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Review: the whole course

Algebra, grade 8 Lesson 27 of 27Practice

Review: the whole course

Functions: a table, a graph and a formula

1

Here are two tables.

x\displaystyle x1234
y\displaystyle y5555
x\displaystyle x1223
y\displaystyle y46810

Which of them describes a function of x\displaystyle x? Explain.

2

Dan walked from home to the park, played there, and walked back home.
The graph shows Dan’s distance from home (in metres) by the time (in minutes).
a. How far is the park from home?
b. How long was Dan in the park?
c. Where is the function increasing? Where is it decreasing? Where is it constant?
d. Which way did Dan walk faster – to the park or back? How many metres a minute did he walk each way?

f(x)\displaystyle f(x)
a

    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

    b

      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

      c, d
      d: on the way to the park

        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

        d: on the way back

          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

          3

          Here is the function y=3x−2\displaystyle {y}={3x-2}.
          a. Fill in the table.

          x\displaystyle x−1\displaystyle -1012
          y\displaystyle y

          b. Is the point (4,10)\displaystyle (4,10) on the function’s graph? And the point (−2,−4)\displaystyle (-2,-4)? Explain.

          The linear function

          4

          A line passes through the points A(0,−1)\displaystyle A(0,-1) and B(2,3)\displaystyle B(2,3).
          Find its slope and its formula.

          A=(0,−1)\displaystyle A=(0,-1)
          B=(2,3)\displaystyle B=(2,3)

          5

          Here is the graph of the function f(x)=−2x+6\displaystyle {f(x)}={-2x+6}.
          Work out the points where it meets the axes, and mark them on the graph.

          f(x)=−2x+6\displaystyle f(x)=-2x+6

          6

          Here are four lines:
          y=3x+1\displaystyle {y}={3x+1}, y=−3x+1\displaystyle {y}={-3x+1}, y=3x−5\displaystyle {y}={3x-5}, y=1−3x\displaystyle {y}={1-3x}.
          a. What is the slope of each of them?
          b. Which of the lines are parallel to each other?
          c. Which of the lines go up, and which go down?

          7

          A candle is 24 cm tall.
          While it burns, it gets 2 cm shorter every hour.
          a. Write a formula for the candle’s height y\displaystyle y (in cm) after x\displaystyle x hours.
          b. Write an equation and solve it: after how many hours will the candle be gone?

            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

            Equations and word problems

            8

            Solve.

            a
              b
                c
                  9

                  Omer’s mother is 3 times as old as he is.
                  In 12 years she will be twice as old as he is.
                  How old are Omer and his mother today?

                  Omer

                    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                    His mother

                      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                      10

                      Two towns are 90 km apart.
                      Two cyclists set out at the same time, each from a different town, riding towards each other.
                      One rides at 20 km/h, the other at 25 km/h.
                      After how many hours will they meet?

                        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                        Systems of equations

                        11

                        Here are the graphs of y=x+1\displaystyle {y}={x+1} and y=−x+5\displaystyle {y}={-x+5}.
                        Mark the point where they meet.
                        Write the solution of the system of equations, and check it by substituting it in both equations.

                        y=x+1\displaystyle y=x+1
                        y=−x+5\displaystyle y=-x+5

                        12

                        Solve the system of equations.

                          13

                          In a café, 2 cups of coffee and 3 croissants cost 51 ₪.
                          One cup of coffee and 2 croissants cost 30 ₪.
                          How much does a cup of coffee cost, and how much a croissant?
                          Write a system of equations and solve it.

                            A cup of coffee (₪)

                              / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                              / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                              A croissant (₪)

                                / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                                / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                                Inequalities

                                14

                                Solve.

                                a
                                  b
                                    15

                                    A class is going on a trip.
                                    Every student pays 75 ₪.
                                    The bus costs 1200 ₪ for the whole class, and entry to the site costs 35 ₪ a student.
                                    At least how many students must go on the trip for the money collected to be enough?

                                      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                                      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power