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Quizzes > High School Quizzes > Mathematics

Unit 1 Practice Quiz: Ace the Basics

Boost Confidence with Practical Review and Practice

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting a high school math practice quiz for unit 1 review and exam preparation.

What is 3/4 + 1/4?
3/2
5/4
1
1/2
Adding fractions with the same denominator, add the numerators: 3 + 1 equals 4, so the result is 4/4 which simplifies to 1. This makes the first option correct.
Solve for x: x + 5 = 10.
x = 0
x = 5
x = 10
x = 15
Subtracting 5 from both sides of the equation gives x = 5. This direct operation confirms that the correct answer is the first option.
What is the area of a rectangle with a length of 8 units and a width of 3 units?
22 square units
24 square units
20 square units
11 square units
The area of a rectangle is calculated by multiplying its length by its width. Here, 8 multiplied by 3 equals 24, making the first option correct.
Which of the following numbers is prime?
2
4
8
6
A prime number has exactly two distinct factors: 1 and itself. Among the options given, 2 is the only number that meets this criterion.
Which decimal is equivalent to 1/2?
2.0
0.25
0.5
0.2
The fraction 1/2 converts to 0.5 in decimal form by dividing 1 by 2. This makes the first answer the correct one.
Simplify the expression: 2(x + 3) - 4.
x + 2
2x + 2
2x - 1
2x + 6
First, distribute the 2 to get 2x + 6, and then subtract 4, which results in 2x + 2. This step-by-step process confirms the correct answer as the first option.
Simplify the expression: 3(a + b) + 2(a + b).
3a + 2b
6ab
5(a + b)
a + b
Both terms share the common factor (a + b), so by factoring it out and adding the coefficients 3 and 2, you obtain 5(a + b). This makes the first option correct.
Solve for x in the equation: 4x - 7 = 9.
5
4
16
7
By adding 7 to both sides, the equation becomes 4x = 16, and then dividing by 4 gives x = 4. This confirms that the first option is correct.
What is the slope of the line passing through the points (2, 3) and (6, 11)?
2
4
3
1/2
Using the slope formula (y2 - y1)/(x2 - x1), we calculate (11 - 3)/(6 - 2) = 8/4, which simplifies to 2. This makes the first option correct.
Evaluate the expression: 5^2 - 3 * 4.
7
17
9
13
First compute 5^2 which gives 25, then calculate 3 * 4 to get 12, and subtracting 12 from 25 results in 13. This validates the first answer as correct.
If the ratio of cats to dogs is 3:4 and there are 9 cats, what is the total number of animals?
15
16
21
12
The ratio indicates that for every 3 cats there are 4 dogs. With 9 cats (which is 3 times 3), there must be 12 dogs, totaling 9 + 12 = 21 animals. This explains why the first option is correct.
Solve for x in the proportion: 2/3 = x/9.
5
4
6
7
Cross multiplying gives 2 * 9 = 3 * x, which simplifies to 18 = 3x. Dividing both sides by 3 results in x = 6, making the first option correct.
What is the value of √81?
7
9
3
8
The square root of 81 is 9 because 9 multiplied by 9 equals 81. This clearly confirms that the correct answer is the first option.
In the sequence 2, 5, 8, 11, ..., which term is equal to 20?
7
8
9
6
The sequence is arithmetic with a common difference of 3. Using the formula a + (n-1)d = term, substituting 2 + (n-1)*3 = 20 gives n-1 = 6, so n = 7, making the first option correct.
Simplify the expression: (1/2) ÷ (3/4).
1/3
4/3
2/3
3/2
Dividing by a fraction is equivalent to multiplying by its reciprocal. Here, (1/2) * (4/3) simplifies to 4/6, which reduces to 2/3, making the first answer correct.
Solve the equation: 3(x - 2) = 2x + 4.
4
6
10
2
Expanding the left side gives 3x - 6; equating it to 2x + 4 and then subtracting 2x from both sides results in x - 6 = 4, and adding 6 yields x = 10. Thus, the correct answer is the first option.
What is the perimeter of a square with a side length of 9 units?
28 units
9 units
18 units
36 units
A square's perimeter is calculated by multiplying the side length by 4. Therefore, 9 multiplied by 4 equals 36 units, making the first option correct.
If the probability of rain on a given day is 0.2, what is the probability that it does not rain?
0.2
0.8
0.5
0.01
In probability, the chance of an event not occurring is found by subtracting the probability of the event from 1. Thus, 1 - 0.2 equals 0.8, confirming the first option as correct.
Which scenario best illustrates a uniform probability distribution?
Measuring the time it takes for a computer to boot
Drawing a card from a deck with an uneven color distribution
Counting the number of students arriving at school each morning
Rolling a fair six-sided die
A uniform distribution implies that all outcomes are equally likely. Rolling a fair six-sided die perfectly fits this description, making the first answer correct.
Factor the expression: x² - 9.
(x - 9)(x + 1)
(x - 3)²
(x - 3)(x + 3)
x(x - 9)
The expression x² - 9 is a difference of squares, which factors into (x - 3)(x + 3). This property confirms the correctness of the first option.
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Study Outcomes

