Algebra Basics Quiz
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Questions and Answers

What is the result of expanding $3(x - 4)$?

  • $3x - 4$
  • $3x + 12$
  • $12 - 3x$
  • $3x - 12$ (correct)
  • The factorization of $y^3 - 4y$ is $y(y^2 - 4)$.

    True (A)

    How many cups can Lauren make with 3 litres of fruit juice, if each cup contains 225 millilitres?

    13

    The area of the floor of a room is 12 m2, which is equal to __________ cm2.

    <p>120000</p> Signup and view all the answers

    Match the following conversions with their correct values:

    <p>6 metres = 600 centimetres 4500 grams = 4.5 kilograms 12 m2 = 120000 cm2 3 litres = 3000 millilitres</p> Signup and view all the answers

    What is the simplified form of $7m + 6n - 2m - 9n$?

    <p>$5m - 3n$ (D)</p> Signup and view all the answers

    The simplified form of $q^5 + q^5 + q^5$ is $3q^{10}$.

    <p>False (B)</p> Signup and view all the answers

    What is the factorization of $t^2 - 10t$?

    <p>t(t - 10)</p> Signup and view all the answers

    What is the simplified form of $g^6 \times g^4$?

    <p>$g^{10}$ (B)</p> Signup and view all the answers

    The expression $k^4 \div k^2$ simplifies to $k^2$.

    <p>True (A)</p> Signup and view all the answers

    What is the simplified form of $5m + 2m - m$?

    <p>6m</p> Signup and view all the answers

    The area of a rectangle is calculated as length times ______.

    <p>width</p> Signup and view all the answers

    Match the geometric shape with its area formula:

    <p>Rectangle = Length × Width Trapezium = (Base1 + Base2) × Height / 2 Triangle = Base × Height / 2 Circle = π × Radius^2</p> Signup and view all the answers

    What is the cube root of 64?

    <p>8 (C)</p> Signup and view all the answers

    Calculate the value of $2^3 \times 4^5$.

    <p>2048</p> Signup and view all the answers

    The area of trapezium is given by the formula: Area = 0.5 × (Base1 + Base2) × Height.

    <p>True (A)</p> Signup and view all the answers

    The expression $8d \times 7d$ simplifies to $______d^2$.

    <p>56</p> Signup and view all the answers

    What is the highest common factor (HCF) of 3780 and 3240?

    <p>180 (D)</p> Signup and view all the answers

    The lowest common multiple (LCM) of 15 and 70 is 210.

    <p>True (A)</p> Signup and view all the answers

    List all the factors of 9.

    <p>1, 3, 9</p> Signup and view all the answers

    The total volume of the cuboid is ______ cm³.

    <p>806</p> Signup and view all the answers

    What is the mean number of matches counted by Becky if she counted 50 boxes with a total of 300 matches?

    <p>10 (D)</p> Signup and view all the answers

    If 16 buses went past the school, how many bicycles went past assuming the ratio of buses to bicycles is 1:4?

    <p>64</p> Signup and view all the answers

    For a sample of 40 people who caught fish, if the total number of fish caught was 140, what is the mean number of fish caught per person?

    <p>4 (D)</p> Signup and view all the answers

    Match the following types of vehicles with the number that went past the school:

    <p>Buses = 16 Bicycles = 64 Lorries = Number needed for angle Cars = To be determined</p> Signup and view all the answers

    Flashcards

    Simplifying powers with the same base

    When multiplying powers with the same base, add the exponents.

    Simplifying powers with the same base (division)

    When dividing powers with the same base, subtract the exponents.

    Simplifying expressions with exponents

    To simplify expressions with exponents, multiply the coefficient by itself for the number of times indicated by the exponent.

    Simplifying expressions with like terms (addition)

    To simplify expressions with like terms, combine the coefficients of the like terms.

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    Simplifying expressions with unlike terms

    To simplify expressions with unlike terms, multiply the coefficients and combine the variables.

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    Area of a Trapezium

    Area of a Trapezium: (1/2) * (sum of parallel sides) * (perpendicular height)

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    Cube root

    Cube root of a number: The number which, when cubed, equals the original number.

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    Prime Factorization

    Prime Factorization: Expressing a number as a product of its prime factors.

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    Expanding brackets

    Multiplying a number by a set of parentheses means applying that number to each term inside the parentheses.

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    Factoring an expression

    The process of finding two or more expressions that, when multiplied together, give the original expression.

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    Simplifying expressions

    To simplify an expression means to combine like terms.

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    Adding exponents (same base)

    To simplify exponential expressions with the same base, add the powers together.

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    Multiplying variables (commutative property)

    To simplify expressions with multiplication involving variables, the order doesn't matter.

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    Factoring expressions

    To factorize an expression, find the greatest common factor of the terms and write it outside the parentheses.

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    Converting square meters to square centimeters

    To convert square meters to square centimeters, multiply by 10000.

