers include rationals (integers, fractions) and irrationals; they cover all points on the number line.
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Solve: (3/4) × (8/9) ÷ (2/3).
(3/4 × 8/9) = 2/3; then (2/3) ÷ (2/3) = 1.
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A shirt costs $40 and is on sale for 25% off. What is the sale price?
Discount = 25% of $40 = $10; sale price = $30.
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Simplify: 5 × (2 + 3) - 4 ÷ 2.
5 × 5 - 2 = 25 - 2 = 23.
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Explain the properties of addition (commutative, associative, identity, inverse).
Commutative: a+b=b+a; Associative: (a+b)+c=a+(b+c); Identity: a+0=a; Inverse: a+(-a)=0.
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Calculate: (2/3) + (1/6).
(2/3) + (1/6) = (4/6) + (1/6) = 5/6.
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Explain the difference between whole numbers and integers.
Whole numbers are non-negative (0,1,2,...); integers include negative numbers (...,-2,-1,0,1,2,...).
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Convert 0.125 to a percentage.
0.125 × 100 = 12.5%.
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Find the value of x: 3x + 5 = 20.
3x = 15, so x = 5.
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State the order of operations (BODMAS/PEMDAS).
Brackets, Orders (powers/roots), Division and Multiplication (left to right), Addition and Subtraction (left to right).
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Differentiate between rational and irrational numbers.
Rational numbers can be expressed as p/q (q≠0); irrational numbers cannot.
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Simplify: 3 + 4 × 2.
3 + 4 × 2 = 3 + 8 = 11.
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Convert 0.75 to a fraction in simplest form.
0.75 = 3/4.
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What is 20% of 150?
20% of 150 = 30.
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Represent -3 on a number line.
Draw a number line and mark the point 3 units to the left of zero.
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Define natural numbers and give an example.
Natural numbers are positive integers starting from 1 (1, 2, 3, ...).
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What is the absolute value of -7?
The absolute value is 7.
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What is the additive inverse of -5?
The additive inverse is 5.
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What is the multiplicative identity for integers?
The multiplicative identity is 1.
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