  1. Understand fundamental mathematical concepts covered in Unit 1.
  2. Analyze problem-solving methods through practice exercises.
  3. Apply learned techniques to solve a variety of math problems.
  4. Identify strengths and areas requiring further review.
  5. Evaluate performance to build confidence for upcoming exams.

Unit 1 Review Cheat Sheet

  1. Differentiate Rational vs. Irrational Numbers - Rational numbers are like well-behaved guests: they either terminate (0.75) or repeat (0.333...). Irrational numbers are wild - non-terminating, non-repeating decimals like √2 or π. Spotting the difference helps you sort numbers faster than a superhero organizing their toolkit! Grade 8 Math Unit 1
  2. Master Integer Exponent Rules - Exponent rules make powering numbers a breeze: when multiplying same bases, add exponents; when dividing, subtract; and when raising a power to another power, multiply. For instance, 3² × 3³ = 3❵. Understanding these shortcuts saves you time and keeps your calculations sharp! Grade 8 Math Unit 1
  3. Approximate Irrational Numbers - Since irrational numbers never end, we round or approximate them to see where they land on the number line. For example, π ≈ 3.14 or √2 ≈ 1.414. These approximations let you compare values and place them accurately in your math map. Grade 8 Math Unit 1
  4. Convert Repeating Decimals to Fractions - Repeating decimals are like secret passwords for fractions - 0.333... unlocks 1/3! Converting them shows the powerful relationship between decimals and fractions. Practice with examples like 0.777... = 7/9 to level up your skills. Grade 8 Math Unit 1
  5. Familiarize with Square & Cube Roots - Square roots ask, "What times itself gives me this number?" Cube roots ask, "What times itself three times?" Knowing these roots is your key to unlocking both quadratic and cubic equations - crack the number code with ease! Grade 8 Math Unit 1
  6. Understand Scientific Notation - Scientific notation is your fast-lane ticket for huge or tiny numbers. Write 3,000 as 3×10³ or 0.0005 as 5×10❻❴ to simplify calculations. It's like using a secret superpower to shrink or enlarge numbers instantly! Grade 8 Math Unit 1
  7. Learn Rigid Transformation Properties - Rigid transformations - translations, rotations, and reflections - are the magic moves that keep shapes' size and shape exactly the same. Mastering them means you can prove congruence like a geometry ninja. Move figures around without breaking a sweat! Illustrative Math: Rigid Transformations
  8. Explore Congruence in Geometry - Congruence means two figures have identical size and shape, so one can become the other through rigid transformations. It's like having two puzzle pieces that fit perfectly no matter how you slide, flip, or spin them. Spotting congruence turns tricky geometry problems into fun challenges! Illustrative Math: Congruence Concepts
  9. Sum of Angles in a Triangle - Every triangle's interior angles always add up to 180°. Whether it's scalene, isosceles, or equilateral, that magic 180° rule never fails. Use it to find missing angles and ace those geometry tests! Math 8 Unit 1: Transformations & Congruence
  10. Solve Square & Cube Equations - Equations with squares and cubes let you find mysterious variables: if x² = 16, then x is ±4! Practice solving these to handle quadratics and cubics like a pro. Embrace the power of exponents to crack the code. Grade 8 Math Unit 1
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