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    Converting grams to kilograms

    To convert grams to kilograms, divide by 1000.

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    What is the Highest Common Factor (HCF)?

    The highest common factor (HCF) of two numbers is the largest number that divides both numbers without leaving a remainder.

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    What is the Lowest Common Multiple (LCM)?

    The lowest common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers.

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    What are factors?

    Factors are numbers that divide evenly into another number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

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    What is the mean?

    The mean is the average of a set of numbers. You can find it by adding all the numbers together and then dividing by the total count of numbers.

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    What is a pie chart?

    A pie chart is a circular chart divided into slices, where each slice represents a proportion of the whole. The size of each slice is proportional to the amount of data it represents.

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    What is a cuboid?

    A cuboid is a three-dimensional shape with six rectangular faces. Each face is a rectangle.

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    How do you calculate the volume of a cuboid?

    The volume of a cuboid is the amount of space it occupies. You can calculate it by multiplying its length, width, and height.

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    How do you find the volume of a cuboid?

    The volume of a cuboid is the amount of space it occupies. You can find it by multiplying its length, width, and height.

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    Study Notes

    Q1

    • Simplify g x g4 = g5
    • Simplify k10 ÷ k3 = k7
    • Simplify (3cd4)2 = 32c2d8 = 9cd8

    Q2

    • Simplify 4m + 2m – m = 5m
    • Simplify 5p × 7 = 35p

    Q3

    • Simplify 6e × 2f = 12ef
    • Simplify 5m + 7k – 2m + k = 3m + 8k
    • Simplify wxwxwxwxw = w5

    Q4

    • The area of a trapezium is ½(a + b)h. In this case ½(6 + 13) × 3 = 28.5 m2

    Q5

    • The area of the rectangle is 9 x 4 = 36 cm2
    • The area of the triangle is ½ x 5 x 4 = 10 cm2
    • The total area of shape ABCD = 36 + 10 = 46 cm2

    Q6

    • The area of the polygon (ABCDEFGH) is 434
    • Area of the rectangle (AFGH) = 28 × 12 = 336 cm2
    • Area of ABCDE = 434 - 336 = 98 cm2
    • Height of the trapezium (CD and HG) is 20 – 12 = 8 cm
    • (18 + CD) × 8 ÷ 2 = 98, which means 18 + CD = 24.5 so CD = 6.5 cm

    Q7

    • The area of the trapezium is ½(a + b)h = ½(13.5 + 17) × 10.4 = 158.6 cm2

    Q8

    • The cube root of 64 is 4
    • 23 x 45 = 8 x 1024 = 8192
    • 800= 23 x 52

    Q9

    • 8d × 7d = 56d2
    • Expand 3(x - 4) = 3x – 12
    • Factorise y3 – 4y = y(y2 - 4) = y(y - 2)(y + 2)

    Q10

    • Simplify 8e + 2f – 11e + 3f = –3e + 5f
    • Expand 2y(3y – 7) = 6y2 – 14y

    Q11

    • Simplify a × 5 × b × c = 5abc
    • Simplify q5 + q5 + q5 = 3q5
    • Simplify 7m + 6n – 2m – 9n = 5m – 3n
    • Factorise t2 – 10t = t(t – 10)

    Q12

    • Simplify b x 3 x e = 3be
    • Simplify p3 + p3 + p3 + p3 = 4p3
    • Simplify 6g – 4h + 2g – 3h = 8g – 7h
    • Factorise 5a – 3a2 = a(5 – 3a)
    • Expand 2(4 – 3w) = 8 - 6w
    • Expand y2(y + 10) = y3 + 10y2

    Q13

    • Change 12 m2 to cm2 =120000 cm2

    Q14

    • Change 6 m to cm = 600 cm
    • Change 4500 g to kg = 4.5 kg
    • Work out the amount of fruit juice left: 3000 – 2925 = 75 ml

    Q15

    • highest common factor of 3780 and 3240 is 22 x 33 x 5 = 22 × 33 × 5 = 540
    • least common multiple of 3780 and 3240 is 23 x 34 x 5 x 7 = 3240

    Q16

    • Factors of 9 = 1, 3, 9
    • Lowest common multiple of 15 and 70 = 210

    Q17

    • Mean number of matches = 2371 / 50 = 47.42

    Q18

    • Mean number of fish caught = 84 / 40 = 2.1

    Q19

    • Mean mark of 20 students = 162 / 20 = 8.1

    Q20

    • Number of bicycles = 16 / 40 = 16/4 = 4
    • Angle for lorries = 9 x 5 = 40°

    Q21

    • Value of x = 806/(15.5 x 8) = 6.5

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    Description

    Test your understanding of fundamental algebra concepts with this quiz. You'll encounter various questions including expansion, simplification, and factorization of expressions. Perfect for reinforcing your algebra skills and preparing for higher-level math.

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